Haji8 Peter Ladreiter

Siegfried J Bauer

Gerald K F Rabl

Wolfgang Mâcher

Wolfgang Voiler

Martina Zhang

UD Gottfried Kirchengast

Dr Reinhart Leitinger

Dr Erich Putz

The Jovian Hectometric Radiation

Mostetschnig for many helpful discussions on several scientific topics. Additionally, I express my thanks to Wolfgang Voiler

The first idea of a magnetic cavity around a planet (the earth) was first postulated by Chapman and Ferraro already in the early thirties. The interest in studies of such a magnetic cavity which is caUed "magnetosphere" was reinforced since the accidentai discovery of the nonthennal Jovian decametric radiation (DAM) by [START_REF] Burke | Observations of a variable radio source associated with the planet Jupiter[END_REF]. However, it was Shain already in 1950 who first observed a radio émission at 18.3 MHz, but it was not yet attributed to Jupiter. This radiation indicated that Jupiter exhibits an intrinsic magnetic field, whereby the radio émission is caused by électrons spiralling around magnetic field Unes in the vicinity of the planet, finding confirmed by the discovery of the Jovian decimetric radiation and the earth's

Van Allen belts by the sateüites Explorer 1 and 3 in 1958.

Later on (1961), the terrestrial magnetosphere was explored by the satelUte Explorer 10 which also determined the boundary of the magnetosphere, the so-called magnétopause. In the solar direction the shape of the magnétopause is approximately a half eUipsoid. The size can be estimated by setting equal the dynamic pressure of the solar wind (supersonic ionized particle stream originating from the upper solar atmosphère) to the magnetic pressure due to the planet's magnetic field. Inside the magnétopause the influence of the planet's magnetic field on the particles gains over the solar wind influence. Thus, physical processes within the magnetosphere are highly controlled by the planetary magnetic field and the rotation of the planet which additionally leads to the génération of electric fields.

Since the Voyager 2 Neptune flyby in August 1989 five well extended planetary magnetospheres are now explored in our solar System: Earth, Jupiter, Satura, Uranus, and Neptune. Ail of these magnetospheres hâve their own characteristics mainly due to different magnetic dipole moments and directions, different planetary spin periods and distances to the sun.

AU these magnetized planets émit nonthermal radiation which is either trapped inside the magnetospheric cavity or escaping from the planet into free space. The sources of the trapped radiation with frequencies genearaUy below 5 kHz are located at the edges of the plasma sheet (current System in the magnetic équatorial plane) and/or the magnétopause boundaries; the radio sources of the escaping radiation axe mostly located in the auroral zones where solar wind particles are precipitating into the ionosphère of the planet. In some spécifie cases, the radi ation may also be generated in the magnetic équatorial plane. The various radio sources are characterized by the spécifie beaming of the generated radiation and the source activity may be affected by solar wind fluctuations. The knowledge of the polarization of the émission is of prime interest for the détermination of the radiation mechanism.

Jupiter is the most powerful and complex radio planet. This fact is due to the strength of its magnetic field, to the presence of Van AUen belts, and to the formation of a plasma torus at the orbit of the satellite Io. In the Jovian radio spectrum (Figure 1.3) we can distinguish the decametric and hectometric components which are believed to escape from auroral zones, and the kilometric radiation emitted from sources at the Io plasma torus. The decimetric or synchrotron radiation is originating from the Jovian Van AUen belts.

We hâve focussed this study on the Jovian hectometric radiation (hereafter HOM) which has been discovered by the Planetary Radio Astronomy experiment aboard the Voyager spacecraft, well before the first encounter in 1979. Except a few studies published after the encounters of Jupiter by Voyager 1 and Voyager 2, many outstanding problems remained unanswered, e.g. is the HOM just an extension of DAM or is it a distinct component ? Where is the location and what is the extension of the source, and is it a corotating source ? What is the polarization of the émission ? How does the Io plasma torus act on the HOM émission ? What about the génération mechanism of HOM ? In this study we hâve considered ail these questions using VI and V2 data recorded in 1979, including the VI and V2 encounters.

In the first chapter we give a description of the Jovian magnetosphere, the interaction with the solar wind, and we discuss the several Jovian radio components. In chapter 2 the characteristics of the hectometric radiation are determined; the effect of latitudinal beaming at 3 frequencies, the local time dependence, the solar wind control on the beaming, and the source extension. In particular we give a hint for the source extension in altitude determined from the low-frequency limit of HOM. We establish that right-hand polarization is associated with sources in the northern hemisphere and left-hand polarization with sources in the Southern hemisphere. In chapter 3 we présent the ray-tracing concept we hâve used to détermine the source locations of HOM.

Additionally we hâve undertaken a three-dimensional study for modeling HOM observations at the Voyager encounters and shown that the HOM source locations must be in the auroral zones along open field lines connected to the magnetospheric tail and polar cusp. Our results explain in detail the strong latitudinal beaming, the solar wind control, the absence of HOM émission when Voyager 1 was within the Io torus, and the absence of Io-control on the HOM.

Concerning the source geometry and the polarization of the émission our results are in agreement with the radiation mechanism, the so-called "Cyclotron Maser Instability" or CMI as first proposed by [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] In chapter 4 we hâve developed a treatment of the CMI in a very low density magnetoplasma which represents the conditions as seen at higher altitude auroral zones within the magnetosphere of Jupiter. The results clearly show the limits where some simplifications are justified and where more complicated analyses are required. In the conclusion are summarized the main results which represent the first comprehensive study of the hectometric émission. More extensive observations of HOM will be undertaken with the Ulysses and Galileo missions where radiospectrographs in the hectometric frequency range will be operating. Prospects and prédictions concerning the HOM will be outlined.

Chapter 1

The Jovian magnetosphere and radio émissions

1.1 The Jpvian magnetosphere At présent time, the best explored magnetospheres are the terrestrial and Jovian magnetospheres. The Jovian magnetosphere, however, is unlike the earth's in its fondamental processes because of the very high magnetic field strength, the rapid planetary spin period (about 10 hours) and, of course, because of the existence of the satellite Io which feeds the Jovian mag netosphere with particles of volcanic origin. The Jovian magnetosphere is powered by slowing down Jupiter's spin, and nearly ail of the magnetospheric plasma cornes from internai sources (satellite Io, ionosphère and current sheet). Contrary, the magnetosphere of the earth essentially extracts ail of its energy and an important fraction of its plasma from the solar wind. The solar wind particles may penetrate into the magnetosphere throughout the auroral zones which hâve an oval form, encycling the magnetic north and south pôles, respectively.

Among the planets in the solar System, Jupiter is unique not only because of its immense size and mass and the variety of phenomena taking place within its environment, but also because of its large magnetic moment. The Jovian magnetosphere usually is described in ternis of three principal régions (Figure 1.1).

Outer magnetosphere

In the outer magnetosphere the magnetic field exhibits large temporal and spatial variations in direction as a joint conséquence of changes in the solar wind pressure and direction of the interplanetary magnetic field. The outer magnetosphere extends from the magnétopause boundary to approximately 30 -50 Jovian radii (Rj) [START_REF] Acuna | Jupiter's magnetic field and magnetosphere[END_REF]. On the nightside, the most promi nent feature is the magnetic tail extending out to a few Astronomical Units (1 AU =1.5* 108 km).

The existence of the tail implies that the solar wind must catch the magnetic Unes of force at the magnétopause and blow them behind the planet. At increasingly larger radial distances from Jupiter the tail magnetic field tends to lie parallel to the équatorial plane of Jupiter (Rucker et al., 1988). As in the case of the earth, the Jovian magnetotail includes a large scale current sheet CHAPTER 1. THE JOVIAN MAGNETOSPHERE AND RADIO EMISSIONS Figure 1.1: Méridional cross section of the Jovian magnetosphere. Three magnetospheric régions can be distinguished: The inner, middle, and outer magnetosphere. For the Jovian radio émissions, the inner magnetosphere including the auroral zones and the Io plasma torus is of primary interest.

separating the northern and Southern tail lobes. Crossing the current sheet the field reverses direction. This current sheet which contains an azimuthal current System can be described by a rigid magnetodisc that bends over at distances beyond r « 60AEj (hinge point) to become finally parallel to the planet's équatorial plane. On the dayside, the outer magnetosphere consists of a région which is located just inside the magnétopause. This région is characterized by a southward magnetic component consistent with the orientation of Jupiter's magnetic dipole direction.

The extension of the dayside outer magnetosphere is highly dépendent on the instantaneous solar 1.1.

THE JOVIAN MAGNETOSPHERE

9 wind pressure which acts on the position of the dayside magnétopause.

1.1.2 Middle magnetosphere

In the middle magnetosphere, which extends from about 6 Jovian radii (Rj) (orbit of Io) to about 30 R j, the magnetic field morphology is dominated by the field generated by the équatorial azimuthal currents of the current sheet (or plasma sheet). Inside of 6 Rj, the effect of these currents is negligible and the magnetic field can be accurately described by the field which is caused by the current Systems in the interior of Jupiter. Beyond approximately 15 Rj, the contribution of the magnetic field due to azimuthal currents exceeds the internai field. The resuit is a stretching of magnetic field fines in radial direction. This is the reason why beyond 15 -20 Rj the field fines are open (i.e. only one footpoint at the planet's surface) in contrast to an undisturbed dipole field. Thus, charged particles from the current sheet hâve access to the planet's auroral zones along open magnetic field fines. Since this scénario takes place at the nightside it is called the tailfield aurora [START_REF] Connerney | Modeling the Jovian current sheet and inner magnetosphere[END_REF].

Inner magnetosphere and Io flux tube

The inner magnetosphere represents the région with a dominating magnetic field which is gen erated in the interior of Jupiter. For a représentation of this internai field, it is convenient to express the flux density B as the gradient of a scalar magnetic potential V. By setting the divergence of B equal to 0, the resulting Laplace équation AV = 0 leads to the expansion of the magnetic field in spherical harmonies. The spherical harmonie coefficients for the Jovian magnetic field are obtained from a least square fit of the measured B values along a spacecraft trajectory. [START_REF] Acuna | The main magnetic field of Jupiter[END_REF] used the Pioneer 11 magnetic field measurements to obtain the spherical harmonie coefficients for the magnetic field of Jupiter (O4 model). The Jovian field can hardly be approximated by a dipole field on Jupiter's surface, since considérable fractions of the quadrupole and octopole terms occur. The magnetic flux density B peaks in the northern hemisphere at 14 T [r=Gauss] whereas a maximum of only about 10 T occurs in the South ern hemisphere. The Jovian dipole moment is 4.2 TRj (1 AEj=71400 km) This magnetic field causes adiabatic motion of charged particles. Thereby, the inner satellites of Jupiter (Amalthea, Io) act as particle absorbers when a particle hits the surface of the satellite. At r=1.8 Rj an anticipated ring of particles has been detected by the Pioneer 11 spacecraft (Jovian Van Allen radiation belts).

One of the most prominent features in the Jovian inner magnetosphere is the existence of the Io flux tube. It is the conséquence of the interaction between Io and Jupiter as illustrated in Figure [START_REF] Acuna | Jupiter's magnetic field and magnetosphere[END_REF].

particles 50, 502, 0 of volcanic origin from the satellite Io. They are ionized immediately after the interaction with the Jovian magnetosphere. The révolution of Io around Jupiter causes a rather uniform distribution of ions and électrons along Io's orbit. The resulting feature is called the Io plasma torus. The peak électron number density of the torus is about 3000/ccm at the orbit of Io and decreases very steeply at the inner side and slowly at the outer side of the plasma torus [START_REF] Birmingham | Obser vations of électron gyroharmonic waves in the structure of the Io torus[END_REF]. Consequently, the Io torus plays a crucial rôle for the génération as well as propagation of Jovian radio émissions.

1.2

The magnetospheric solar wind interaction: The généra tion of planetary radio émission

The interaction of the solar wind with a planetary magnetic field is a complicated physical phenomenon. For simplification, it is convenient to define three different steps or effects [START_REF] Parker | Solar wind interaction with the geomagnetic field[END_REF].

1. The first effect of the interaction is the bow shock upstream in the solar wind from the obstacle which is the planetary magnetic field (Figure 1.1). This shock exists because the solar wind bulk speed exceeds both the sound and the Alfven velocity in the solar wind.

The solar wind characteristics are modified by the passage through the shock, an increase of the température and density and a decrease in speed occur.

2. The second effect is the formation of the magnétopause which represents a dynamic balance between the pressure of the planetary magnetic field and the kinetic and magnetic pressure of the solar wind.

3. The third effect is the stretching out of magnetic field fines of force behind the planet to form an extended magnetotail on the nightside. The space between the last closed field fine on the dayside and the first stretched field fine on the nightside (Figure 1.1) includes a neutral région where the solar wind plasma easily enters the magnetosphere.

Some of the solar wind particles (mostly protons and électrons) depending on their energy distribution may reach the planet's upper atmosphère. The régions where the solar wind particles can reach the upper atmosphère (thereby producing aurorae borealis in the case of the earth) are called auroral zones. Similar auroral précipitation from the nightside (current sheet) has already been discussed. In general, the footprints of auroral field lines build ovals surrounding the northern and Southern magnetic pôles. Throughout several physical mechanisms a considérable fraction of the électron energy can be converted into electromagnetic radiation, subsequently producing planetary radio émissions.

1.3

The Jovian escaping radio émission Among the five known radio planets in our solar System (Earth, Jupiter, Saturn, Uranus, and Neptune) Jupiter is the most extensive concerning the frequency range and complexity, and most powerful concerning the total emitted power. This is demonstrated in Figure 1.3 where the radio émission from the different planets are shown for comparison. To avoid confusion associated with the names of the several radio components, the subséquent abbreviations will be used throughout: The wavelengths of the respective émissions are indicative for the band where the maximum power flux is observed. The average power of these radio components is shown in Figure 1.3 and the dominant rôle of Jupiter is clearly visible: ail émissions except Jupiter's are in the kilometric range1; The Jovian spectrum also covers the decametric range which is a conséquence of the unique planetary magnetic field strength of Jupiter. The radiation extends from 20 kHz to about 40 MHz and is strongly modulated by the Jovian radio spin period lasting exactly 9h 55min 29.7s. The distinct components occur at their characteristic frequency range and are generated at different source régions in the magnetosphere of Jupiter.

Decimetric radiation

The decimetric radiation is a smooth émission which is generated by trapped électrons with high energies in the Jovian radiation belts between 1.6 and 3 Rj [START_REF] Carr | Phenomenology of magnetospheric radio émis sions[END_REF]. This synchrotron radiation consists of intégral harmonies of fj sina (/c being the électron cyclotron frequency and a the électron pitch angle) rather than of fc (as the lower frequency radio components).

The émission covers a frequency range from 80 MHz to 300 GHz with a spectral peak at 800

MHz. A periodic variation in the total flux density is observed as the planet rotâtes, generally with two maxima and two minima per rotatation. The maxima are detected when the observer is in the magnetic équatorial plane where the polarization is found to be linear. A weakly circulai-polarized component alternâtes between right-hand and left-hand polarization as the planet rotâtes. The émission tends to be strongest when certain longitudes are facing the observer. In addition, the occurrence and intensity of the Io DAM component is dépendent on the orbital phase of Io.

Continuous monitoring of DAM by fixed frequency and swept frequency receivers revealed the CHAPTER 1. THE JOVIAN MAGNETOSPHERE AND RADIO EMISSIONS characteristic Jovian longitude émission zones known as sources Io-A, Io-B, Io-C, Io-D and their respective dependence on CML and Io-phase (e.g. [START_REF] Carr | Phenomenology of magnetospheric radio émis sions[END_REF]. Moreover, some of the Io dépendent émissions exhibit short-time variations on timescales of milliseconds which aj*e known as S-bursts. In a frequency-time diagram, the S-bursts appear as short-time features which drift toward lower frequencies with time. S-bursts are believed to be generated from distinct électron beams which cause émission of short duration. Other modulations with timescales of seconds are due to interplanetary scintillation effects and are called L-bursts.

In most of the cases (especially above 15 MHz), DAM is right-hand polarized when observed in the northern Jovian hemisphere and left handed when observed from the Southern hemisphere.

This is consistent with radio waves propagating in the fast extraordinary (R-X) mode. With a few exceptions, almost ail of the émissions from the radio planets are generated in the R-X mode, suggesting a common génération mechanism. It is commonly accepted that the Io-dépendent émission is emanating from sources located within the Io flux tube at magnetospheric altitudes where the local gyrofrequency is less but nearly equal to the observed wave frequency. The émission is beamed within a hollow cône, the source magnetic field direction being the symmetry axis, with a near perpendicular cône half apical angle. In contrast, the non-Io DAM is generated elsewhere, possibly at higher magnetic latitudes near the tailfield auroral zones or the north and south polar cusps. The broadband kilometric émission (bKOM) recurs favourably when the Jovian northern dipole tip nods toward the observer. The occurrence probability is reduced for higher frequencies. The émission is right-hand polarized when seen in the northern hemisphere and left-hand in the Southern hemisphere. The sources of bKOM axe located most probably at the edges of the Io plasma torus near the magnetic équatorial plane.

The narrowband kilometric émission (nKQM) is very narrow in bandwidth (20 -60 kHz) and is a quite smooth émission in contrast to bKOM. The nKOM reoccurrence period is typically 3% -5% higher compared to the other Jovian émissions. Consequently, it lags the Jovian rotation period. The polarization is contrary to that of bKOM. The nKOM sources are also believed to be near the Io torus but distinct from the bKOM sources.

The HOM component occurs from about 40 kHz (or even below) up to a few MHz (the upper limit is not precisely determined) with a spectral peak at about 1 MHz. From dynamic spectra it cannot unambiguously be seen that the HOM component is distinct from the DAM, but it is certainly distinct from the kilometric components. Very few papers hâve been devoted to the HOM émission and the authors found some of the beaming characteristics and established a solar wind control. Thereby, increasing solar wind pressure at Jupiter enhances the HOM energy output. Ln any case, the HOM remains the least investigated radio component without any consensus to date concerning the source location. Furthermore, the polarization behaviour

was not yet understood. It is the main purpose of this work to overcome this lack of investigation in order to explain the characteristics of HOM.

Chapter 2

The Jovian hect omet rie radiation Radio Astronomy (PRA) experiment [START_REF] Warwick | Planetary radio astronomy experiment for Voyager missions[END_REF]. The major emphasis of the PRA experiment was to study the freely propagating waves generated in planetary plasmas. In order to observe also the immense frequency range of Jovian émissions, two types of receivers hâve been implemented on the spacecraft. The high frequency (HF) band receiver consists of 128 investigations which helped to détermine the DAM beaming characteristics. With the exception of the DAM and the highest frequency part of HOM, no other planetary radio émission was detected in the high band range.

THE HECTOMETRIC (HOM) OBSERVATIONS

The hectometric (HOM) observations

It was exclusively the low frequency receiver which measured the kilometric radio émissions from the earth, Jupiter, Saturn, Uranus, and also Neptune. The major part of the Jovian hectometric spectrum, including the spectral peak near 1 MHz, also occurred in the low band.

The Jovian hectometric émission was measured simultaneously from Voyager 1 and Voyager 2 in 1979. Moreover, HOM was détectable sometimes in 68 out of the 70 channels (from 39.6 to 1326 kHz) and was the dominant émission above 500 kHz (Figure 1.4a). The HOM is strongly modulated by the Jovian spin period and shows an émission gap around 200°CML. Sometimes, HOM activity was observed down to about 40 kHz especially near the Voyager encounters.

The polarization pattern of HOM shows a complicated behaviour, not common with the higher frequency DAM nor with any KOM component [START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF]. These severe constraints on HOM are used to détermine the émission characteristics, source locations, and génération processes. None of these properties hâve been thoroughly investigated before this study. It is the purpose of the présent work to enhance the knowledge of planetary radio émissions, especially of the HOM component, whose properties axe only poorly known. Any investigation on planetary radio émission also rises our understanding and knowledge of magnetospheric processes and solar wind interactions. '

2.3

The phenomenology of the hectometric radiation 9,1979). Typical HOM observations recorded at the dayside are shown in Figure 2.2. The émission shows a "gap" near 200°CML. At this longitude, the northern magnetic pôle is tilted toward the observer. We notice that the émission gap is wider for V2, which approached Jupiter at higher Jovicentric latitudes. The geometrical explanation of the observed HOM pattern is given in the bottom panel. Assuming that HOM escapes the planet within a quite narrow beam centered near the dipole équatorial plane, the observations are easily accounted for because V2 is out of the beam for a longer period than VI. This essential resuit of a sharply beamed HOM émission in magnetic latitude was first evidenced by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF], studying the cruise phases of VI and V2 and several earth orbiting satellites.

An important step to characterize the HOM is to détermine the average beam width in lati tude of the émission. Thereby, the émission activity start and stop times (interpreted as beam crossings) within one Jovian rotation are noted and they can be considered in terms of mag netic latitude taken from the spacecraft trajectory. Thus, the extension of the beam is found in magnetic coordinates. The data axe collected over several months centered on the respec tive encounters. Figure 2.3 présents the average northern beam limit taken from 3 analyzed frequencies, namely /=558 kHz, /=942 kHz, and /=1326 kHz for VI and V2 observations, respectively. When approaching the planet, the normalized détection threshold (bottom scale)

decreases. Consequently, the apparent northern beam limit increases and peaks near the encounter for both spacecraft. Some VI HOM observations can be used to détermine the Southern beam extension when leaving the beam at Southern magnetic latitudes near 20°CML (Figure 2.2). Assuming that the beam axis (or center) lies exactly between the actual northern and Southern beam limits, the average magnetic déclination of the beam axis (beam center) was calculated to be +1.6°. Consequently, the whole beam width can be obtained by a mirror image normalized détection threshold (10 23Wm 2Hz-1) of the VI and V2 northern beam extensions with respect to the beam axis at 1.6°(dashed Une in Figure 2.3). The sUght offset of the beam axis from the magnetic equator is most Ukely due to the asymmetries of the Jovian magnetic field with respect to an idealized dipole field. The apparent total beam width in latitude therefore reaches about 20°near the encounters and 10°f

arther away from Jupiter, and the beam width is, of course, a function of the normalized dé tection threshold which decreases when approaching Jupiter. Our résulta are in agreement with those of [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] who obtained a total HOM beam width of 10°at large distances from the planet and the beam axis at 2°-3°magnetic latitude. We additionally determined the instantameous beam width from stereoscopic VI and V2 observations, which also agréé with the former results. The detailed work is developed in [START_REF] Ladreiter | Jovian hectometric radiation -Beaming, polarization, source extension, and solar wind control[END_REF]

(Appendix A)
and former results by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] are confirmed.

Local time dependence of the beaming

A further interesting characteristic of the HOM is derived when comparing the occurrence probabüities of dayside and nightside observations. This is visualized in dramatically when the spacecraft switched from the day-to nightside. We are able to state precisely that the beam is a few degrees larger (extending to higher magnetic latitudes) on the dayside than on the nightside.

Polarization

The polarization of HOM shows a puzzling behaviour which is more complex than that of the DAM or KOM émission. In order to investigate the polarization we picked out time periods where the polarization response of the PRA antenna brought out clear results (see Appendix A). its northern limit and LH-polarization at its Southern limit (Figure 2.5, lower panel). Within the mixed polarized HOM beam, northern and Southern hemisphere source components compete in intensity and the observer records occasional polarization reversais. The polarization results strongly indicate that the émission is radiated in the fast extraordinaxy (R-X) propagation mode.

Source extension in altitude

Knowing the propagation mode of HOM, the hectometer source extension in altitude can be derived from the HOM low-frequency limit. The high-frequency limit is not well known but it is generally accepted that it is about 3 MHz and may be as high as 7 MHz. To find the HOM source extension we determined the low-frequency limit of HOM from the PRA data for each Jovian rotation in 1979 for VI and V2, respectively. The lowest observed HOM frequencies down to 20-40 kHz were observed close to the respective encounters (because of the lowest normalized détection threshold). Since the HOM is propagating in the fast extraordinary (R-X) mode, the source région near the right hand cutoff frequency at 40 kHz extends to altitudes higher than 6 Rj, whereas the sources of the high HOM frequency limit must be located at about 2 Rj from the center of the planet. of TKR (Gaüagher and D'Angelo, 1981) or for SKR [START_REF] Desch | Evidence for solar wind control of Satura radio émission[END_REF][START_REF] Desch | The relationship between Satura kilometric radiation and the solar wind[END_REF] and is now also established for HOM (e.g. [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF][START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF][START_REF] Rabl | Solar wind dependence of the Jovian hectometric radio émission: Comparison between Voyager 1 and 2 observations[END_REF]. For HOM the solar wind ram pressure and/or density are found to influence the HOM energy output. In this study we hâve cross-correlated the solar wind parameters density and velocity (10 h averages) with the HOM low-frequency limit and the instantaneous beam width. The solar wind data for VI were investigated from January 5, 1979 until March 1 and for V2 from January 5 until June 30, which represent the respective preencounter periods in 1979.

The solar wind data were ballistically projected from the spacecraft to Jupiter, in a manner described by [START_REF] Desch | The relationship between Satura kilometric radiation and the solar wind[END_REF]. We hâve also corrected the artificial data trends due to observations at different spacecraft-Jupiter distances in the HOM parameters as well as in the solar wind data. To see whether the calculated corrélation coefficients are statistically significant

or not, we used a test based on the Student's distribution [START_REF] Spiegel | Statistics, Schaum's outline[END_REF].

According to the results it can now be stated that the arrivai of a high density solar wind stream at Jupiter will enhance the HOM energy output, activate low frequency HOM sources located at 6 -7 Rj and widen the HOM beam to higher magnetic northern latitudes and possibly to higher magnetic Southern latitudes.

Summary of the HOM characteristics

Chapter 3

Ray-tracing in the Jovian magnetosphere: The hectometric source locations

3.1

The method of ray-tracing Ray-tracing calculations can help détermine or confirm important details about a wave's origin, plasma mode, and polarization. Additionally, ray-tracing can help obtain a better understanding of propagation effects. Information is obtained about source région characteristics such as location and extent. Furthermore, characteristic wave modes and polarization of the wave can be inferred by matching ray-tracing calculations with observations such as the angular extent of an émission. Applied to the magnetosphere of Jupiter, ray-tracing is a useful technique that provides insight into propagation effects caused by the Io plasma torus. This includes réfraction and réfection of the hectometric radiation near the torus. The refractory effects create shadow zones for régions where radiation is not allowed, not only because of the characteristics of the génération mechanism, but also because of the intervening plasma between the source région and the spacecraft. Ray-tracing of HOM in the Jovian magnetosphere is therefore a high challenge in the field of radio astronomy. However, résulta obtained from ray-tracing should be critically tested with respect to the validity of the models used throughout the analysis.

Ray-tracing concepts

A ray-tracing analysis seems necessary when the characteristic frequencies in the magnetoplasma (e.g. électron plasma frequency /p, électron cyclotron frequency fc) are in the same order of magnitude as the frequency of the wave /. Because of the presence of the Io plasma torus, a comprehensive analysis leading to the détermination of the HOM source location is not possible without ray-tracing which includes ail effects of refraction on a ray in the course of its propagation from the source into free space. The dérivation of the mathematical tools required for ray-tracing are given in detail in Appendix E, so only a short version is given here. The ray-tracing computer program is based on the cold plasma formulation of the refractive index [START_REF] Stix | The Theory of Plasma Waves[END_REF]. A set of first order differential équations (canonical ray équations), expressed in spherical coordinates, are solved numerically (Appendix E)-At a given point in space, the program calculâtes the refractive index surface for R-X mode waves based on magnetic field and plasma models for the Jovian magnetosphere. Next, the program takes an incrémental step perpendicular to the refractive index surface; this dénotés the direction of the group velocity and energy flow, and is identical with the ray direction. Then, a new point in space is found and the steps are repeated.

The wave normal direction changes according to Snell's law when the wave travels through the magnetoplasma. Generally, the directions of the ray and the wave normal do not differ too much except in régions where the refractive index is considerably less tlian unity. To perform a ray-tracing study, analytical magnetic field and plasma models must be implemented to describe the plasma in the Jovian magnetosphere.

3.3

Assumptions: Magnetic field and plasma models, and gén ération mechanism

For the représentation of the Jovian magnetic field, we implemented the 0\ model [START_REF] Acuna | The main magnetic field of Jupiter[END_REF] providing spherical harmonie coefficients which characterize the dipole, quadrupole, and octopole contributions. The 04 model has been derived from Pioneer 11 measurements and is supposed to be the best représentation of the Jovian magnetic field at présent. The électron density model in the Jovian magnetosphere also including the Io plasma torus is provided by [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]. Even simplified at best, the Jovian plasma torus acts as a divergent lens for waves in the kilometric and hectometric wavelength range. The Io torus électron number density is displayed in Figure 3.1. The innermost isodensity contour refers to iV=3000/ccm and corresponds to a plasma frequency of fp= 500 kHz. Divine and Garrett give also density and energy models for charged particles of different species in the Io torus and in magnetospheric régions out to 170 Rj.

Since the hectometric émission propagates high above the ionospheric level the use of an ionospheric model is not necessary. It is further assumed that the scale heights of the gradients in the magnetic field and plasma models are small compared to the wavelengths of the HOM range. The électron température is believed to be sufficiently small to allow for the cold plasma dispersion relation.

Before performing ray-tracing in a systematic matter one should introduce some constraints due to the génération mechanism of the radiation. The principles of the supposed mechanism are discussed in detail later on, so only general comments are provided here. Most of the radio émissions (and also the HOM) are generated in the extraordinary (R-X) wave mode.

The most promising among the génération théories for planetary radio waves is the Cyclotron Maser Instability (CMI) by [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF]. The radiation is generated by the résonance of upgoing loss cône particles with the upper frequency branch of the extraordinary wave mode.

For simplified conditions Wu and Lee derived expressions for the wave growth and beaming properties of the émission. It is found that the émission escapes the source in a hollow cône beam, the source field line being the cône axis (Figure 3.2). The sources are located at régions where the wave frequency / is approximately equal to the local électron gyrofrequency /c. The half cône opening angle 6 is nearly perpendicular with respect to the local magnetic field. The mechanism is most efficient if the plasma frequency fv is considerably less than the gyrofrequency. The CMI mechanism is able to explain importait details observed so far from planetary radio émissions.

Ray-tracing calculations

The HOM latitudinal beaming, solar wind control, polarization pattern and local time effect as derived in chapter 1 give severe constraints on the possible source locations together with the use of a génération model which provides some dues about the radiation pattern from the source. A systematic investigation in order to localize the HOM sources is performed via raytracing in a meridian plane. Later on, a fully three-dimensional ray-tracing study is performed to establish and confirai the derived HOM sources. We first test several sources (labeled by the dipole shell parameter L) and find the maximum possible wave normal angle 9 at which the radiation from these sources can be observed within the HOM beam which occurs in the vicinity of the Jovian magnetic equator. Corresponding to the HOM polarization measurements, only the R-X mode is considered for ray-tracing. According to the CMI, the radio sources are located at magnetospheric heights where the wave frequency is slightly higher than the gyrofrequency.

Because of the very low ratio /p//c at a distance of a few Jovian radii where the HOM sources are located, notable wave refraction near the source is not expected. (///c=l-05) for varying cône half angles 0 and for 2 frequencies, /=300 kHz and /=500 kHz. In ail of the plots, the rays associated with the "critical angle 0CTnr> above which no more émission can be detected by the spacecraft near the magnetic équatorial plane are emphasized by thick lines. Two important facts can be stated by inspection of Figures 3.3 and 3.4. First of ail, there exists a focussing of HOM émission parallel to the magnetic équatorial plane when 9 is less but close to 9cj.it-At 9 = 90 the rays also point in the required direction but émission consisting of these rays fail to describe the observations near encounter (for a detailed discussion, see Ladreiter and Leblanc, 1990a,b [Appendices B and C]). Secondly, we see a dependence of 9c-a as a function of the L parameter of the source: The higher the L value of the assumed source location, the higher the angle 0CTtt up to which observations are possible.

In Figure 3.5 we hâve plotted the angle 9versus several investigated frequencies. For the development of Figure 3.5, arbitrary source locations in both hemispheres (subscripts N and S)

were taken. The dashed lines dénoté the interpolations for L-10, 15, and 30. Because the Jovian magnetic field can be accurately described by a dipole at larger distances from the planet, we suppose that no important azimuthal asymmetries occur. One important interprétation of Figure 3.5 is that no strong dependence on the initial wave normal angle 9 arise for different émission frequencies (for fixed values of L). We further see that émission for nearly perpendicular cône half angles is only possible for sources at high values of X, say L=15-30 (when 9crit = 70°-90°). For the hectometric component actual cône half angles are not known, but the kilometric radiations from the earth and Saturn, as well as the Jovian decametric radiation are emitted at large wave normal angles (i.e. about 70°-90°). Assuming similar values of 9 for HOM, the émission source is consequently located at high auroral zones at both hemispheres, probably between X=15 and Z=30.

3.5

Location of footpoints of the HOM source field lines overlapping these auroral régions. Thus, the HOM sources hâve direct access to charged particles from the tail and possibly from the dayside polar cusp. This could easily explain the solar wind control as well as the sharp latitudinal beaming of HOM due to the refraction of rays at the Io torus. The rays become finally directed parallel with respect to the magnetic équatorial plane and could therefore be detected by the Voyager spacecraft (Figures 3.3 and 3.4). HOM source locations at high latitude field lines can therefore account for most of the HOM characteristics.

frequency (kHz) On the contrary, HOM sources within the Io flux tube can neither explain the observed solar wind control nor the HOM activities down to about 40 kHz. X mode émission at /=40 kHz cannot be generated for r< IRj. For this alone reason, the Io torus can be eliminated as possible source location for HOM.

3.6

Three-dimensional modeling of the HOM

Shadow zone of the émission

The results on the HOM source location were derived from two-dimensional ray-tracing, the ray paths being considered only in a meridian plane. To establish definitely the obtained source locations, we additionally performed a three-dimensional analysis in order to model the hectometric observations from Voyager 1 and Voyager 2. the lower panel exhibits a recording just before the V1 encounter. The différence concerning the émission patterns between the two panels is striking. The upper panel shows the well known émission gap near 200°CML and émission maxima at System III longitudes where the spacecraft crossed the magnetic équatorial plane (dashed vertical lines). In contrast to this, the lower panel shows no émission during times of magnetic equator crossings. Higher activity zones occur at higher northern and Southern magnetic latitudes.

Similar as in Figure 2.2 a straightforward way to interpret these observations is to consider the HOM activity in terms of magnetic latitude. Then, the observations reveal the existence of a "shadow zone" where no émission occurs near the magnetic équatorial plane at short distances from the planet. Farther away, this shadow zone is filled and the emisson is beamed nearly parallel to the magnetic équatorial plane. This trend could already be seen in Figures 3.3 and 3.4: Pénétration of rays in the innermost régions of the plasma torus is inhibited because of the enhanced plasma density. Consequently, a shadow zone near the magnetic equator is produced near Jupiter.

We are now interested to study the HOM in the context of a three-dimensional investigation. In order to model the HOM observations, we restrict ourselves to the study of /=500 kHz (typical HOM frequency) and to the source locations already determined in the foregoing sections. To take an intermediate value between L=15 and £=30, we chose £=20 for the further analysis. of the actual situation. The fit is remarkable good when we bear in mind that the formation of the shadow zone is a joint conséquence of the beaming properties, source locations, and the refractive properties of the Io torus.

Similar good results for higher frequency HOM components are obtained when the density of the Io torus is enhanced more dramatically. A factor 2-3 for the peak density is sufficient to accurately account also for the HOM émission around 1 MHz. Several authors (e.g. [START_REF] Jones | Source of broadband kilometric radiation[END_REF] suggest in fact a torus peak density that is enhanced by a factor of three with respect to the présent one.

Latitudinal beaming and intensity profile

As a last test for the vaUdity of the HOM source locations we perform a simulation of the HOM observations via three-dimensional ray-tracing for given source locations and beaming characteristics. The sources axe assumed to be uniformly distributed in longitude along the auroral ovals (L=20) at both hemispheres. The radiation escapes the sources (/ « fc) within a narrow hollow cône beam within 6 -70°and 6 = 80°(cône wall half thickness A9 = 5°) and with a maximum intensity at 75°. At the actual point of observation the contributions of ail sources are incoherently added including ail effects of focussing and diffraction of the waves. To simulate a uniform distribution in longitude, 9 subsources at each hemisphere, equally spaced in longitude, were taken for the calculation. For a detailed discussion of the analysis, the reader is referred to Appendix C.

We investigated the formation of the HOM latitudinal beaming by plotting the conical émission pattern that Voyager would hâve observed during two Voyager rotations at different radial distances from the planet. The upper panel of Figure 3.10a shows the situation one Jovian rotation after closest approach (designated as Rotation # 1). The shadow zone is visible at small radial distances and vanishes when the spacecraft is beyond r=16 Rj. The corresponding intensity profile (lower panel) shows émission dropouts when the spacecraft crossed the shadow zone. This situation no longer accounts for observations at large radial distances (Figure 3.10b).

The space where the shadow zone occurs in the upper panel of Figure 3.10a is now filled with the narrow HOM émission beam where the intensity is enhanced. Thus, one important resuit of this investigation is the accurate theoretical modeling of the HOM latitudinal beaming which was first established based on longterm statistical analyses by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF]. For the sake of illustration, compare Figure 3.10b with Figure 2.2, bottom panel. Furthermore, the calculated HOM profile in the lower panel of Figure 3.10 reveals the well-known HOM émission pattern with the characteristic émission gap near 200°CML.

Figure 3.11 shows a sequence of observations (dashed profiles) during several Jovian rotations.

Superimposed the calculated profiles are plotted. Both, the observed and theoretical profiles (calculated for the indicated parameter set) are normalized for each rotation separately. The overall situation which is typical for HOM observations at different distances from the planet is well-fitted and the sudden change in the HOM observations when the spacecraft approached the planet can also be predicted by the model. Although the overall simulation is far from being perfect (we do not expect otherwise, because of the simplifications made in our assumptions) the major structures are explained very well, suggesting that the modulation of HOM can be associated with a source located at high latitude auroral zones.

Discussion of the results

The results in Figures 3.9, 3.10, and 3.11 were calculated for a set of parameters ///c, 9, A0, the torus density model p(f% and a given L parameter of the source locations (indicated at the top of Figure 3.11). The first three parameters were selected to be in agreement with the cyclotron maser mechanism which is now the most promising theory for the génération of radio émissions. The Io torus density model was determined by in situ observations, but it is an average model, and it suffers (very likely) temporal fluctuations. Therefore, we hâve verified how that parameter may influence the results. The only free parameter is the L shell of the source field lines. Ladreiter and Leblanc (1990a) hâve shown, that 15 < L < 30 accounts for the HOM observations for nearly perpendicular 9. With the use of L=20 (to take an intermediate value) we hâve shown that the modeled émission is in agreement with the observations for a fully three-dimensional investigation as well. The fact that HOM may be visible at ail System III longitudes when the viewing geometry is favourable strongly suggests that HOM is active over a wide range of longitudes. The inferred parameter set may therefore be considered as highly relevant and justified in association with the Jovian hectometric radiation. In addition, the source location of HOM at the auroral zones explains the solar wind control of the HOM since the solar wind particles hâve direct access to these régions. RAY-TRACING IN THE JOVIAN MAGNETOSPHERE: HOM SOURCES (1987) reported that the HOM and non-Io DAM should emerge from a common source because of a similar solar wind control of both émissions. However, it has also been suggested in the literature that HOM is a separate component because of its own spectral peak near 1 MHz.

As a conséquence of our investigation we are now able to State that the HOM spectral peak possibly arises from the focussing of the émission, being caused by the Io plasma torus. Outside the beam, the intensity is considerably weaker, so that the overall flux (over a solid angle of 2%) may be highly overestimated. Consequently, the spectral peak could vanish and the HOM is seen as the low-frequency extension of the non-Io DAM which is also generated at high magnetic latitudes but obviously is less extended in longitude.

Chapter 4

The HOM radiation mechanism

The Cyclotron Maser Instability

Ten years ago, in '1979, Wu and Lee developed the theory of the cyclotron maser mechanism for the génération of planetary radio émission. This mechanism is commonly accepted to be the relevant theory for auroral radio émissions. Other théories cire not discussed here but they are reviewed elsewhere (e.g. [START_REF] Genova | Les émission radio aurorales des planètes[END_REF]. The Cyclotron Maser Instability (CMI) theory States that radio waves can be generated and ampMed by résonance with auroral électrons spiralling around magnetic field lines, having free energy (unstable électrons). The amplification of electromagnetic X-mode waves is generally favoured since the gyration of électrons around magnetic field lines is in the same sense as the E-vector of the fast X-mode.

The purpose of this section is a treatment of the CMI in a very low density magnetoplasma where fp/fc < 0.01. This represents conditions as found in the higher altitude auroral zones within the magnetospheres of Jupiter (HOM sources) and Saturn (SKR sources). We dérivé simple expressions relating the normalized (to the light velocity c) parallel bulk velocity /3\\0 of a given électron distribution function to the frequency f of the most amplified wave (in terms of fc) and to the emergence angle 9 when the radio source is situated in a low density magnetoplasma. We first hâve to study the dispersion relation and the growth rate. This leads to the formulation of the résonance condition which is discussed in detail for /p//c << 1. where u = 2irf, k^yk± axe the components of the wave vector parallel/perpendicular with respect to the magnetic field B, F dénotés the électron distribution function in the velocity space (v||,vj.), J\ is the Bessel function, and V = 1/^/1 -u2/c2 = 1/^/1 -fi2.

It is further assumed that the cold (ionospheric) électrons solely support the wave propagation, whereas the hot precipitating électrons forming the instabilités in the distribution function axe only responsible for the amplification of the wave.

The growth rate for the CMI is expressed in terms of the imaginary part ut-of the angular frequency u = ur + iu{. An approximate formula for the R-X mode wave is given by [START_REF] Wu | Kinetic cyclotron and synchrotron maser instabilités: Radio émission processes by direct amplification of radiation[END_REF]:

7T2U>p r+oo r oo Qjp Ui = -£T J0 ujr -k\nPcg^- (4.2)
In Equation ( 4.2), it is further assumed that ur >> (-u « u>r), and the argument of the Bessel function J[ in Equation (4.1) is small leading to j[2 = 1/4 and, moreover, the term associated with dF/dv\\ can be neglected compared to the term with dF/dv±.

Although some of the assumptions made for the dérivation of the dispersion relation and the growth rate are very questionable after the recent Viking measurements in the TKR source région [START_REF] Louarn | Trapped électrons as a free energy source for the AKR[END_REF], they are sufficient for our purpose because the aim of this study is to discuss the résonance condition occurring in the denominator of Equation ( 4.1) and in the argument of the 6 function in Equation (4.2).

Electron distribution function

Before staxting to discuss the conditions for wave résonance with energetic particles at the source région, let us study a typical électron distribution function as measured by the S3-3 satellite [START_REF] Croley | Signature of a parallel electric field in ion and électron distributions in velocity space[END_REF]. Three unstable features with positive dF(v)/dv± (providing free energy for wave growth) axe visible in Figure 4.1. Firstly, the loss cône région associated with the upwaxd side of the distribution function (ascending électrons), secondly, the accelerated downgoing élec trons (forming a holelike feature), and thirdly, the trapped électrons near the u_i_-axis. The latter axe suggested to be trapped throughout a time-varying (or space-varying) paxallel electric field (Louaxn et al., 1990) between their magnetic mirror point above the ionosphère and a second mirror point due to the paxallel electric field along auroral field fines. The corresponding electric potential has been reported to be about 3 kV over a distance of several eaxth radii [START_REF] Croley | Signature of a parallel electric field in ion and électron distributions in velocity space[END_REF]. Although a common conclusion has not been drawn yet, it is generally accepted that TKR is likely to be excited by two instabifities, axising from the loss cône and/or holelike région. These two régions are chaxacterized by a relatively small (3±0 which leads to an essential simplification when studying the résonance condition. For a given wave (£, /) this résonance contour can be found in the velocity space by solving the cold plasma dispersion relation [START_REF] Budden | Radio Waves in the Ionosphère[END_REF][START_REF] Stix | The Theory of Plasma Waves[END_REF]. For the fast extraordinary (R-X) mode these contours are ellipses entirely placed at either the upward or downward side of the distribution function [START_REF] Dusenbery | General concepts on the génération of auroral kilometric radiation[END_REF]. This is visualized in Equation ( 4.3) where lj must be greater than ljc/T because the R-X cutoff frequency fnx is always higher than fc. Since the résonance condition must be fuLfilled, this eau only be achieved when k\\v\\ > 0, therefore requesting that fc|| and uy point in the same direction. Thus, upgoing waves can only be amplified by ascending électrons and downward propagating waves only by descending électrons.

Properties of résonant contours

Regarding the distribution function in space for different wave emergence angles (illustrated in Figure 4.2). For a given 9, we distinguish three areas in the diagram. Firstly, the région above / = /rx (R-X cutoff frequency) where no propagation of R-X mode waves is possible. Secondly, the area outside of the so-called separatrix Se and inside / = /rx where no résonant contours exist for the respective 0, and, thirdly, the région inside the separatrix where résonant ellipses do exist. For a given point in the normalized f -fP space placed exactly on a separatrix, the résonant ellipses shrink to a point. The deeper a point in the normalized f -fp space is placed inside the separatrix, the larger is the extension of the résonant ellipse.

Adapted résonant contours in the électron distribution function

When considering the loss cône or the hole-like instability providing free energy for the génération of radio émissions, we limit our discussion to ellipses with small extensions in the velocity space.

In the normalized f -fp space, the respective area is located at or slightly inside the regarded separatrix. For points exactly on the separatrix, the formalism greatly simplifies because the ellipse resulting from the relativistic résonance condition (Equation 4.3) shrink to a point and after some algebraic transformations (see Ladreiter, 1990 [Appendix D] for details) one obtains important wave characteristics in terms of the parallel électron bulk velocity /?||c of theunstable région.

n cos 9 = /?||0

(4.4) / _ 1 /c \A^( 4.5)
For the dérivation of Equations (4.4) and (4.5) it was also assumed that the distance d of the center of the ellipse from the origin in velocity space is equal to the parallel bulk velocity (3\\0 (see Appendix D,Figure D.2). Equation (4.5) States that in the limit of our assumptions, the ratio f/fc is only dépendent on /?||0 regardless of the wave normal angle 9. Equation (4.4) requires further analysis to express 9 exclusively in terms of (3\\0.

4.3

Amplification of radiation via the cyclotron maser mecha- where vg dénotés the group velocity.

For a net amplification g must be greater than 0. For the terrestrial kilometric radiation, the exponential gain factor was calculated by Omidi and Gurnett (1984) and important results were derived. Because of the lack of measured distribution functions for the auroral régions of Jupiter and Saturn we hâve to simulate the most important feature -the loss cône -in the électron distribution function. The électrons with very small équatorial pitch angles hâve their mirror points in the planet's atmosphère and are therefore lost by collisions with atmospheric particles.

They consequently produce a lack of ascending électrons for small pitch angles dF/dvj_ > 0 which leads to the loss cône instability.

We now make important simplifications before calcidating g in terms of /p/ fc and 9. They are listed in the following:

1. The cold plasma détermines the wave propagation along the ray path /1 -I2.

2. Existence of a magnetic dipole field with VB\\B. The direction of B is kept constant along the ray path. This is a good approximation near the magnetic polar régions.

3. No refraction of the propagating wave.

4. fpffc = constant along ray path.

5. Instability (dF/dv± > 0) is caused by a loss cône superposed by a parallel electric field.

6. No wave absorption after phase of amplification.

7. u>i is taken to be constant when the corresponding résonant ellipse is lying within the space of instability.

8. /i is the point where the résonant ellipse of the corresponding wave enters the unstable région and I2 is the point where the semimajor axis b exceeds that région (Appendix D, 9. The loss cône angle a is taken to be 15°but it is not infinitely steep, permitting A a = 2°because the variable interaction altitude of the impacting électrons in the planetary atmosphères produces this scattering in a (Appendix D).

10. Equation (4.2) is solved for a given ratio /p//c (kept constant along the ray path) and generally two solutions are derived near branches 61 and &2, respectively.

Since Ui is constant between /1 and /2, Equation (4.6) can be written

f12 & , x 9 = ui ~m = (4.7) J11 w)
where T is the interaction time of the électron -wave résonance.

The exact calculation of T as a function of 9 and fp/fc is described in Appendix D using the above assumptions. So only the results are presented here in Figure 4.3 for 9 = 70°. In the top panel (a) we show the normalized interaction time T against /p//c for the two branches b\ and 62 as defined in Figure 4.2. We see that T is generally higher for branch 61 which corresponds to lower refractive indices n (bottom panel) and consequently to lower group velocities vg. Moreover, a dramatic increase of T is observed when fp/fc is reaching its highest values (« 0.14). This can easily be understood in the middle panel (b) which shows the wave-particle interaction length L (between li and /2). We see a maximum of L reaching 10~2ro when fp/fc is near its maximum.

Assuming rQ to be about 2 -3 planetary radii (distance of radio source from the planetary center), we obtain L « 200 km for the earth and L « 2000 km for the giant planets Jupiter and Saturn. We note that for branch 61 when considering low values of /p/fc (< 0.01) the interaction length L drops down to lower than 10-7ro which corresponds only to a few meters which might be not realistic. The previous findings can be discussed very critically when considering Figure 4.3c. There we hâve drawn the refractive indices given at /1 (full line) and f2 (dashed line).

Especially for 61, refraction effects arise because of the low refractive index n (Figure 4.3c).

It is not possible to calculate these effects since the directions of Vn are not actually known.

However, this is highly relevant for the branch 61 and is quenching the gain after the phase of amplification.

For a given 9 the maximum interaction time T is reached near the vertex of the respective separatrix (hatched areas in Figure D.6 of Appendix D), but also in this région, the increase of the refractive index along the ray path is quite important so that subséquent damping may also overcome the initial gain. One solution where we can unambiguously state that damping after the phase of amplification is most unexpected is branch 62 for lower /p//c. There, the refractive index is near unity and the group velocity nearly the light velocity c which explains the moderate gain. The particle interaction length is 10"3ro (r0: a few planetary radii) which can be compared to the dimensions of an auroral arc. We are confident that in the limit of our calculations, plasma conditions corresponding to branch 62 are relevant for the amplification of radio émissions. In contrast, for branch 61 n -0 for fp/fc << 1 therefore Equation (4.4) cannot be fulfilled for typical values of 0\\O ~0.1 and possible amplification is highly questionable.

Results

With the results of the preceding sections (the wave growth as given for branch 62 [n -1] is relevant for the amplification of radio émission), Equation (4.4) can be rewritten in the limit n -1 (Figure 4.3c) for branch 62 cos 6 = /?||0 (4.8) Thus, we are able to express the wave normal angle 0 (Equation 4.8) and the ratio //fc at the source (Equation 4.5) in terms of the parallel bulk velocity when fp/fc is very low. The graphs of 0(/3\\o) and f/fc{P\\0) are plotted in Figure 4.4. In addition, we show the scale for the respective électron energies. For energies of 10 keV (which are expected in the Jovian auroral zone) the resulting values for 9 and f/fc are 78°and 1.027, respectively. This, in retrospect, confirms the assumptions for the wave normal angle 9 and f/fc in our three-dimensional raytracing study and demonstrates the large degree of consistence when linking the CMI to auroral radio émissions. Further, this investigation agréés with a theoretical study on the Saturnian radio émission [START_REF] Galopeau | Theoretical model of Saturn's kilometric radiation spectrum[END_REF]. These authors modeled the Saturnian radio spectrum best for a nearly perpendicular 9 when /p//c << 1.

Discussion

During the présent investigation we analyzed the CMI in plasmas which are largely dominated by the magnetic field (/p//c < 0.01). This study is highly important, however, because of the applications to the low-frequency auroral émissions of Jupiter and Satura. Within the sake of simplifications, we derived the wave emergence angle 9 and ///c at the source as a function of the parallel bulk velocity /3\\0 provided that the amplification of the wave is due to the loss cône or the holelike instability.

One of our most important findings is that the refractive index at the source is near unity because f/fc has been shown to be about 1.01 for plausible électron energies (1-10 keV), thus, the source région is sufficiently distinct from the R-X cutofF. The quenching of the interaction time due to the high group velocity vg in this région is compensated by the long interaction length which is possibly as long as an auroral arc. On the other hand, when n -*• 0 in a low density source région, the group velocity is very small which would enhance the gain, but the interaction length is only in the order of meters or even below which is probably not realistic.

Concerning the wave emergent angle 9 at the source, which is found to be « 80°for électron energies from 1-10 keV, the results agréé favourably with the study of the theoretical radio spectrum of SKR performed by [START_REF] Galopeau | Theoretical model of Saturn's kilometric radiation spectrum[END_REF] and are consistent with the large wave normal angles determined in a theoretical study for TKR (Le Queau et al., 1984a,b). Chapter 5

Conclusion and prospects

HOM characteristics

From observations pf the Jovian radio émission at bectometric wavelength (HOM) obtained by

Voyager 1 (VI) and Voyager 2 (V2) in 1979, the latitudinal beaming at three selected frequencies /=1326 kHz, 942 kHz, and 558 kHz is determined. We find that the total beam width is between 10°and 20°depending on the normalized (to the earth-Jupiter distance) détection threshold.

The beam center of HOM is found to be situated at about +1.6°magnetic (dipole) déclination.

On the nightside the beam width is a few degrees («4°) narrower compared to the dayside. We establish that right-hand polarization is associated with the northern hemisphere and left-hand polarization with the Southern hemisphere which is consistent with wave propagation in the R-X mode. From the analysis of the frequency limits of HOM, we détermine a source extension from 2 Jovian radii (Rj) out to about 7 Rj, by assuming an émission close to the R-X cutoff frequency. The beaming results, and the HOM low-frequency limits are compared with the solar wind parameters. We find that increases in the solar wind density and/or pressure are well correlated in time with the lowest frequency limits of HOM and the largest beam widths. A strong corrélation is consequently obtained between those two parameters and the HOM energy.

This supports the idea that a high density solar wind stream at Jupiter enhances the HOM energy output, extends the source régions to higher altitudes on auroral field fines, and widens the HOM beam to higher magnetic latitudes.

Ray-tracing and HOM source location

Ray-tracing using reafistic magnetic field and plasma models has been performed to locate the Jovian hectometric radiation (HOM) sources. To consider only a few possible source locations, we hâve assumed that the radiation mechanism is the Cyclotron Maser Instabifity (CMI), and taken into account the characteristics of the HOM including the results by [START_REF] Ladreiter | Jovian hectometric radiation -Beaming, polarization, source extension, and solar wind control[END_REF] (=Appendix A). The émission is assumed to escape from the planet in the extraordinary wave mode within a thin beam of hollow cônes whose apexes are distributed uniformly in longitude at the northern and Southern hemispheres at altitudes where the gyrofrequency fc is less but nearly equal to the observed wave frequency. The rays are traced from possible sources 49 located at ///c=1.05 and labeled by the dipole shelI parameter L. For each source, we hâve determined the emergence wave normal angle 0^.,* above which the rays no longer travel within the HOM émission beam nearby the magnetic equator. We show that the HOM sources cannot be located on field lines within the Io flux tube. However, wave refraction due to the Io torus plays a crucial rôle for the propagation and beaming of the waves toward the magnetic equator.

It is found that HOM sources located at field lines 15 < L < 30 agréé best with the observations when assuming that the cône half angle of émission is about 70°-90°with respect to the local magnetic field. Thus, the source is associated with the tail field aurora where the magnetic field lines connect the polar région to the Jovian magnetic tail and is extended in altitude from 2 to 7 Jovian radii (Rj). Our results explain in detail the radio phenomenology of the hectometric radiation, in particular the strong latitudinal beaming, the solar wind control, the absence of HOM émission when Voyager 1 was within the Io torus, and the absence of Io control on the HOM.

Three-dimensional modeling of the HOM

To model the Jovian hectometric radiation, we additionally performed three-dimensional raytracing at a typical HOM frequency of /=500 kHz. The source locations are assumed to lie along magnetic field lines L-20 as determined by Ladreiter and Leblanc (1990a) (=Appendix B). Furthermore, the sources are distributed uniformly in longitude at magnetospheric heights, where the cyclotron frequency is less but nearly equal to the wave frequency. The émission is beamed at large angles (70°-80°) with respect to the magnetic field and propagates in the extraordinary (R-X) mode. Our study can account for the major characteristics of the HOM radiation as observed by the Planetary Radio Astronomy (PRA) experiment aboard Voyager 1 and Voyager 2 during the encounter period and at large distances from the planet. Thus, geometrical eflFects are taken into account. The modeled radiation pattern reveals the existence of a shadow zone at the magnetic (dipole) équatorial plane extending to about 20 Jovian radii (AEj), which was actually observed by both Voyagers. The results from our ray-tracing analysis account for the strong latitudinal beaming of the radiation, observed at large radial distances from Jupiter, as well as for the polarization properties. Moreover, the modeled intensity profiles, compared with observations at various distances from Jupiter, show a remarkable agreement.

However, a better fit to the observations is obtained when the Io torus électron density (from [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]) is enhanced by 15 %. This study confirms that the HOM sources are located along open magnetic field lines with footprints in the tailfield auroral ovals in both hemispheres. We suggest that HOM is the low-frequency extension of non-Io DAM, since the observed spectral peak of HOM near 1 MHz could be produced by the focussing of the radiation due to refractory effects of the Io torus.

HOM génération mechanism

Considering the Cyclotron Maser Instability [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] within low density magnétoplasmas (/p//c < 0.01) we dérivé simple expressions relating the wave emergent angle 9 and the ratio ///c at the source to the normalized (to c) parallel bulk velocity /3\\0 of the insta bility (characteristic for an électron distribution function) via the équations cos(0) = /?||0 and f/fc = (1 -P\\0)~l/2-During this investigation we considered the loss cône and holelike instability to be responsible for wave amplification. Both of these régions exhibit a relatively small perpendicular energy. We found that for f3\\0 corresponding to 1-10 keV, 9 is found to be nearly perpendicular with respect to the magnetic field and 9 decreases when (3\\0 increases. The wave frequency is slightly above the gyrofrequency, but is substantially distinct from the R-X cutofF;

thus, the refractive index is near unity at the radio source. No strong refraction along the ray path is therefore expected for /p//c << 1. The results are highly relevant for the lower frequency auroral émissions of Jupiter (low frequency DAM and HOM) and of Satura (lower frequency SKR) where very low density magnetoplasmas (/p//c < 0.01) do in fact exist at the respective source régions. Therefore, these radio components escape from the respective radio sources in form of hollow cône beams with large cône apical angles.

Summary

Source location: High latitude auroral field lines (L = 15 -30) at heights where ///c » 1.

The ratio /p//c is very low (« 0.001-0.01).

Source extension: From 2 Rj to 7 Rj along auroral field lines at both hemispheres. The sources are distributed over a wide range of longitudes.

Emission pattern: Hollow cône, half apical angle 9 = 70°-90°, cône wall thickness A9 «9

Génération mechanism: Cyclotron Maser Instability (CMI).

Relation to other émissions: Low-frequency extension of non-Io DAM, distinctly different from Io DAM and KOM.

General comments: Occurrence of a shadow zone near the magnetic équatorial plane at dis tances less than 15-20 Rj. Beyond, the émission is confined within a quite narrow beam (latitudinal extension 10°-20°) near the magnetic equator. The émission is local time dépendent.

Prospects

The study of the Jovian hectometric radiation enabled us to understand the main characteristics of the radiation such as the properties of HOM as well as the source location in the Jovian magnetosphere. The présent analysis also clearly shows a straightforward way how to proceed step by step from the observations of HOM to the émission characteristics, source locations, and finally to a link to the génération mechanism. This finally leads to a comprehensive view of HOM also in the context with other planetary émission components. However, the Voyager spacecraft only explored régions close to the Jovian équatorial plane, so no observations about the HOM activity beamed in high latitudes are available at présent. Future spacecraft missions such as Galileo and Ulysses will provide the opportunity to collect further data leading to a deeper study of yet unresolved details conceraing the hectometric radiation.

émission. A number of studies hâve been conducted on the latitudinal beaming of these radio émissions. For the non-Io DAM émission a strong latitudinal beaming has been evidenced from ground -based observations [START_REF] Gulkis | Radio rotation period of Jupiter[END_REF][START_REF] Carr | The twelve-year periodicities of the decametric radiation of Jupiter[END_REF][START_REF] Carr | Recent decametric and hectometric observations of Jupiter[END_REF][START_REF] Barrow | Latitudinal beaming and local time effects in the decametre-wave radiation from Jupiter observed at the earth and from Voyager[END_REF] and more recently from spacecraft and ground-based simultaneous observations (Poquerusse and [START_REF] Poquerus8e | First direct measurement of the beaming of Jupiter's deca metric radiation[END_REF][START_REF] Barrow | Arc structures in the Jovian decameter émission observed from the earth and from Voyager[END_REF]Maeda andCarr, 1984, 1988).

The latitudinal beaming of the KOM émission was derived from the occurrence probability in terms of System III (1965) longitude (CML) or of Jovimagnetic latitude of the spacecraft [START_REF] Kurth | Low frequency radio émissions from Jupiter: Jovian kilometric radiation[END_REF][START_REF] Desch | The occurrence rate, polarization character, and intensity of broadband Jovian kilometric radiation[END_REF]Leblanc and Daigne, 1985a,b;[START_REF] Daigne | Narrow band Jovian kilometric radiation; occurrence, polarization, and rotation period[END_REF][START_REF] Jones | Source of broadband kilometric radiation[END_REF][START_REF] Leblanc | The kilometric Jovian radio sources at the Io torus[END_REF]. with an extension of 10°centered on 3°magnetic latitude. This model is in agreement with the degree of corrélation between the two spacecraft separated by up to 3°in Jovigraphic latitude.

Later on, [START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF] found further a local time dependence of the HOM émission by comparing day and nightside observations. The nightside recordings show an émission gap of HOM intensity at about 60°CML whereas at the dayside there occurred a local maximum of émission at that longitude.

The émission at HOM wavelength has been found to be strongly polarized. [START_REF] Lecacheux | Some spectral characteristics of the hectometric Jovian émission[END_REF] reported that the source of circular polarization of the HOM (left-hand source) is opposite to that of the DAM (right-hand source). On the other hand, [START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF] reported that the fundamental polarization sense of the HOM may hâve reversed after encounter. This polarization reversai was not understood and attributed to local time variations.

A solar wind control of HOM was demonstrated by [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF] and by [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF]. Further results are given more recently by [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. Zarka and Genova found that the sector structure of the interplanetary magnetic field highly Controls the long term intensity fluctuations at hectometer wavelengths. [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF] found a significant positive corrélation between the solar wind plasma density and the HOM émission output by using a cross corrélation analysis. [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF] furthermore showed that the HOM activity is correlated to the non-Io DAM, but not to the Io-DAM, suggesting that the HOM and non-Io DAM are two components of the same radio émission, and implying a > 4Rj source extent along high latitude field lines. A recent study of [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF] shows that the higher energy HOM is correlated with the solar wind density, pressure, and the interplanetary magnetic field magnitude. They additionally found that the non-Io DAM is also correlated with the solar wind speed which might argue that HOM and non-Io DAM are not emitted from the same source.

The HOM component was not thoroughly investigated, however, and many outstanding problems still remain unanswered; e. g. is the HOM component just an extension of DAM or is it a distinct component ? Where is the location and extension of the source and is it a corotating source ? What is the polarization of HOM after Leblanc and Daigne (1985a) and [START_REF] Lecacheux | Polarization and localization of the Uranian Radio Sources[END_REF] hâve studied the orientation of the electrical plane of the antennas with respect to the physical plane, at low frequencies ? Does the beaming of the HOM émission also dépend on the solar wind ?

In this paper we treat some of these questions using VI and V2 data from the low-frequency band of the PRA experiment recorded in 1979, including the VI and V2 encounters. In section A.2, we calculate the angular beam width of the radiation for 3 fixed frequencies from the occurrence of the HOM émission in System III (1965) longitude (CML) and from the spacecraft position.

We compare Voyager 1 (VI) and Voyager 2 (V2) results and investigate also the polarization behaviour. Section A.3 deals with the low-frequency limit of HOM and we give a hint for the source extension, assuming that the source is near the cutoff of the fast extraordinary (R-X) mode centered on auroral field lines. In section A.4, we correlate solar wind parameters with the HOM beaming, and with the low-frequency limit of the émission.

A.2 Beaming of the Jovian hectometric radiation [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] derived their émission beam axis by analyzing the émission peaks in the occurrence probability histograms as a function of magnetic latitude rather than a function of CML. The extension of the émission beam was derived somewhat arbitrarily based on the standard déviation in magnetic latitude of the émission peaks.

Our détermination of the beam width is made from a different approach and two methods hâve been used. The first is from analysis of the émission beginning and ending as a function of magnetic latitude, the second is from the occurrence probability, also in terms of magnetic latitude. The results of the beaming will be presented as a function of the spacecraft distance to Jupiter, of the observed HOM frequency, and of local time; also a comparison of the beaming resulting from simultaneous observations will be made. Finally, we investigate the polarization of the émission.

A. 2.1 Observations

For our investigation we used VI and V2 data of the low-frequency band of the PRA experiment recorded in 1979, including the VI and V2 encounters, respectively. The low-frequency band consists of 70 channels starting from 1.2 to 1326.0 kHz, each of them with a bandwidth of 1 kHz separated by 19.2 kHz. The PRA antenna consists of two crossed monopoles which allow the sense of polarization to be determined. For a detailed description of the PRA experiment, see [START_REF] Warwick | Planetary radio astronomy experiment for Voyager missions[END_REF].

The occurrence of the HOM émission as a function of System III longitude for a fixed frequency is a quite stable feature for many consecutive rotations for both spacecraft. With a few exceptions near the respective encounters where ghost images occur, the beginning and ending of the émission can be easily detected in a time interval of « 4 months centered on the respective encounters.

A.2.2 Methods of analysis

In the first method, in order to détermine the beaming we analyzed at a given time period the émission beginnings and endings in our observations as a function of the (dipole) magnetic latitude. Following this procedure rotation by rotation, we obtain for each rotation one oflf-and one onset centered around 200°CML which delineate the northern beam limits. Sometimes, also the Southern spacecraft beam crossings are visible, in particular during the VI inbound trajectory (due to the lower Jovicentric déclination). If so, the Southern limit of the beam is also determined. We named the first beam Crossing, occurring after the gap centered at about 200°C ML which dénotés a beam entry from the magnetic northern side, the EARLY beam northern the subséquent rotation number but, in order to simplify the situation, the early and late beam data are attributed to that rotation number in which the early beam entry occurs.

The northern and Southern beam limits are representing the magnetic dipole latitudes of the respective beam crossings. Performing this calculation during several rotations, we obtain aver ages and standard déviations for the beam limits. In general the Southern beam limit could not be determined with sufficient accuracy because the spacecraft most of the time did not leave the beam at its Southern side. For the northern side there are only a few cases where the space craft (especially VI before encounter) observed no beam northern exit during one rotation (no émission gap at 200°CML). If so, we hâve no exact information about the beam limit in this case. Our calculated average from the northern beam limits for several rotations is therefore less than the true average. By assuming a gaussian distribution of the calculated beam limits from each rotation around the true average, we are able to correct our calculated average to the true one. The same holds for the standard déviation. The détermination of the beam limits was performed for three typical hectometer frequencies f\ = 1326 kHz, fi = 942 kHz, fs = 558 kHz.

In the second method we détermine a System III longitude range which includes a certain probability of émission by regarding a CML diagram of the relative occurrence probability of HOM (Figures A.2a,A.2b). The beam limits are then simply the respective Jovimagnetic that beam width, calculated by our first method, if the occurrence probability peak reaches 1.

In provided us with a high data rate. When considering the observations, we notice that the beaming dépends on the spacecraft Jupiter distance because of the increasing intensity with respect to a constant threshold. This distance effect was not corrected because the beam width would then be dépendent on the choice of the threshold normalized to any assumed distance.

Instead, as the intensity is not normalized, the beam width appears to be a function of radial distance due to the variation of the corresponding normalized threshold at 4.04 Rj. Throughout this investigation a détection threshold corresponding to a flux density of 5 • 10-2OWm'"2Hz-1 was used for observations at ail radial distances. Therefore only results taken from data at the same radial distance can be compared. We divided our basic data set into several "sections"

where each section represents a certain radial distance being centered on this section. For VI The standard déviations are found to be about 2°, somewhat lower for high frequencies and higher for low frequencies.

We can see a trend to higher northern beam Umits for both spacecraft when the spacecraft Jupiter distance and therefore also the normalized détection threshold decrease. In general, the early and late northern beam Umits show approximately the same values except for the V2 preencounter period at /=1326 kHz. We therefore conclude that the magnetic dipole equator is a good frame of reference for the beaming at hectometer wavelengths. By comparing VI and V2 results at the same radial distances before encounter, we find that the beam is thicker for V2 than for VI although we would expect the same beam width at the same distance for both spacecraft. That is obviously not the case and we conclude therefore that the beaming is not This local time efFect in the HOM beaming is also shown in Figures A.3 and A.4. We observe that the beam width changes dramatically when the spacecraft switched from the day-to the nightside. We are able to precisely State that the beam is a few degrees larger (extending to higher magnetic déclination) on the dayside than on the nightside. A similar efFect was found by Leblanc and Daigne (1985a) For the Jovian kilometric radiation.

The local time dependence can also be clearly seen when we compare VI data after encounter with V2 data before encounter at approximately the same distance (756 Rj), when simultaneous observation was possible (about Rot. number 2050). In this case we took 20 rotations centered on Rot. number 2050 For VI and V2, respectively. The résulta are also plotted in Figures A.3 Comparing V2 results beFore encounter with those obtained after encounter, we see the larger beam in the preencounter data as expected. For the VI data the beam after encounter is also narrower than that for V2 before encounter although the local time dependence is less striking in this case. In general the average northern beam limit is about 10°magnetic latitude on the dayside and about 8°on the nightside.

General aspects of the HOM beaming and degree of corrélation from simultaneous observations by VI and V2. [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] determined the location of the sheet where the HOM beam is centered and found about 3°northern magnetic latitude based on the Bm{n equator and about 2°when they took the magnetic dipole equator as frame of reference. This sheet which is conical can be visualized as a locus for the instantaneous beam axis when observed over several rotations.

We are also able to détermine the location of this conical sheet in particular when VI reached magnetic Southern déclinations where also the Southern beam limits could be seen. Assuming that this sheet is exactly between the northern and Southern limits, we took the averages of the beam limits when Southern beam information is also présent. From these we find that the location of this sheet which dénotés the beam center (beam axis) is situated at about 1.6°Jovimagnetic (dipole) latitude. This would be in excellent agreement with the resuit of [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] if they had also assumed the magnetic dipole equator as frame of reference. From our calculations we obtained by assuming that the beam axis is at 1.6°magnetic latitude a total beam width of about 20°when the observations are made close to Jupiter (which corresponds to a very low normalized (to earth, 4.04 AU) threshold of 3.4 • 10-23Wm"2Hz"1 at « 210Rj) and about 10°farther away (détection threshold of 10'21Wm"2Hz-1 at « llOOAEj, (Figures A.3 and A.4). The latter resuit is comparable to the results of [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF].

We can obtain more information on the beam widths by computing the degree of corrélation of simultaneous observations from the two spacecraft. [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] hâve already investigated the corrélation of simultaneous observations given by VI and V2 as a function of the angular séparation. They found decreasing corrélation when the spacecraft latitude séparation increased and, with a least squares fit, they predict 100 % decorrelation for a latitude séparation First of ail we try to obtain the beam width for which 100 % decorrelation for a latitude angular séparation of 4.7°occurs as found by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF].

We take a to be 0°, which means that the magnetic latitude of the beam axis (3°) equals the Jovicentric decUnation of VI before encounter (« 3°). We further include the small varying local time différence of « 2°between VI and V2 during the respective observations. To fit the observations best (full circles in In the histograms of the relative occurrence probabiUty of émission as a function of CML in Figure 1 of [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF], we notice that the two émission peaks observed by a single spacecraft do not hâve the same height, notably for the IMP 6 and RAE 1 satellites. This effect cannot be explained, neither by a latitudinal nor by a direct local time effect. If the HOM émission beam does not dépend on System III longitude, one would expect that the observed émission peaks should hâve the same height in the histograms because the spacecraft crosses the beam twice during one Jovian rotation. In the case of low Jovian magnetic decUnation of the spacecraft, we expect only one peak which should be centered at 202°CML. The différence of the peak height in the observations could be explained by assuming that the émission is at least weakly enhanced at given System III longitude and is not emitted uniformly. This effect was less clear in the data of the Voyager spacecraft, so this possible anisotropy of the source does not influence our beaming calculations.

To summarize our beaming results, we hâve verified the strong HOM beaming found by Alexan- who showed that the antenna physical plane of the two crossed équivalent dipoles does not coincide with the antenna electric plane at frequencies below 7 MHz. The orientation of the electric plane was first studied by Leblanc and Daigne (1985a,b) by analyzing the polarization reversais of the Jovian bKOM. The radiation appeared unpolarized when the angle 9 between the source direction and the normal to the monopoles was 9C = 70°± 3°, and the azimuth of the source relative to the physical monopoles <j>c = 20°(see Figure 1 of [START_REF] Leblanc | OverView of the Uranian radio émission: Polarization and constraints on source locations[END_REF].

TOTAL JOVICENTRIC ANGULAR SEPARATION -i-i-i-«-|-i-*-i-i-|-i-i-i i 2* y y JOVIGRAPHIC LATITUDE SEPARATION
Only when 0 < 70°, was the apparent polarization correct; for 6 > 70°it was opposite to the true polarization. For arbitrary 4> the antenna electric plane was determined by [START_REF] Lecacheux | Polarization and localization of the Uranian Radio Sources[END_REF]. In order to détermine the true polarization of the incoming waves, we must therefore take into account the variation of the angles 9 and <f> during the VI and V2 encounters.

Voyager 1 date 790118

Rotation 1808 1809 nated by left-hand polarization (narrower émission gap near 20°CML). This also holds for V2

observations but the effect is less clear. In general the beam contains the two polarizations with a tendency toward RH-polarization at its northern limit and to LH-polarization at its Southern limit (see Figure A.9, bottom panel). We further found that the polarization pattern for lower frequencies < 600 kHz becomes different from that at higher frequencies and sometimes even appears to be reversed. A more intensive study on this topic has been made by Ortega-Molina and Lecacheux (1990b).

A.3 HOM source extension in altitude

In this section we will estimate the hectometer source extension in altitude from the HOM lowfrequency limit. The high-frequency limit is not well known but it is generally accepted that the HOM high-frequency limit is about 3 MHz and may be as high as 7 MHz [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. It has been suggested that the HOM émission is the low-frequency limit of non-Io DAM [START_REF] Lecacheux | Some spectral characteristics of the hectometric Jovian émission[END_REF][START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF] although there are reasons for treating HOM separately; on one hand, HOM has a distinct spectral peak near 1 MHz [START_REF] Brown | Spectral behaviour of Jupiter near 1 MHz[END_REF], and on the other hand the occurrence of the émission as a function of System EH longitude differs from that of the non-Io DAM.

To find the HOM source extension we determined the low-frequency limit of HOM from the P RA data for each Jupiter rotation in 1979 for VI and V2, respectively. Ln general, the HOM lowfrequency limit is within the KOM frequency range, although we did not hâve any difficulties in On the other hand, on this point, we are in particular interested down to which frequency HOM can be active. In a given time interval, VI and V2 results do not show the same low-frequency limit but in general the same overall fluctuations.

Assuming that the radiation is emitted in the fast extraordinary (R-X) mode, the source région near the right-hand cutolf frequency at /=40 kHz extends to altitudes higher than 6 Rj (see e.g. a R-X cutoff isocontour plot as given by [START_REF] Green | Ray tracing of Jovian kilometric radiation[END_REF], whereas the source of the high HOM frequency limit must be situated at about 2 Rj from the center of the planet.

We further investigated the corrélation between HOM low-frequency limits simultaneously ob served by both spacecraft. Brackets indicate the respective data in Figure A.11. The first pair of brackets delineate a preencounter period for both spacecraft. We found for this first period a higher corrélation than for the second period which includes preencounter data for V2 and postencounter data for VI (second pair of brackets). The data trend due to the aforementioned distance effect was eliminated before correlating the data sériés. The low-frequency limits measured by V2 on the dayside are therefore not as strongly correlated with the VI low-frequency limits on the nightside. This supports a local time dependence for the low-frequency limit of hectometric émission, although the effect is not dramatic in this case.

A.4 Solar wind control of the HOM émission

In section A.2 we showed that the beaming is dépendent on the observer's distance to Jupiter. We eliminated the dependence on radial distance by comparing results obtained from observations at the same distance and we observed additional fluctuations which cannot be due to a dependence on distance. We will see in this part that these fluctuations are mainly due to solar activity.

As already mentioned, a significant corrélation between HOM energy and solar wind parameters, especially the solar wind density, was first etablished by [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF]. [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF] additionally found a corrélation between HOM energy and both, the solar wind pressure (highly influenced by the density) and the interplanetary magnetic field. They used linear cross corrélation and the method of superposed epochs and the results are normalized by expressing the degree of corrélation in terms of modified standard error (for the superposed epochs).

In this study we hâve correlated the solar wind parameters density and velocity (10 hr averages)

with the HOM low-frequency limit, and the early and late northern beam limits (Jupiter rota tion averages). The two northern beam limits (early and late) were averaged and the obtained beam limit is taken for the analysis. The solar wind data for VI were investigated from January wind data sériés and shifted one with respect to the other, if necessary. We hâve also corrected the artificial data trends due to the observations at different spacecraft-Jupiter distances in the HOM output parameters (low-frequency limit and northern beam limit).

Concerning the statistical significance of the corrélations we used a different method for the détermination as done by [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF]. Our method, which is described by [START_REF] Spiegel | Statistics, Schaum's outline[END_REF], represents a test for the significance of the corrélation coefficient based on the Student's t-distribution. This distribution replaces the gaussian distribution if the number of data points v of the correlated time sériés is not infinité. If v > 30, the différence between the two distributions is quite small, however. The corrélation is significant, when the following équation is true for a given corrélation coefficient r:

|r| • yjv -2 y/l -r2 (A.l)
The quantity t is given in tables (see e.g. [START_REF] Spiegel | Statistics, Schaum's outline[END_REF]. For high v the 95 % confidence level of significance is reached when Equation (A.l) is true for t=1.65, and the 99 % confidence level for t=2.33.

This test is valid for significance for only one corrélation coefficient between two time sériés with lag time 0. We are therefore forced to modify the test somewhat to obtain the significance level for a few corrélation coefficients centered at lag time 0. Since Desch and [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF] found that the HOM émission output does not lag very much the solar wind input, whenever, we only accept in our analysis corrélation coefficients of lag times from -2 to +3 data points (= Jovian rotations). This leads to 6 corrélation coefficients r(-2),• •r(3), and the highest (in case of positive corrélation), or the lowest one (in case of négative corrélation) is taken for the test (Equation A.l). The négative lag times which dénoté acausality (because in this cases the HOM output is seen earlier than the solar wind input) is included because of the uncertainty of solar wind propagation from the spacecraft to Jupiter. Because of the use of 6 coefficients we hâve to modify the quantity t to 2.33 for the 95 % confidence level and to 2.93 for the 99 % confidence level.

To test our method, we hâve correlated solar wind density (hereafter SWD) and HOM energy for VI and V2 observations and we confirm significant corrélation for V2 observations (higher than the 99 % confidence level, hereafter denoted as C99) as already reported by [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. For VI the corrélation is not as strong but higher than the 95 % confidence level (C95).

The solar wind density, the HOM energy, and the HOM low-frequency limit are given for VI in

A.4.1 Results

Table A.2 summarizes ail corrélations performed for VI and V2 data and their degree of signif icance. The corrélation between the solar wind density increases and the HOM low-frequency limit (LFL) is shown to be only poor (hereafter denoted as Cpoor) for VI data, whereas for V2

the corrélation reaches C99.

The solar wind density correlates well with the northern beam limit (for VI: C99, for V2: C95).

Care is needed correctly to interpret these results especially for VI because as in this case many points (« 30%) were interpolated in the original data. This may artificially produce higher corrélation. For V2 this problem does not occur because of the sufficiently high Jovicentric déclination of the spacecraft (see also section A.2).

The strong corrélation between the solar wind density and HOM émission led us to correlate also the HOM energy with the other HOM parameters and we found that some corrélations become even stronger. In detail, we found that the HOM energy is correlated extremely well (>> C99)

with the HOM low-frequency limit for the two spacecraft. This means that the frequency range increases when the intensity increases. Also significant corrélation was found for the beam limit for V2, but only poor corrélation for VI. For the calculations of V2 data we did not include ail data from January 5 -June 30 because many interpolated values (« 50%) occur at the first 4 months for the beam limit. Therefore only data from April 28 to June 30 were considered in the analysis. As already mentioned the V2 data are more reliable than VI concerning the beam At last no apparent corrélation is seen between the solar wind speed and any of the HOM émission parameters. Concerning the HOM energy, this was also concluded by [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF].

The main conclusion of our analysis is that the solar wind density does not only influence the HOM energy, but also the HOM low-frequency limit and at least partially the hectometer beaming* The solar wind pressure gives similar results due to the proportionally higher fluctuations of the density compared to the velocity. We also demonstrated that the HOM energy influences even stronger the HOM émission geometry, in particular the HOM low-frequency limit but, this is no causal relationship since it is in fact the solar wind which influences the HOM energy and the other HOM parameters. We hâve seen that the solar wind density and in particular the HOM energy influence the other HOM parameters. Therefore we reanalyzed the hectometer beaming for the respective spacecraft by comparing them with solar wind activity during the observations. In general we found there a higher HOM beam width for V2 compared to VI (see Figures A.3 and A.4) for dayside observations. The différence between the VI and V2 beam northern excursions was especially striking (about 2°) at distances of 630 Rj and 210 Rj. Figure A.14 compares VI and V2 solar wind density and HOM energy measured at about 210 Rj on the dayside. We note the higher solar wind density and the higher HOM energy for V2 observations. Similar results were found for observations at distances of 630 Rj on the dayside where also a thicker beam was seen from V2. No apparent différence in the solar wind density could be seen at 420-ftj, however, where we observed approximately the same beam width for the two spacecraft (Figures A.3 and A.4).

A.5 Conclusion

In this paper we présent further support for strong HOM beaming with the beam axis situated to the north of the magnetic dipole equator (1.6°). On the dayside the émission beam width was found to be about 10°-20°for the normalized détection thresholds 10~21Wm"2Hz~1 -3.4-10-23

Wm"2Hz-1, respectively. On the nightside the beam was found to be narrower (by about 4° compared to the dayside). We further calculated the theoretical corrélation of simultaneous observations of the VI and V2 spacecraft and found agreement with the observations. This resuit is compatible with the beam half-width of 5°and beam axis of 3°magnetic northern latitude found by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF]. For DAM émission, [START_REF] Warwick | Dynamic spectra of Jupiter's decametric émission[END_REF] derived from ground based observations an émission beam half angle of 9°, whereas Poquerusse and [START_REF] Poquerus8e | First direct measurement of the beaming of Jupiter's deca metric radiation[END_REF] concluded from combined spacecraft and ground based observations a beaming of the Io controlled DAM of less than 9°. As found by Leblanc and Daigne (1985a,b), bKOM is emitted above 11°northern and Southern magnetic latitude, thicker on the dayside and thinner on the nightside.

We analyzed PRA data at three frequencies and mostly found the maximum beam width between 942 kHz and 1326 kHz which is fully compatible with the results of [START_REF] Brown | Spectral behaviour of Jupiter near 1 MHz[END_REF], who found the spectral peak of hectometric émission at about 1 MHz.

The polarization measurements of the HOM data indicate that right-hand polarization is associated with the northern hemisphere and left-hand polarization with the Southern one, without reversai from dayside to nightside observations.

Analyzing the HOM low-frequency limit in the PRA data, we see that HOM is sometimes emitted at frequencies as low as 40 kHz. The observations are strongly influenced by the increase of relative intensity when the spacecraft-Jupiter distance decreases. Nevertheless, a hectometer source extension from about 2 to 6 or 7 Rj is deduced with the assumption that the émission is emitted in the R-X mode near the R-X cutoff frequency. The strong influence of HOM by the solar wind and the location of the low-frequency sources farther away than 6 Rj from the planet give strong evidence that the sources of hectometric émission are located along auroral field lines on each hemisphere as already suggested by [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF].

The relationship between solar wind activity and HOM émission intensity was first derived by [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF], [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF], and by [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. In both of the more recent studies, corrélation was found between the solar wind parameters such as density and/or pressure and the HOM intensity. We extended these calculations for the other HOM parameters such as the HOM low-frequency limit and the beaming. The solar wind density and/or pressure also influences the HOM low-frequency limit and the HOM beaming. The solar wind speed does not influence any HOM parameter.

The HOM energy correlates even more strongly with the HOM low-frequency limit and the beaming than does the solar wind. Interpretating these results, we conclude that the solar wind density and/or pressure exerts an influence not only on the HOM intensity but also on the HOM source extension and beaming. The arrivai of a high density solar wind stream at Jupiter will therefore enhance the HOM energy output, activate low-frequency HOM sources located at 6-7

Rj on auroral field lines, and widen the HOM beam to higher magnetic northern latitudes and possibly to higher magnetic Southern latitudes.

A number of results on the phenomenology of the HOM émission hâve been given in this paper and theoretical considérations concerning the exact source location should assume a source which emits radiation according to these characteristics. Ray-tracing calculations are under way in order to clearify this topic.

B.l Introduction

The radio spectrum of Jupiter which is known as the most powerful emitter in our solar Sys tem consists of four distinct components: the decametric components (Io DAM and non-Io DAM); the kilometric émission (KOM) which contains a broadband (bKOM) and a narrowband (nKOM) component; and an émission at hectometric wavelengths, the so-called Jovian hectometric radiation (HOM). Since the accidentai discovery of DAM by [START_REF] Burke | Observations of a variable radio source associated with the planet Jupiter[END_REF] from ground-based observations, the DAM component has been investigated for more than three A solar wind control of HOM was established by [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF] and [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF]. Further results were more recently given by [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF] found that the sector structure of the interplanetary magnetic field highly Controls the long-term intensity fluctuations at hectometer wavelengths. [START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF] derived a significant positive corrélation between the solar wind plasma density and the HOM émission output by using a cross-correlation analysis. [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF] furthermore showed that the HOM activity is correlated to the non-Io DAM activity, but not to the Io DAM, suggesting that the HOM and non-Io DAM are two components of the same radio émission. The study of [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF] exhibits that the higher energy HOM is in corrélation with the solar wind density, pressure, and the interplanetary magnetic field magnitude.

In a recent study, [START_REF] Ladreiter | Jovian hectometric radiation -Beaming, polarization, source extension, and solar wind control[END_REF] with the Southern one. These results axe consistent with an émission excited in the right-hand extraordinary (R-X) mode from both hemispheres. The observed polarization reversai from dayside to nightside is due to the change of the antenna geometry with respect to the spacecraft trajectory and the position of the radio sources. [START_REF] Lecacheux | Ray tracing in the Io plasma torus: Application to the PRA observations during Voyager l's closest approach[END_REF] has investigated the location of radio sources at 300 kHz using a ray-tracing technique. The obtained source locations for both the ordinary and the extraordinary mode are situated in the Southern hemisphere at the Jovimagnetic cartesian coordinates X = 5.0 -5.2 Rj and Y « -2.2 Rj. However, it is difficult to find a physical génération mechanism which is able to émit radiation from that spécifie point. Moreover, no distinct source location has been given

for / ^300 kHz. In the absence of a definitive source location for the hectometric radiation, further work has to be done to find its radio-emitting régions, and this paper can be considered as a first step in this respect.

The ray-tracing technique is a powerful tool to locate the radio sources, but it is important to point out that there exists no unique solution for the source régions. Therefore, it is necessary to introduce a distinct génération mechanism at the source and to take into account the characteristics of the émission.

Most of the ray-tracing work has been done for the earth and the Jovian magnetosphere in order to find the sources of terrestrial kilometric radiation (TKR) and of the Jovian radio émis sions. For the eaxth, the first ray-tracing of TKR was done by [START_REF] Jones | Propagation characteristics of electromagnetic waves in the mag netosphere[END_REF] using

the assumption that TKR propagates in the ordinary (L-O) wave mode. The ray-tracing study performed by [START_REF] Green | The angular distribution of auroral kilometric radiation[END_REF], results in an R-X émission mode for TKR. We notice that at that time, no direct satellite measurements were available. Now it is established by space craft measurements that the auroral radio émissions from the planets eaxth, Jupiter, Satura, and Uranus axe generated in the extraordinary (R-X) mode. [START_REF] Hashimoto | A réconciliation of propagation modes of auroral kilometric radiation[END_REF] presented the first three-dimensional ray-tracing based on the Cyclotron Maser Instability theory (CMI) [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] which is the relevant génération mechanism for the auroral radio émissions. [START_REF] Hashimoto | A réconciliation of propagation modes of auroral kilometric radiation[END_REF] traced L-0 and R-X waves with initial wave normal angles from 60°to 90°w ith respect to the magnetic field vector. He pointed out that it is the combination of L-0 and R-X mode waves that describe the observations of the angulax extent and the prédominance of the R-X mode of TKR.

For the Jovian decametric radiation, the first three-dimensional ray-tracing was done by [START_REF] Hashimoto | A theory of the Io phase asymmetry of the Jovian decametric radiation[END_REF]. Their calculations closely match the observations of DAM activity, and they confirm that the decametric radiation sources may well be described by hollow émission cônes. A very comprehensive study on the Jovian decametric arcs was performed by [START_REF] Menietti | Jovian decametric arcs: An estimate of the required wave normal angles from three-dimensional ray tracing[END_REF]. They ray traced DAM émission and varied the propagation angle at the source until the observations were fitted. They concluded that the initial wave normal angle is a function of the émission frequency (also suggested by [START_REF] Goldstein | The formation of arcs in the dynamic spectra of Jovian decameter bursts[END_REF] and found this angle to be « 80°at 10 MHz (the vertex frequency of the arc). This angle decreases to « 70°at the high (30 MHz) and low-frequency (2 MHz) extensions of an arc. Electron ener-gies in the order of 10 keV are required to match the proposed wave normal angles. Electrons with energies of that order of magnitude are assumed to precipitate in the Jovian auroral région according to a study of [START_REF] Horanyi | The précipitation of energetic heavy ions into the upper atmosphère of Jupiter[END_REF].

For the Jovian kilometric radiation, ray-tracing was performed by [START_REF] Green | Ray tracing of Jovian kilometric radiation[END_REF] by assuming that KOM is radiated in the L-0 mode from Io torus field lines near the planet. They were able to predict an observed shadow zone where no émission can be detected because of the Io plasma torus. Since Leblanc and Daigne (1985a,b) reanalyzed the polarization measurements and established that the correct sense of polarization of KOM is right-handed, the results of [START_REF] Green | Ray tracing of Jovian kilometric radiation[END_REF] hâve to be reinterpreted. Alternative studies by [START_REF] Jones | LatitudinaJ beaming of planetary radio émissions[END_REF][START_REF] Jones | Radio wave émission from the Io torus[END_REF][START_REF] Jones | Io plasma torus and the source of Jovian kilometric radiation (bKOM)[END_REF] and Leblanc and Daigne (1985a,b) locate the sources of the Jovian kilometric radiation at the Io torus by suggesting a Z to O mode conversion mechanism. In that approach, the beaming is the resuit of the radiation mechanism itself.

The purpose of this paper is to détermine the source location of the HOM by using a raytracing technique. To consider only a few possible source locations, we hâve assumed that the génération mechanism is the CMI, and hâve introduced the characteristics of the émission. These characteristics are summarized in section B.2. We hâve also considered the observations during the Voyager 1 (VI) closest approach which are relevant to our study. In section B.3 we hâve developed a simple geometrical model and assumed that an émission of hollow cônes should fulfill the observation of a beamed émission. It will be demonstrated that magnetic field lines linked to the Io torus can be eliminated as possible sources for HOM. In section B.4 we introduce our ray-tracing calculations, the rays being traced from the point of observation back to their sources near Jupiter. We will show that the Io torus plays a crucial rôle for the propagation and refraction of waves at hectometric wavelengths. This leads finally to the détermination of the HOM radio-emitting régions. The results are discussed in the context of the other Jovian radio components, in particular the non-Io DAM and KOM (section B.5).

B.2 Observations

Shortly after the discovery of the low-frequency spectrum of Jovian radio émission by the Planetary Radio Astronomy (PRA) experiment aboard Voyager 1 and 2, the HOM émission was thoroughly explored for the first time. The PRA experiment [START_REF] Warwick | Planetary radio astronomy experiment for Voyager missions[END_REF] consists of a radio receiver that steps in frequency from 1.2 kHz up to 40 MHz and an orthogonal pair of crossed monopoles which allow the sense of polarization to be determined. The instrument is operative in two distinct frequency bands; the low-frequency band contains 70 channels separated by 19.2 kHz with a bandwidth of 1 kHz, respectively, from 1.2 to 1326 kHz. The most striking feature in the low-frequency band is the appearance of the HOM and KOM émissions.

The high-frequency band extends from 1.2 to 40 MHz where HOM may be observed at the lowest frequencies, and DAM from about 5 to 40 MHz. DAM mostly occurs in the form of nested families of arcs on a frequency-time diagram whereas HOM generally does not exhibit an arclike structure. However, some drifting features in the HOM frequency range hâve been interpreted

as the lower legs of arcs that hâve their vertices in the DAM range [START_REF] Boischot | Radio Jupiter after Voyager: An overview of the Planetary Radio Astronomy observations[END_REF]. [START_REF] Carr | Phenomenology of magnetospheric radio émis sions[END_REF] pointed out that DAM émission is sometimes entering frequencies below 2 MHz.

Then, the HOM high-frequency limit can no longer be distinguished from the DAM. The purpose of this study is actually to know if HOM is related to DAM, and the knowledge of HOM location is a first step in this respect. In our investigation we axe concerned with frequencies below 1

MHz where the major part of HOM is observed. The results of several studies concerning the HOM axe already mentioned in the introduction and can be summaxized as follows:

1. The hectometer émission can be described in terms of a narrow, curved sheet at a fixed magnetic latitude (centered at about 2°northwaxd the magnetic dipole equator) into which the émission is beamed to escape Jupiter. The thickness of this sheet is reported to be about 10°, but may reach over 20°because of a higher détection sensitivity neax the encounter. Moreover, the émission dépends on local time. The fact that HOM is strongly beamed in latitude plays a key rôle in our further analysis to search for HOM source locations.

2. The low-frequency limit of HOM is found to be of the order of 40 kHz. No exact détermi nation about the high-frequency limit of HOM has been reported so fax, but it is generally accepted that this limit is about 3 MHz and may sometimes reach 7 MHz. Following a R-X cutoff contour plot (see e.g. [START_REF] Green | Ray tracing of Jovian kilometric radiation[END_REF], it was concluded in Paper 1 that the HOM source extension in altitude is from 2 to about 7 Rj (from Jupiter's center)

when considering the high-and low-frequency limits of HOM.

3. The polaxization pattern of HOM is more complex than that of the DAM or KOM. Nevertheless it is now established that the polaxization is predominantly right-handed when associated with observations in the northern hemisphere and therefore it corresponds to the R-X wave propagation mode.

4. The HOM is strongly correlated with the solar wind. The solax wind density and/or ram pressure influence the HOM energy, and the sector structure of the interplanetaxy magnetic field triggers this corrélation. The density and/or ram pressure also influence the HOM beaming and the low-frequency limit. Enhanced solar wind activity produces a higher HOM energy output, broadens the HOM beam, and activâtes low-frequency HOM sources at large distances from the planet. It has been generally found that the solax wind speed does not influence any HOM output paxameter.

5. The occurrences of the hectometer and the kilometer émissions axe different when ordered in terms of System III (1965) longitude (CML). Although the frequency range of the two émissions may sometimes be overlapped at low HOM frequencies (/ < 400 kHz), the broadband kilometric radiation (bKOM) occurs axound 200°CML, whereas HOM is situated axound 0°CML. This is explained by a different latitudinal beaming of the bKOM compaxed to HOM (for the latitudinal beaming of bKOM, see Leblanc and Daigne, 1985a).

6. When compaxing the hectometer émission with the higher frequency non-Io DAM, no striking change is visible to distinguish one from the other. The occurrence in terms of CML of the radiation changes slightly when switching from the non-Io DAM to the HOM frequencies (see Alexander et al., 1981, Figure 6). On the other hand the occurrence of the HOM at the lowest frequencies generally exhibits a smaller extension in System III longitude than at the higher frequencies (see Paper 1, Figure 10). 8. By the inspection of Voyager 1 observations at Jupiter's closest approach (CA), we notice an absence of HOM (Figure B.l), although the spacecraft was near the magnetic équa torial plane. A strong HOM émission would be expected there, however, because of the latitudinal beaming of HOM [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF]; Paper 1). Instead, a bursty émission is observed which has been interpreted as upper hybrid résonance noise [START_REF] Warwick | Voyager 1 planetary radio astronomy observations near Jupiter[END_REF] and n + 1/2 gyroharmonic waves [START_REF] Birmingham | Obser vations of électron gyroharmonic waves in the structure of the Io torus[END_REF]. This absence of HOM can not only be due to wave refraction through the Io torus since the high-frequency part of the HOM is affected, too. The HOM émission pattern near the closest approach is therefore assumed to be a conséquence of a spécifie source location.

Ail these characteristics must be taken into account for the détermination of the source location.

It is the purpose of the subséquent sections to eliminate step by step locations which cannot apply for those requirements.

B.3 HOM source location: A geometrical approach

In this section we présent a geometrical approach to hâve a first indication about the HOM source locations. Ail effects of ray réfraction axe neglected which correspond to a complété absence of the Io plasma torus. Furthermore, the wave refraction at the source which is thought to be small [START_REF] Hashimoto | A theory of the Io phase asymmetry of the Jovian decametric radiation[END_REF]) is also neglected.

Let us assume that the radiation escapes from the planet in the form of thin hollow cônes distributed at ail longitudes in the northern and Southern hemispheres. The sources are thought to be the apexes of these cônes located in altitudes where the wave frequency is somewhat higher but nearly equal to the local gyrofrequency. In a first attempt, we will search for field lines labeled with the dipole shell parameter L on which the sources may be located to produce radiation along the magnetic équatorial plane. Thus, we will analyze the émission cône half angle 80 as a joint function of the L parameter of the source field line and the wave frequency / (which is taken to equal the gyrofrequency fc) in the Jovian dipole field. The angle between the direction of the wave normal (parallel to the magnetic équatorial pleine) and the direction of the magnetic field vector at the source (Figure B.2) is defined to be 0O (later on, the cône half angle will be generally labeled as 8). Only sources on field lines which exhibit a sufficiently high cône half angle 80 for ail frequencies can be considered as possible source locations. On the other hand, HOM was detected within a sheet with a thickness of about 20°centered 2°d egrees northward of the magnetic équatorial plane [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF]Paper 1). This implies that the radiation is propagating in a small range of directions nearly parallel to the magnetic équatorial plane. As we will show in this section, only émission cônes which hâve one edge directed nearly parallel to the magnetic equatoral plane in the magnetic meridian plane provide an émission maximum there as required for the HOM beaming model.

For a given wave frequency / (which is assumed to be equal to the local gyrofrequency fc)

corresponding to a given altitude on a field line labeled L, the initial wave propagation angle 80 is a function of the shell parameter L and the frequency / when we introduce a dipole field model. In a dipole field the cône half angle 0o between the local magnetic field vector and L appear as parameter lines in the f-0o plot. For X=6 which dénotés a field line in the Io plasma torus, 90 is less than 30°at /=1000 kHz and is approximately equal to 0°at /=300 kHz. This is inconsistent with the large cône half angles required by the CMI mechanism when the ratio /p//c is very small, which is the case in the Jovian magnetosphere at distances larger than 3 Rj (except near the Io torus). We therefore conclude that a hectometer source in the Io plasma torus is not compatible with an émission in hollow cône beams. Furthermore, the torus field lines cannot provide source régions with cyclotron frequencies down to 40 kHz. Since fc < fRX, this holds also for the R-X cutoff frequency fax-Instead, magnetic field lines with a high shell parameter (L > 20) appear to be favoured candidates in the hollow cône émission model. First, these field lines exhibit larger cône half angles 90, about 50°-70°from 400 to 1000 kHz. Second, for / > 400 kHz, 90 is only a small varying function of / for field lines with high-X parameters. Third, waves with frequencies as low as 40 kHz may be excited on these field lines.

One important resuit of this preliminary approach is that field lines L < 10 must be excluded as the sources of HOM if we taie into account the lowest frequencies (40 kHz) reached by HOM. This is shown in Figure B.3 where 90 becomes « 0°for /=40 kHz and X=10. For the lowest HOM frequencies,(/ < 400 kHz), 9Q reaches very low values even for field lines with higher L.

Therefore we conclude that the refractive effects near the Io torus cannot be neglected for the lower HOM frequencies.

B.3.1 Simulation of the HOM latitudinal beaming

We suppose that the intensity of the radiation is distributed uniformly along the sheet of the hollow cônes but is distributed as an error function with a characteristic half-width a perpendicular to this sheet. This sheet half-width a of the émission cône was derived to be very small (< 1°) ( [START_REF] Queau | The maser synchrotron instability in an inhomogeneous medium: Application to the génération of the auroral kilometric radiation[END_REF]. Let us consider ail of the émission cônes distributed uniformly on each hemisphere. Then we can simplify the situation by considering projections onto a celestial sphere surrounding Jupiter. A given event is represented by a point on this sphere at the corresponding magnetic déclination and System III (CML) longitude. Since in our model the hollow émission cônes are distributed along ail longitudes at both hemispheres, the azimuthal dependence vanishes, and we can express the émission intensity produced by ail of these hollow cônes as a symmetric function of magnetic latitude 6. For a given frequency, this intensity function will further dépend on the L parameter of the magnetic field line on which the source is assumed, on the cône half angle 9 and also on the characteristic cône half-width a. with L =40, 20, and 6. The émission hollow cônes are assumed to be distributed uniformly in longitude on both hemispheres at altitudes where fc = /=1000 kHz (calculated from the Jovian dipole). For one set of conditions (characteristic half-width of the émission cône a = 1°, fe = f-1000 kHz, and 9 = 60°), a source at field lines with L=20 exhibits an intensity peak near the magnetic equator.

locations for HOM when hollow cône émission is assumed. In this model, the sources are restricted to field fines in high magnetic latitude in the polar région. On the contrary, we see that the exclusion of ail refractory effects does not lead to satisfying results conceraing an exact source location, and problems arise concerning the low cône half angle 9 for the lowest HOM frequencies. We therefore expect that the Io plasma torus highly influences the HOM émission, in particulai-in the lower frequencies. To confirm our findings and to locate the sources properly, a ray-tracing study including ail effects of refraction is required. This is performed in the subséquent section.

B.4

Ray-tracing of Jovian hectometric radiation

B.4.1 Concept of ray-tracing

In the previous section, we had an indication of the hectometer source field fines from a first approach. To find the location of these sources more accurately, we performed a ray-tracing studies hâve been published on this topic (e.g. Dusenbery and Lions, 1982;Le Queau et al., 1984a,b;Omidi and Gurnett, 1984;Omidi et al., 1984;[START_REF] Wu | Kinetic cyclotron and synchrotron maser instabilités: Radio émission processes by direct amplification of radiation[END_REF][START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF].

Including assumptions about the génération mechanism, the input required for our ray-tracing calculation may be summarized as follows. The rays are traced from possible sources (labeled by the dipole shell parameter L) located at ///c = 1.05. For each source the propagation angle 6 with respect to the magnetic field is varied ajid we détermine the wave emergence angle above which the rays no longer travel within the HOM émission beam. According to the prédictions of the CMI and the polarization measurements of HOM, only the R-X mode is considered for ray-tracing. From this analysis, we expect to dérivé the parameter L on which the HOM sources axe located as a function of the cône half angle 9.

As already stated, we take ///c=1.05 to be valid at the sources in our analysis. However, we varied this value in order to see how low the ratio ///c can go without the rays suffering important refraction during the propagation in the vicinity of the source. We found that for ///c below 1.01-1.02, refractory effects near the source arise for rays with the largest emergence angles (« 90°). We can therefore extend the validity of our ray-tracing results which will be derived in the subséquent sections to ratios ///c > 1.01. Below this value, the ray paths near the source strongly dépend on ///c which is not accurately known.

B.4.4 Ray-tracing computation

The HOM spectrum is largely extended in its frequency range, and therefore we made calcu lations for the spécifie frequencies / = 40, 150, 300, 500, 800, and 1000 kHz. An example is shown in Figure B.5 where we hâve traced rays at /=150 kHz, which is near the lower end of the HOM frequency range. AU rays are released at CML=200°where the magnetic dipole meridian plane coincides with the Jovigraphic meridian plane. Generally, the ray paths divert a little in the azimuthal direction, but in this study we hâve only considered projections onto a meridian plane. Rays off the meridian plane are not taken into account but a three-dimensional treatment of the HOM émission cônes is in progress. For each source, the wave normal angle is chosen such that the wave is finally traveUng parallel to the magnetic équatorial plane. This Unked to cônes with a smaUer angle 9 (in order to émit radiation which becomes finaUy paraUel to the magnetic équatorial plane) than the sources situated at higher altitude field Unes.

We recaU that 90 is one possible value of the cône half angle to allow one edge of the émission cône to be directed paraUel to the magnetic equatoral plane. 90 has already been determined as f= 150 kHz / / fa source. = 1-05 Distance (Rj) Let us détermine now the maximum value 9 which will be denoted as Qcrit, above which the final ray direction falls out of the observed beaming near the magnetic equator. Observations near the encounter show that HOM may be visible up to magnetic northern latitudes of 10°-15°and possibly also at the same magnetic Southern latitudes. Thus the ray is considered to fall out of the HOM beam when its final direction deviates more than ±15°from the magnetic equator. ncluding the critical angle 0^,* which is deduced by allowing the rays to hâve a final direction deviating by only ±15°from the magnetic équatorial plane. When /=300 kHz, we dérivé for 9crit the values 75°(£=15) and 80°(£=22), and for /=500 kHz, the values 84°(£=15) and 88°(£=22). We conclude that the relation #cr,*(£) is not a dramatically varying function of the frequency. Moreover, the Io torus highly influences the angle 0^, and an absence of the torus would decrease 0^,* down to about 60°for /=300 kHz when £=15. Therefore we emphasize that the presence of Io plasma torus plays a crucial rôle for émission at hectometric wavelengths in the way that the émission is beamed in the direction of the magnetic equator. This happens predominantly for large 9 when we consider sources on field lines with high £. However, for source locations at field lines near the Io plasma torus, this is not the case (Figure B.7). /=300 and 500 kHz, respectively. At sufficiently high wave normal angles 0, the torus diffracts the waves away from the magnetic equator, so that the critical angle 0^becomes very low.

The required HOM beaming can only be obtained if we assume low cône half angles 0 of the order of 50°-60°. As will be discussed later, this requires unplausible high électron energies to generate waves with such low cône half angles when /p//c at the source is very low. here the magnetic latitude of the spacecraft is highest within one Jovian rotation. At 110°C

Regarding

ML which corresponds to 6 = 0°, no HOM émission at lower frequencies has been detected.

To give more detail on this important point, investigations including in particular PRA data near the Voyager encounters are in progress.

Regarding the polarization, a mixture of right-hand polarization (rays from the northern hemi sphere) and left-hand polarization (from the Southern hemisphere) is expected at distances beyond the shadow zones in The index N refers to sources in the northern hemisphere and S to sources in the Southern one.

We see that 0^* is a small varying function of the shell parameter L for £ > 15. For £ < 15, 9^decreases substantially with £. Moreover, for a given L, 0^* is somewhat higher for sources in the Southern hemisphere (except for /=40 kHz which is discussed below). This is explained by the fact that the Io torus does not lie exactly in the dipole équatorial plane. hemispherical asymmetry.

At /=40 kHz, the lowest observed frequency, the ray-tracing results show that 0^.,* is no longer a monotonie function of the shell parameter L: the radiation is beamed parallel to the magnetic équatorial plane for L > 20 and 0^,* < 90°but only for a rather limited range of 0. For L < 20, ail the rays propagate in the same direction for a large range of B and this direction is sometimes distinct from the HOM beaming. Contrary to the higher HOM frequencies, the substantial asymmetry between both hemispheres is preliminary due to plasma sheet currents which influence the magnetic field strength and consequently also the ray paths.

We hâve demonstrated that a final ray direction parallel to the magnetic équatorial plane can be achieved for both 6 « BQ and 0«0cri* which we hâve determined by ray-tracing in Figures B.6 and B.7. A priori we cannot décidé which of the two possibilités accounts for the real situation, but when considering the observations, we can draw conclusions which may favour 0*0cru over 0 « 0o.

If 0 were 0o for ail HOM frequencies, the Io torus would hâve no influence on the émission, and 0 would be very low at the lowest frequencies. This problem was already encountered in section is only a mild function of the assumed ratio ///c at the source which varied from 1.02 to 1.2 in their investigation. A cône half angle of 9 = 79°has already been suggested by [START_REF] Dulk | Apparent changes in the rotation rate of Jupiter[END_REF] to account for the Io related components of DAM. With his émission cône model, he could account in a rough way for the active Io phase régions (Io-A and Io-B source). [START_REF] Goldstein | Théories of radio émissions and plasma waves[END_REF] reported that DAM émission can be explained in terms of a thin conical sheet with an opening angle of 70°-90°. More recently, [START_REF] Bagenal | Io's Alfvén wave pattern and the Jovian decametric arcs[END_REF] investigated the Io DAM source geometry and found an opening angle of « 70 -72°to account for Io-A and Io-B observations. It is noteworthy that similar cône half angles are suggested for the auroral kilometric radiation (AKR) by Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF]. In their theoretical studies, the authors accounted for 9 to be of the order of 70°-80°for AKR. For Jovian HOM, the ratio fp/fc is very small at the source régions which supports the assumption of a large (nearly perpendicular) cône half angle (e.g. [START_REF] Wong | Electromagnetic cyclotronloss-cone instability associated with weakly relativistic électrons[END_REF].

It is, however, difficult to extrapolate these results to the HOM sources at a distance of several Jovian radii from the planet, but in the absence of direct measurements, we will consider similar cône half angles as already established for Jovian DAM and AKR in order to avoid the assumption of unplausible high électron energies in the case of a small 9. Thus for our further investigation, we will consider 6 > 70°in the absence of lower cône half angles for other radio components.

B.4.5 Détermination of HOM sources

As previously stated, the ray-tracing calculations were performed for CML=200°, although the PRA observations at HOM frequencies usually exhibit an émission gap near that longitude. It was derived by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] and in Paper 1 that this gap is exclusively a conséquence of the strong latitudinal beaming of HOM near the magnetic equator. On the other hand, it is not necessary to trace rays for ail System III longitudes for the following reason: for the distances where the hectometric radiation sources are located, the Jovian magnetic field exhibits a strong dipole character, and therefore no substantial azimuthal dependence in a Jovimagnetic coordinate System. We verified this by tracing a few rays as we did for the construction of Figure B.8 but from different System III longitudes. We noticed that the calculated angles 9^as a function of L for a given HOM frequency deviate at maximum only by 3°-4°from the values of 9crit reported in Figure B.8. This is the conséquence of the strong magnetic field asymmetry on Jupiter's surface which is weakened at larger distances from the planet. The Io torus is nearly symmetric with respect to the magnetic dipole equator, and therefore there exists only a small refraction effect dépendent on the azimuth. Consequently, we extend the validity of Figure B.8 out to ail system III longitudes without a significant error.

For our purpose, we hâve estimated the probable cône half angle 9 as between 70°and 90°(based on the information given for other auroral radio émissions). Regarding Figure B.8, the field line L=15 is roughly associated with 9> 70°and L=30 with 9^% > 90°. Thus, in so far as 9

is not better determined, we suggest that HOM sources are located at field Unes having a sheU parameter somewhere between L=15 and L=30. The HOM sources aire consequently determined to be distinct from Io torus field Unes and are therefore not linked to Io dépendent DAM sources via magnetic field Unes. From Figure B.8 we see that there is no dramatic dependence of the initial wave normal angle 9 on the émission frequency for the derived source locations.

Consequently, along a given field Une, the cône half angle does not change very much from the highest to the lowest hectometric frequencies. If L of the source field Unes were about 8-10, then the cône half angle would be a strong function of frequency and would decrease substantially for the lowest HOM frequencies.

B.4.6

Location of the footpoints of HOM source field lines After the détermination of the possible L parameters for the HOM source field lines, we projected the footpoints of these field lines onto the Jovian surface. We performed this for the field lines £=15 and £=30, and we expect the HOM sources on field lines with their footpoints lying between the £=15 and the £=30 ovals on the surface depending on the exact value of the cône half angle 0. Since the Jovian field is not an exact dipole, points with the same £ parameters (derived from the dipole) calculated at different altitudes (as done for the several frequencies in Figure B.8) generally do not lie on the same line of force. In any case, the déviation is not substantial, so we assume that points with the same £ values are situated approximately on the same line of force. The use of the centered dipole approximation is justified by noting that at distances of the Jovian HOM sources (farther than 3 Rj), the dipole is largely dominating Jupiter's magnetic field structure. Moreover, the calculation is most simplified when considering the £ shell parameter instead of the invariant latitude calculated from the O4 model. with £ parameters between 15 and 30. The solid line gives the tail field auroral oval for each hemisphere. They are calculated by [START_REF] Connerney | Modeling the Jovian current sheet and inner magnetosphere[END_REF], the outer oval with inclusion of the current sheet and the inner one without it. The tail field auroral zone can be visualized as the boundary of field lines connecting to the magnetic tail from polar régions. We notice that our determined HOM sources lie within these calculated tail field auroral zones which hâve direct access to particles precipitating from the tail. We consider this source location to be most compatible with both the observations and the génération mechanism. Since HOM exhibits a local time effect, not ail of the field lines along the auroral ovals shown in Figure B.9 may be active at the same time. We will discuss the conséquence of the obtained HOM source locations and applications to the phenomenology of the émission in the context of the other Jovian radiation sources.

B.5 Discussion

We derived the HOM source locations by performing a ray-tracing study and considering the émission characteristics in detail. The obtained source location dépends on the validity that HOM can be represented in an émission of hollow cônes distributed in longitude at the northern and Southern hemispheres. Furthermore, we assumed that the radiation is generated slightly above the local gyrofrequency in the extraordinary wave mode. Our ray-tracing investigation based on the observations of HOM strongly indicates that the HOM sources lie within the tail field aurora whose field lines connect the polar régions to the Jovian magnetic tail, at distances from 2 to 7 Rj from Jupiter's center. The exact source location in magnetic latitude is related

NORTH POLE SOUTH POLE CML 0°CML 0°.
. calculated without current shoot Figure B.9: Foot points of HOM source field Unes projected onto the Jovian surface (hatched area) and tail field auroral ovals (taken from [START_REF] Connerney | Modeling the Jovian current sheet and inner magnetosphere[END_REF] for the northern and Southern hemisphere, respectively. The outer auroral oval was calculated with the inclusion of the Jovian current sheet and the inner one without it. The HOM sources are located remarkably well within the space between these ovals.

to the assumed cône half angle 9. However, an HOM source at the tail field auroral région accounts for a large variety of the phenomenology observed so far. (1) The strong latitudinal beaming of the émission is caused by the wave réfraction at the Io plasma torus. In addition, to account properly for observations at / > 1 MHz, a peak électron density corresponding to a plasma frequency of 1 MHz is required in the torus.

(2) The extension of the HOM down to 40 kHz is accounted for with an initial wave normal angle somewhat lower than that for the higher HOM frequencies, but still 9 > 70°. In contrast, sources at (and near) Io torus field Unes could not provide émission at frequencies as low as 40 kHz.

(3) The location of the radio source in the tail field aurora may convincingly explain the solar wind control observed for the HOM émission. High energetic particles originating from the solar wind precipitate into the auroral zone and therefore directly influence the conditions of génération. (4) The absence of HOM émission for distances less than « 6 Rj is due to both the location of the sources at high altitude polar régions and the refraction of the radiation at the edges of the plasma torus. (5)

The émission is not influenced by Io as would be expected for a source in the tail field auroral zone.

The location of the other Jovian radio sources has already been treated by a large number of researchers, and it is well estabUshed that the Io DAM sources Ue along field Unes connecting the Io torus. Our findings argue therefore for distinct Io DAM and HOM sources which were also derived by [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF] from a différent line of reasoning. Concerning the non-Io DAM a definitive conclusion is less easy to draw. As the refractory eflfects of the Io torus gradually die away for frequencies higher than «2-3 MHz [START_REF] Lecacheux | Ray tracing in the Io plasma torus: Application to the PRA observations during Voyager l's closest approach[END_REF], one cannot daim that HOM varying cône half angle derived from the observations. In the case of 9 = 55°HOM could be interpreted to be the low-frequency extension of the non-Io DAM.

C.l Introduction

Since the Voyager 1 spacecraft approached Jupiter as near as 4.9 Jovian radii (AEj), the Planetary Radio Astronomy (PRA) receiver [START_REF] Warwick | Planetary radio astronomy experiment for Voyager missions[END_REF] was able to collect a rich variety of radiation phenomena, which had never before been seen. This data set provides the first opportunity to observe the Jovian radiation from inside the Io plasma torus. Besides the well known decametric radiation which has been observed from ground based stations for more than three décades now, the Voyager spacecraft discovered émission below 1 MHz, the Jovian kilometric radiation (KOM) and the higher frequency hectometric radiation (HOM). The hectometric component covers a large frequency range and may sometimes be active down to 40 kHz [START_REF] Boischot | Comparative study of the "Radio -Planets[END_REF][START_REF] Ladreiter | Jovian hectometric radiation -Beaming, polarization, source extension, and solar wind control[END_REF]). The high-frequency limit is not well-determined but certainly reaches up to 3 MHz (see e.g. [START_REF] Carr | Phenomenology of magnetospheric radio émis sions[END_REF], and it is suggested to be as high as 7

MHz [START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. Most of the studies of hectometric radiation are concentrated on the observations in the low band of the PRA receiver which scans 70 channels from 1326 kHz down to 1.2 kHz in steps of 19.2 kHz.

The latitudinal beaming of HOM was first established by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF]. They emphasized that HOM is strongly dépendent on the magnetic latitude of the spacecraft and that the radiation is sharply beamed within a thin sheet (thickness of 10°) near, but centered somewhat north (about 2°) the magnetic dipole équatorial plane. The periodic variations of HOM in terms of System III longitude are consequently due to the varying Jovimagnetic déclination of the ob server within one Jovian rotation. Statistical observations [START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF] confirmed this latitudinal beaming of HOM and additionally provided evidence for a local time dependence of the émission. Ladreiter and Leblanc (1989, hereafter Paper 1) re-examined the latitudinal beaming of HOM and found that the total beam width is between 10°and 20°, depending on the normalized détection threshold. Additionally, we showed that the HOM beam width is 4°n

arrower on the nightside than on the dayside.

The solar wind control of HOM was investigated by several authors [START_REF] Zarka | Low frequency Jovian émission and solar wind magnetic sector struc ture[END_REF][START_REF] Desch | Direct evidence for solar wind control of Jupiter's hectometerwavelength radio émission[END_REF][START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF][START_REF] Barrow | Solar wind control of Jupiter's hectometric radio émission[END_REF]. It has been shown that the HOM energy output dépends on the solar wind density, pressure, and the sector structure of the interplanetary magnetic field (IMF). However, [START_REF] Rabl | Solar wind dependence of the Jovian hectometric radio émission: Comparison between Voyager 1 and 2 observations[END_REF] demonstrate that the IMF sector transitions are not responsible for stimulating the HOM energy output. In Paper 1, we additionally found the low-frequency extension and the HOM beam width to be influenced by the solar wind. The solar wind control on HOM argues for sources located on open magnetospheric field fines rather than on closed ones.

The HOM component often exhibits a mixed, and sometimes time-varying polarization pattern.

Previous studies [START_REF] Kaiser | Voyager spacecraft radio observations of Jupiter: Initial cruise results[END_REF], Alexander et al., 1981;[START_REF] Boischot | Radio Jupiter after Voyager: An overview of the Planetary Radio Astronomy observations[END_REF] could not convincingly explain the rather complicated polarization behaviour of HOM. After the détermi nation of the electric antenna plane of the PRA experiment by Leblanc and Daigne (1985a) and the détermination of the polarization response of the antennas (Lecacheux and Ortega-Mofina, 1987;Ortega-Mofina and Lecacheux, 1990a), it has now been established that right-hand polar ization (RH) is mainly associated with the northern hemisphere, and left-hand (LH) polarization with the Southern hemisphere. Thus the polarization of HOM is consistent with émission in the extraordinary (R-X) mode (Paper 1, Ortega-Mofina and Lecacheux, 1990b).

A first step in finding the HOM radio emitting régions in the Jovian magnetosphere was made INTRODUCTION 103 by [START_REF] Lecacheux | Ray tracing in the Io plasma torus: Application to the PRA observations during Voyager l's closest approach[END_REF]. He performed a ray-tracing study in a meridian plane taking into account PRA-observations within the Io plasma torus. For /=300 kHz, he found a source in the Southern hemisphere located at L = 6 -7 Rj. The fact that this source is not located in a région where the wave frequency is clearly related to the plasma frequency or gyrofrequency makes the results not entirely convincing.

Very recently, Ladreiter and Leblanc (1990a, hereafter Paper 2) determined the source locations of the hectometric radiation via ray-tracing analysis (also in a magnetic meridian plane). In that work, they introduced the characteristics of the HOM as found by [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] and Paper 1. To put further constraints on the source locations, we considered the Cyclotron Maser Instability (CMI) [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] as the relevant génération mechanism based on the HOM polarization measurements. The results strongly suggest the tail field auroral zones to be favoured candidates for the sources of HOM. The sources cover a wide range in longitude in both hemispheres which is consistent with the beaming of HOM in magnetic latitude. The obtained HOM sources, which axe confined between L-15 and L-30 at radial distances where the wave frequency is slightly higher than the local gyrofrequency, also convincingly explain the solar wind control of HOM since the solar wind particles hâve direct access to the radio sources through the magnetic tail or the polar cusp.

The purpose of this study is to account for the HOM observations by assuming the source locations and émission characteristics as determined in Paper 2. In particular, we hâve taken advantage of the fact that Voyager 1 passed very close to the planet, and we noticed that during the period of its closest approach, HOM was not observed near the magnetic équatorial plane.

In turn, when the spacecraft was at larger distances (> 20Rj) from the planet, the émission occurred favourably at low magnetic latitudes. A fully three-dimensional investigation has been performed in order to model the HOM observations and to make detailed comparisons with the observed pattern.

Our analysis is similar to that already performed by [START_REF] Gulkis | The main source of radio émission from the magnetosphere of Uranus[END_REF] in the case of Uranus. These authors also modeled Uranian P RA observations also by inferring initial source parameters. In the case of Jupiter, the procedure is more difficult because the excursions of the Voyager spacecraft in magnetic latitude are very limited, and because of the existence of the Io torus which alters the ray paths considerably. Thus, a three-dimensional ray-tracing study for the hectometric frequency range is necessary.

In section C.2, we présent typical HOM observations and discuss the change in the HOM émission pattern on a fixed frequency plot when Voyager 1 was approaching Jupiter. In section C.3, the ray-tracing procedure is briefly presented, and we introduce the HOM source locations and émission characteristics from Paper 2. In section C.4, we show that a shadow zone near the magnetic equator is produced for distances less than about 20Rj. This shadow zone is due to the presence of the Io torus which behaves like a divergent lens for frequencies in the hectometric range. In turn, it focusses the radiation near the magnetic équatorial plane farther away from Jupiter. In section C.5, the modeled intensity curves, which are obtained from a detailed investigation for /=500 kHz, are compared with the observed pattern. We simulate the overall features when the spacecraft was near the planet and account for the strong HOM latitudinal beaming which is observed at large distances. The implications of these results are discussed in the conclusion (section C.6). unable to penetrate régions corresponding to low magnetic latitudes near Jupiter. This builds a région of no illumination near the Jovimagnetic équatorial plane which will be called the shadow zone. This shadow zone is expected to be the conséquence of spécifie émission properties at the source (i.e. source location and beaming pattern) and of the presence of the Io plasma torus located at about 6 Rj from the planet. The occultation zone due to the émission properties at the radio sources dépends on the choice of the source locations and the propagation angles.

C.2 Observations

The extension of the shadow zone is further strongly influenced by the Io torus which becomes opaque especially for the lower frequency range of HOM. Substantial refraction, however, may occur up to frequencies of a few MHz [START_REF] Lecacheux | Ray tracing in the Io plasma torus: Application to the PRA observations during Voyager l's closest approach[END_REF], depending on the torus peak électron inspecting the torus électron number densities shown in Figure 11 of [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF], we can unambiguously State that it corresponds much doser to the revised density model by [START_REF] Bagenal | Revised ion températures for Voyager plasma measurements in the Io plasma torus[END_REF] (their Figure 1) than to the old model (Figure 12 We now intend to simulate the émission intensity pattern as would hâve been observed by Voyager 1 when the selected émission characteristics and source locations are entirely accounted for. To simplify the calculation in our model, the originally continuously (in magnetic longitude) distributed sources are replaced by 9 equally spaced subsources in each hemisphere, respectively.

These subsources behave identically, having the same power and, of course, the same émission lobes. Each subsource is located on a magnetospheric height where ///c=1.02 (f=500 kHz) and consists of an émission cône with an opening angle 9 = 75°and cône half-width A9 = 5°. The conical radiation pattern of a subsource is simulated by initializing the azimuthal angle in steps of 9°around the magnetic field line which defines the cône axis. This procedure is perfomed for 9 = 70°, 75°, and 80°in order to détermine the outer limits of the émission lobes as well. Thus, 120 rays were launched per subsource. The normalized subsource beam profile is specified by the following function (taken from [START_REF] Gulkis | The main source of radio émission from the magnetosphere of Uranus[END_REF], Equation 2 and Figure 5)

f(«) = l(l + cos[36-(fl-75)]) (C.l) f(0)= 0 [9 > 80°], 70°]
adapted for our purpose. f{9) is the relative power per unit solid angle radiated in any direction making an angle 9 with respect to the positive direction of B in the northern hemisphere or to the négative direction of B in the Southern hemisphere. f(9) becomes zéro when 36 • (9 -75) is not in the range [-180., 180.] i.e. for ail 9 less than 70°and greater than 80°and has a maximum for 9 = 75°. The three-dimensional subsource beam pattern is found by rotation of f( 9 In fact, both of these characteristics may account for HOM, but only the local time effect has been thouroughly studied at the présent time [START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF]; Paper 1).

C.5.2 Application to the observed latitudinal beaming

To check the validity of our inferred HOM sources and émission parameters, we hâve modeled the HOM latitudinal beaming, and compared it with the observations of [START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] and At the closest approach (labeled CA) n+1/2 gyroharmonic waves and upper hybrid résonance émission occurred, associated with Voyager's traversai of the Io torus [START_REF] Birmingham | Obser vations of électron gyroharmonic waves in the structure of the Io torus[END_REF].

The "ghost" feature (labeled G in in agreement with the observations for a fully three-dimensional investigation as well. The fact that HOM may be visible at ail System III longitudes when the viewing geometry is favourable strongly suggests that HOM is active over a wide range of longitudes. The inferred parameter set may therefore be considered as highly relevant in association with the Jovian hectometric radiation.

C.6 Summary and Conclusion

We hâve performed a fully three-dimensional ray-tracing study to model the Jovian hectomet ric radiation. The source locations are assumed to fie along magnetic field fines with £=20 as determined by Ladreiter and Leblanc (1990a). We hâve demonstrated that cyclotron rés onant X-mode sources distributed in a large range of longitudes in both Jovian hemispheres can account for the major characteristics of the HOM radiation. In particular, our modeling reveals the existence of a shadow zone at the magnetic équatorial plane extending to about 20 Rj which was actually observed by VI and V2. We hâve been able to simulate the strong HOM latitudinal beaming which was observed at large radial distances from the planet as well as the complex polarization within the HOM beam arising from the mixing of the contributions from both hemispheres. For hectometric wavelengths, the Io torus behaves like a divergent lens which prevents the rays from penetrating into low magnetic régimes near the planet but, in turn, focusses the radiation near the magnetic équatorial plane far from Jupiter. Additionally, the comparison between the predicted and observed intensity profiles exhibits a remarkable agreement when bearing in mind that the calculated curves dépend on the source locations, émission characteristics, and the Io torus density model. However, to better fit the HOM observations, a somewhat enhanced density model is needed, in agreement with [START_REF] Jones | Radio wave émission from the Io torus[END_REF] who modeled the Jovian kilometric radiation.

The ray-tracing calculations were thoroughly performed for /=500 kHz. However, we also tested the situation for higher frequency HOM. It is found that the shadow zone narrows for the higher frequency components and that an increase of the Io torus peak density by a factor of 2-3 is required to fully account for /=1000 kHz also. We hâve considered in detail VI observations because it approached Jupiter much doser than did V2. However, we verified that our modeled HOM pattern is also in agreement with V2 observations. In this study we hâve taken into account radial and longitudinal effects of the HOM observations. The effects when varying the HOM source locations in magnetic latitude hâve already been discussed in Paper 2.

To consider only the cruise portion of one single spacecraft is not sufficient for the dérivation of significant results. The quite stable and répétitive pattern of HOM, well defined in System III longitude when observed at large distances from Jupiter might lead to the assumption of a source confined to a small range of longitudes (Ortega-Molina and Lecacheux, 1990b) which, in turn, hardly accounts for the phenomena observed near closest approach nor for the HOM beaming.

The main resuit of this study is that the HOM source locations are along open magnetic field Unes with foot prints at the auroral ovals, confined within a wide range of longitudes and located in both hemispheres. In this context, the solar wind control on HOM can be simply understood.

During the modeling of the HOM émission pattern, we pointed out that the sharp HOM beaming is the conséquence of the focussing of the radiation near the magnetic équatorial plane due to the refractory effects of the Io torus. However, without this focussing, the HOM intensity as seen by the spacecraft would hâve been lower than actually observed. Since this focussing effect is supposed to be strong for émission in the HOM frequency range, the spectral peak of HOM might be produced artifically. This, in turn, implies that HOM is most probably the low-frequency extension of the non-Io DAM as already suggested by [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF], but HOM is possibly active in a wider range of longitudes. Future spacecraft missions such as Galileo and Ulysses will provide the opportunity to collect further data leading to a deeper study of yet unresolved details concerning the hectometric radiation.

of AKR. They treated the CMI only as a local phenomenon so it cannot be decided from their investigations, whether or not the amplified wave suffers damping when traveling away from the source.

Although a large amount of publications on the CMI theory has been performed, a comprehensive study is required to link the solutions of the whole dispersion relation to an inhomogeneous treatment of the theory. A major step in this regard was done by [START_REF] Pritchett | Génération and propagation of kilometric radiation in the auroral plasma cavity[END_REF] who performed two dimensional particle simulation in an auroral arc and determined the overall growth via three dimensional ray-tracing. They obtained the observed wave amplitudes within a distance of wave particle interaction in the order of the dimensions of an auroral axe.

Furthermore, no general consensus has been reached about the unstable feature in the électron distribution function which is most likely responsible for the génération of planetary radio émis sions. Recently, [START_REF] Louarn | Trapped électrons as a free energy source for the AKR[END_REF] put evidence that also the région of "trapped électrons"

(appearing at the u^-axis) in the distribution function may provide free energy for the amplifica tion of waves, thus enhances the number of unstable régions (loss cône, holelike région, trapped électrons) which compete for providing the largest amount of free energy.

This paper does not aim to settle the controversy of the preferred instability région. Instead the purpose is a treatment of the CMI in a very low density magnetoplasma where /p//c < 0.01. Most of the papers dealing with the CMI so far considered /p//c > 0.01 to be applicable to the terrestrial auroral radio émissions. Our study concerns the sources of the lower frequency radio émissions from Jupiter (DAM low frequencies, HOM) and Satura (SKR lower frequencies)

which are supposed to be located in régions where /p//c < 0.01. We dérivé simple expressions relating the normalized (to the light velocity c) parallel bulk velocity /3\\a of a given électron distribution function to the frequency / of the most amplified wave (in terms of fc) and to the emergence angle 9 when the radio source is located in a low density magnetoplasma. To achieve this, we first recall a typical électron distribution function to see the characteristics of the régions of free energy which are necessary for wave amplification (section D.2). We discuss the relativistic résonance condition to dérivé the waves (k, /) for which the résonant contours are largely embodied in an assumed loss cône instability for a given fc and /p. Similar studies were presented by [START_REF] Dusenbery | General concepts on the génération of auroral kilometric radiation[END_REF] and applied to the conditions in the earth's aurora.

We shall see that for a given 9 there axe several possiblities for amplification depending upon the values fp and fc in the source région. Further, it will be demonstrated, that an homogeneous treatment leads to strong overestimations of the growth (section D.3). Nevertheless for a plasma with fp/fc < 0.01 we dérivé a very simple criterion which leads to an expression of the quantities 9 and // fc at the source in terms of the parallel bulk velocity /3\\0. We discuss our results within distribution has already been performed by Omidi and Gurnett (1984).

In this paper we will focus our attention on the calculation of Equation (D.12) in an idealized distribution function which exhibits a loss cône instability. We intend to calculate the expected growth for waves with a constant 9 for ail possible values /p//c inside S$. From this analysis we expect to dérivé the value of n for which a wave with given 9 is most probably amplified.

When the used distribution function is not precisely specified, there is no way to calculate via Equation (D.2). Therefore several constraints hâve to be made to calculate g via Equation (D.12). They are listed in the following and should kept in mind to avoid misinterpretations when evaluating the degree of validity of the obtained results.

1. The cold plasma governs the wave propagation along the ray path l\ -12

2. Existence of a magnetic dipole field with VB\\B. The direction of B is kept constant along ray path. This is a good approximation near the magnetic polar régions.

D.3.2 The loss cône instability

Before calculating Equation (D.12) it is necessary to specify the loss cône feature in the modeled distribution function. [START_REF] Persson | Electric field parallel to the magnetic field in a low density plasma[END_REF] showed that in the presence of a parallel electric field, the ). For AV (potential différence between the radio source and the ionosphère), 2 kV is assumed corresponding to best fits of the S3-3 measurements [START_REF] Croley | Signature of a parallel electric field in ion and électron distributions in velocity space[END_REF]. Notice that the ellipses between 1 and 2 are mainly embodied in régions dF/dv± < 0. Close below the loss cône instability, dF/dv± fa 0, thus considérable quenching of the gain is not expected.

where a is the loss cône angle.

If ail électrons were lost below a given mirror point Bm, the slopes of the loss cône boundaries would be infinitely steep, thus leading locally to dF/dv± -oo. A more realistic view is that the mirror point in the ionosphère (where the électrons are lost) is statistically varying for each électron within the électron mean free path. Therefore the électron distribution in the loss cône does not drop down abruptly, but within an angle Aa reported to be in the order of 0.5 -2° (Omidi and Gurnett, 1984). Consequently, a loss cône angle (a « 15°) calculated for a distribution function at 2-3 planetary radii (Equation D.14) will be used together with Aa = 2°( Figure D.5) to détermine the gain factor g. Auroral radio sources like at the earth (AKR),

Jupiter (low frequency DAM, high frequency HOM), and Saturn (SKR) are typically found at 2-3 planetary radii. Within this approximation, we do not limit our loss cône instability around a given value /?||0. Instead, it is assumed that the unstable région covers a large range of /3||. The more realistic restriction to /?||0 will be performed later.

Since u>i is constant in our approximation between l\ and I2 Equation (D.12) may be written Figures D.8 and D.9 show solutions of Equation (D.17) for 9 = 70°and 80°, respectively. The used electric field potential is 2 kV [START_REF] Croley | Signature of a parallel electric field in ion and électron distributions in velocity space[END_REF]. In the case of Jupiter and Satura, this potential différence between the radio sources and the ionosphère may certainly be higher, but the choice of AV is not of primary interest here. Figures D.8a and D.9a show the normalized interaction time T against /p//c for the two branches 61 and 62 as defined in Figure D.6. We see that T is generally higher for branch 61 which corresponds to lower refractive indices n and consequently to lower group velocities vg. Moreover, a dramatic increase of T is observed when fp/fc is reaching its highest values. This can be easily understood in Figures D.8b cind D.9b which show the interaction length L (between l\ and I2). We see a maximum of L reaching 10~2ro when /p//c is near its maximum (9 = 70°) and somewhat less for 9 = 80°. Assuming r0 to be about 2 -3 planetary radii, we obtain L « 100 km for the earth and L « 1000 km for the giant planets Jupiter and Satura (9 -80°). For 9 = 70°, the values L become « 200 km and « 2000 km, respectively. We note that for branch bi when considering low values of /p//c (< 0.01) the interaction length L drops lower than 10~7ro which corresponds only to afew meters given at /i (full line) and I2 (dashed line). Inspecting branch 61, we notice that even in the small interaction length given for small fp/fc the index of refraction changes substantially (from « 0 to 0.1). Thus, the assumption that 9 remains constant in this région is rather questionable, in particular when gra<LB\\grad n. Moreover, after the short period of possible amplification, the amplitude of the wave is probably damped when the résonant contours encounter favourably régions with dF/dv± < 0 above the loss cône feature. These facts are in particular relevant for branch b\ and they are ail working in the sense to quench the calculated amplification. Now it is also clear that a significant change of the refractive index within a few meters does no longer allow to use the tools of geometrical optics, even as local approximation. Therefore the results

given for branch 61, particulary at the smallest fp/fc must be taken with caution.

Looking at plasma conditions fp/fc where the peak interaction time T is reached (connection of branch &i and 62)» that means fp/fc « 0.067 for 0 = 80°and fp/fc « 0.137 for 6 = 70°, the refractive index also changes significantly between /1 and /2, namely from about 0.65 to 0.85 (Figures D.8c and D.9c). Thus, important refraction is expected, too. It is, however, difficult to overcome this approximation of no refraction, because the refraction highly dépends on the direction of grad n, which is in general not necessarily parallel to gradB.

For the reasons given above, the interaction time T and consequently the overall growth may be significantly overestimated, in particular for branch 61. Contrary, for branch 62, the calculated T (shorter than for branch 61) is reasonable within the context of our approximation because, firstly, the index of refraction is near unity which means that the effect of subséquent refraction is indeed negligible, and secondly, because the interaction length « 10"3ro is comparable to the dimensions of an auroral arc.

Our results of the calculation of the interaction time T indicate that T exhibits a maximum where branches 61 and 62 are connected, or in other words, when /p/fc reaches a maximum at T might be overestimated also for these régions because of the approximations we hâve used: the assumption of no refraction along ray path, and no wave absorption after the phase of amplification are not very appropriate there. On the contrary, when considering low values fp/fc < 0.01, it is unlikely that the sources are located near n -0 (branch 61), since the interaction lengths are probably to small. Moreover, it seems difficult for these waves to reach free space (n = 1) without suffering significant damping after the phase of amplification.

In Figures D.8a and D.9a we note that there is a link between the wave emergence angle 9 and the value /p//c where the interaction time T reaches a maximum. In a previous study, Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF] found the relation sin 0^= nearly perpendicular to the source magnetic field line (0 « 80°) at a frequency slightly higher than the électron gyrofrequency (f/fc ~1.01). Réfraction of the wave during its propagation into free space is found to be negligible since the refractive index at the source is near unity.

Consequently, 9 ~9oo where 9^is the emergence angle measured fax away from the source in free space. These results are consistent with the findings of [START_REF] Galopeau | Theoretical model of Saturn's kilometric radiation spectrum[END_REF] who demonstrated a quasi perpendicular propagation of the SKR low frequencies generated in a low density magnetoplasma throughout their theoretical modeling of the Saturnian kilometric radio spectrum.

D.4 Discussion

During the présent investigation we analyzed the CMI in plasmas winch are largely dominated by the magnetic field (/p//c < 0.01). This study is highly important, because of the applications to the low-frequency auroral émissions of Jupiter and Saturn. With some useful and plausible simplifications, we derived the wave emergence angle 9 and ///c at the source as a function of the parallel bulk velocity (3\\0 (Equations D.ll and D.26) provided that the amplification of the wave is due to the loss cône or the holelike instability. Significant basic results obtained by Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF] were confirmed or elaborated in the présent paper.

One of our most important findings is that the refractive index at the source is near unity because ///c has been shown to be about 1.01 for plausible électron energies (1-10 keV), thus, the source région is sufficiently separated from the R-X cutoff. The quenching of the interaction time due to the high group velocity vg in this région is compensated by the long interaction length which is possibly as long as an auroral axe. On the other hand, when n -0 in a low density source région, the group velocity is very small which would enhance the gain, but the interaction length is only in the order of meters or even below which is probably not realistic.

Concerning the wave emergent angle 9 at the source, which is found to be « 80°for électron energies from 1-10 keV, the results agréé favourably with the study of the theoretical ra dio spectrum of SKR performed by [START_REF] Galopeau | Theoretical model of Saturn's kilometric radiation spectrum[END_REF]. Therein, a nearly perpendicular emergence angle was obtained for the lower frequency sources of SKR which are imbedded in a low density plasma. In the case of Jupiter, the choice of a nearly perpendicular 9 throughout the study of the hectometric radiation sources performed by Ladreiter and Leblanc (1990a,b) is strongly supported by the présent results. The hectometric sources lie at high altitudes in the Jovian auroral zones which are also largely density depleted [START_REF] Ladreiter | The cyclotron maser instability: Applications to low density magnetoplasmas[END_REF]Leblanc, 1989, 1990a).

One of the main difficulties we encountered throughout our approximations is that in the case of a low density magnetoplasma, the hot électron component may gain over the cold component which is significantly changing the propagation of the radio waves. [START_REF] Pritchett | A simulation study of kilometric radiation génération along an auroral field line[END_REF] dealt with this problem and performed particle simulations in high altitude auroral zones and took into account varying ratios of hot and cold électrons. Moreover, they include the effect of a parallel electric field making the analysis rather realistic. In their study, they found that the amplified radiation is highly concentrated in the perpendicular (with respect to the magnetic field) direction. Furthermore, the radiation tends to occur in régions where kc/u>c « 0.96 and ///c « 0.99, i.e. n = kc/u « 1. In fact by including the effect of hot électrons, the radiation For the définition of the refractive index surface, consider a coordinate System with the spherical coordinates r, 9,(f> (Cartesian coordinates u,v,w) centered on a point in the plasma which is defined by Ne and B. Let B be parallel to the tn-axis. For a given frequency /, the refractive index dépends only on d. Consider a surface in which the radius to each point is equal to n(i?).

According to Equation (E.l), there exist two such surfaces, one for the X-wave and one for the O-wave. Since n dépends only on t? for a given point in the medium, each surface is a surface of révolution around the tu-axis with the u -u-plane (i9 = 7t/2) as a plane of symmetry. The resulting surfaces are called "refractive index surfaces". In free space (Ne=B=0) both surfaces are simply unit spheres around the origin.

E.l.2

The directions of the wave normal and the ray When there is no superimposed magnetic field, the refractive index n in a plasma does not dépend on the direction of the wave propagation; the wave normal and the ray directions are therefore identical. The wave normal is defined to be perpendicular to the planes of constant phase, whereas the ray dénotés the direction of energy flow. When the magnetic flux density is not zéro, the directions of a ray and the associated wave normal are in general different, because the refractive index n dépends on the direction of the wave normal. This is true in a homogeneous medium and a relation between the ray and the wave normal direction eau be found. The results then can be used to trace the ray paths in an inhomogeneous, but slowly varying medium. To dérivé the ray direction for a given wave normal in a magnetoplasma we start from the expression of the wave electric field (e. g. [START_REF] Budden | Radio Waves in the Ionosphère[END_REF]. From Equation (E.4), we see that v?=const i.e. the wave normal, the ray and the magnetic field are coplanar. Thus y? can be chosen to be 0. Let the ray direction make an angle a with the wave normal i.e. an angle 90 -a with respect to the iu-axis and let r0 be the distance from the origin. We hâve u = rQ sin(tfG -a), u=0, w = rQ cos(t?0 -a). By substituting u, u, w in Equation (E.5), we obtain the angle a which détermines finally the ray direction. After some algebraic We notice the important reciprocal properties of the wave normal and the ray. For a given point in the medium, the ray direction is the normal to the refractive index surface and the wave normal direction is the normal to the ray surface. This is emphasized in Figure E.2 (from [START_REF] Budden | Radio Waves in the Ionosphère[END_REF] where we show the refractive index surfane and the ray surface for whistler mode waves which hâve frequencies below the gyrofrequency. We see that for any wave normal angle t?, the ray direction is confined within a small angular range around the magnetic field. This explains the "guiding" of whistlers along magnetic field fines.

E.2

The ray équations E.2.1 Equations for the refractive index surface and the ray surface With the results of the preceeding sections, we are able to détermine qualitatively the ray path in a magnetoplasma. To describe the situation mathematically, we shall find équations which describe the refractive index surface and the ray surface. We recall that the instantaneous ray direction dx/dt is normal to the refractive index surface. This can be emphasized by where dx/dt is the ray velocity Vr (t: time), nx, ny, nz are the components of the refractive index n and G dénotés the refractive index surface which we obtain as follows. We define a three dimensional space to be called the " refractive index space" with the Cartesian coordinates nx, ny, nz which are parallel to the axis x,y,z in ordinary space. Let the wave normal take ail possible directions. Then the locus of the point nx,ny,nz for ail possible directions defines the refractive index surface. The refractive index is given by Appleton-Hartree formula (Equation E.l) and dépends on the position x,y,z and the direction of the wave normal nx,ny,nz. This is indicated by writing n(x, y, z, nx, ny, n2 where a dot represents d/dt.

In section E.l we found that the wave normal direction is normal to the ray surface. This can be emphasized by writing where F dénotés the ray surface and we find it in a similar way as we found the refractive index surface. Consider a three dimensional space to be called the "ray space" in which the Cartesian coordinates are i, ÿ, i and are parallel to x,y,z of the ordinary space. Draw a line from the origin of the ray space in the direction of the ray and with length equal to the ray velocity Vr-\Jx2 + y2 + z2. The end-points, which define the wave front after unit time, represent the ray surface. nray is the ray refractive index and is given by nray = c/Vr (Equation E.13). It is a function of x,y,z and the ray direction which we indicate by nroy(x, y, z,x} ÿ, z). The équation for the ray surface F can be written (by inversion of Equation E.13) F(x, y, z, x, y, z) = yjx2 + y2 + z1 nrav(x, y, z, x,y,z)-= 1 (E.18)

The constant of proportionality in Equation (E.17 where a and b dénoté the end points on the ray path. When Equation (E.27) is evaluated for a number of ray paths between a and 6, its value is an extremum for the actual ray path. Let us substitute dt by ds, using (ds/dt)2=x2 -f y2 -f i2 and Equation (E.18). We obtain (E.28)

which is Fermat's principle. It States that the time of travel of a wave crest along the ray path from a to 6 is stationary with respect to small variations of the path. Here, the time of travel is a minimum. In other words, the ray path from a to 6 is such that the time of travel of the wave front along this path becomes a minimum. Thus, by using the relations between G and F we hâve seen that the wave propagation accounts to Fermât 's principle of stationary time.

Equation (E.28) is given in Cartesian coordinates. However, Fermat's principle accounts for any chosen coordinate System. We may therefore introduce spherical polar coordinates which are more convenient to study ray paths in planetary magnetospheres. Therefore Equations (E.16) and (E.23) which are the ray équations can be written in spherical coordinates r, 0, <f> P\. This is emphasized by Equations (E.30). A new wave normal direction nrj = nro + hrAt, ng\ = noo + hgAt, n^i -n^0 + h^At occurs at the point P\. At Pi, a new ray direction is calculated and the steps are repeated. Thus, the ray path through the medium is found. Before this procedure is amenable for calculation on a computer, the ray Equations (E.29) and (E.30)

hâve to be expressed in terms of plasma density and magnetic field models which characterize the regarded medium (e.g. planetajy magnetosphere, ionosphère etc.).

E.3

Application of the ray équations for ray tracing in plane- We use dn/dü as derived from Equation (E.l), and further Equations (E.37), (E.34) and substitute them in the ray Equations (E.33). These équations détermine the direction of the ray (defined by r,0, <fi) at a given starting point and for a given wave normal direction when we provide a magnetic field model B(r,0,<f>) which intervenes in Equations (E.36).

We shall use the results from Equations (E.33) to calculate the variation in the wave normal direction during the wave propagation with the second set of ray Equations (E.30). Substitute

Equations (E.29) in Equations (E.30)

  of résonant contours to the électron distribution function .... D.3 Amplification of the radiation D.3.1 The exponential gain factor D.3.2 The loss cône instability 127 D.3.3 Analysis

1. 2 .

 2 Figure 1.2: Schematic représentation of the induced current System flowing approximately parallel to the field Unes in the Io flux tube linking Io to the Jovian ionosphère (taken from[START_REF] Acuna | Jupiter's magnetic field and magnetosphere[END_REF].

For

  Jupiter the émission is much more complex and we can distinguish 5 components: Io DAM: Io-controlled Jovian decametric radiation non-Io DAM: non Io-controlled Jovian decametric radiation HOM: Jovian hectometric radiation bKOM: Jovian broad-bandwidth kilometric radiation nKOM: Jovian narrow-bandwidth kilometric radiation

Figure 1 .

 1 Figure 1.4 shows an example of the wide frequency range of the radio émissions from Jupiter recorded by the Planetary Radio Astronomy (PRA) experiment aboard the Voyager spacecraft.*NKR is not shown in Figure1.3 but it is expected to be similar to UKR

Figure 1 . 4 :

 14 Figure 1.4: Dynamic spectra of the Jovian radio émissions, recorded by the Planetary Radio Astronomy experiment aboard Voyager. Increasing darkness indicates increasing intensity (from Kaiser and Desch, 1984).

  DAM radiation which is observed from ground based stations, the kilometric and hectometric components were first detected via the PRA-experiment on board the Voyager spacecraft. The kilometric émission lies in the range between 40 kHz and possibly 1 MHz with a spectral peak near 100 kHz. Like the DAM, the KOM is répétitive in terms of the Jovian rotation period.

  greatest advances in the field of radio astronomy was made by the successful Voyager mission which enabled the exploration of the magnetospheres of the outer planets Jupiter, Sat ura, Uranus, and Neptune. Since the Neptune flyby of Voyager 2 in August 1989, the Voyager mission became one of the most exciting in the history of space flights. Since 1977, the two Voyagers flew a distance of more than 7 billion km. The trajectories of both Voyagers are shown in Figure 2.1a. After the launch of both spacecraft in 1977, Jupiter was reached in 1979. Satura was visited in 1980 by Voyager 1 and 1981 by Voyager 2, which continued its journey to the outer planets and encountered Uranus in 1986 and -very recently -Neptune in 1989. Both Voyagers were favourably designed to receive radio signais from ail of the radio planets via the Planetary

  Figure 2.1: (a) Trajectories of the Voyager 1 and Voyager 2 spacecraft. Also shown are the dates of the respective planetary encounters. While Voyager 1 had only a Jupiter and Saturn flyby, Voyager 2 additionally encountered Uranus and Neptune, (b) OverView of some of the experiments aboard Voyager. The antennas of the planetary radio astronomy experiment are erected within a plane perpendicular to the magnetometer boom. The Voyager observations were transmitted to the earth via the high gain antenna.

  radiation is the most powerful émission measured by the low frequency band receiver of the Voyager PRA experiment. It has been observed since several years, starting short after the launch of the Voyager spacecraft in 1977 and ending in 1980 just before the Saturn encounters. An extremely high data rate was provided during a period of about 4 months centered on the respective Jupiter encounters of Voyager 1 (March 5, 1979) and Voyager 2 (July

  Figure 2.2: Voyager 1 (upper panel) and Voyager 2 (middle panel) observations of the Jovian HOM during one Jovian rotation, respectively. The observed émission pattern can be interpreted in terms of a HOM beaming in magnetic latitude which is sketched in the bottom panel.

Figure 2 . 3 :

 23 Figure 2.3: Average northern beam extension (average of /=558 kHz, /=942 kHz, and /=1326 kHz) plotted as a function of the normalized (to the earth-Jupiter distance) détection threshold. Thick Unes are plotted for VI and thin Unes for V2.

  Figure 2.4: Occurrence probabilities of VI and V2 preencounter (upper panel) and postencounter (lower panel) observations recorded during 40 Jovian rotations, respectively. Notice the high asymmetric shape of the émission gap centered at about 200°CML during nightside observations.

A

  Figure 2.5: Relative occurrence probability of HOM at /=942 kHz for VI postencounter observations when the two polarizations are treated separately (top panel). A schematic HOM beam which corresponds to the observations is plotted below.

3. 3 .

 3 Figure 3.1: Electron density contours for the Jovian plasma density model (from Divine and Garrett, 1983).

Figures 3 .

 3 Figures 3.3 and 3.4 show examples of ray-tracing from several possible source locations

Figure 3 .

 3 Figure 3.6 shows the footpoints of the derived source locations (15 < L < 30) and the tailfield aurorae where particle précipitation is most probable. The footpoints of the HOM sources are

Figure 3

 3 Figure 3.4: (right panels) Same as Figure 3.3 but for sources at field lines L-8 and L=10. Rays originally emitted with 0 nearly perpendicular to the local magnetic field are diverted away from the magnetic equator.

Figure 3 . 5 :

 35 Figure 3.5: The value 0crit as a function of the frequency / and the L parameter of the source field line determined from the ray-tracing calculations at 200°CML. Dashed lines indicate the interpolated 9erit for L=10, 15, and 30 from the given data. N and S refer to sources in the northern and Southern hemisphere, respectively.

  Figure 3.7 displays VI observations where the émission in the upper panel was observed fax from Jupiter (notice scale at the top) whereas

Figure 3 .Figure 3

 33 Figure 3.8 shows the évolution of waves with 0 = 75°from two point sources, one at each hemisphere at £=20. The rays form a shadow zone near the magnetic equator which is consistent with the observations in Figure 3.7b.We are further interested to study the extension of the shadow zone for the fixed values £=20 and /=500 kHz, but for varying half cône angles 0 and Io torus densities which are derived by multiplying the density values of the actual model by Divine and Garrett with a constant factor. The three panels of Figure3.9 represent the used different density models. We plotted

  Ray-tracing of HOM émission (hollow cônes, 9 = 75°) emanating from sources located at L-20 in both hemispheres. A shadow zone near the magnetic équatorial plane is produced because of the refraction at the Io torus (size of Io not in scale). the boundaries of the shadow zone for 9 = 70°and 9 = 80°. The thick Unes on the respective spacecraft trajectories indicate épisodes of extremely low émission. Thereby, the shadow zone is présent inside about 18 Rj which is approximately predicted in the middle panel (15 % enhanced plasma density) for both half cône angles. Moreover, the middle panel accounts very well for the observations inside of 10 Rj for 9 = 80°. However, the recordings around 15 Rj are a somewhat better fit in Figures 3.9a and c, but we consider Figure 3.9b as the best description

Figure 3

 3 Figure 3.9: HOM shadow zones projected onto a meridian plane for 6 = 70°and 9 = 80°. Superimposed is the Voyager 1 trajectory during the encounter period. Significant épisodes of lowest or no HOM activity are represented by thick Unes on the trajectory. Plots 3.9a,b,c where calculated based on the indicated density models.

Figure 3 .

 3 Figure 3.10: Modeled HOM émission cônes as if they were seen from Voyager 1 along its trajectory (thick lines) and the corresponding intensity profiles, (a) For short radial distances, a shadow zone for the émission is calculated as observed. (b) For large radial distances, the characteristic HOM beam is formed.

  (0 « 90°, n (refractive index) « 1, / « fa fp << /c, the dispersion relation à(iü, k) can be significantly simplified[START_REF] Wu | Kinetic cyclotron and synchrotron maser instabilités: Radio émission processes by direct amplification of radiation[END_REF] A(tü, k) = 1 -c2k2 dF dv± . dF +k"v±d^, VA.Jl2(k±V±/uJc) _ Q (W-Wc/T-*||V||) (4.1) 39

Figure 4 . 1 :

 41 Figure 4.1: Typical électron distribution function taken by the S3-3 satellite in the auroral région of the earth. The three occurring instabilities dF/dv± > 0 are marked by arrows.

  Figure 4.2: Properties of résonant ellipses in the normalized (to fe) f -fp space for given wave normal angles 9. The areas where ellipses exist are enclosed by the respective séparatrices S$ on which the ellipses shrink to a point.

  serves to calculate a;,-for a given électron distribution function (Figure4.1).However, to see whether or not the initially amplified wave suffers damping along the further ray path, one must calculate the exponential gain factor along the ray path I1

Figure

  Figure D.5), ellipses 1 and 2).

Figure 4

 4 Figure 4.3: (a) Normalized interaction time T, (b) wave-particle interaction length L, and (c) refractive index at /i (full line) and /2 (dashed line) for 9 = 70°as a function of fp/fe-For low fp/fc, two solutions exist (61, 62).

  Figure 4.4: Wave emergence angle 6 and f/fc in terms of the parallel bulk velocityThe scale for the électron energies E is also given assuming E\\ « E.

  Figure A.l shows typical HOM émission before encounter during one Jovian rotationfor VI (top panel) and for V2 (center panel). Note that the émission gap centered at about 200°C ML is wider for V2 than for VI. Contrary, the VI data show a little émission gap centered near 20°CML which is not visible in the V2 data. This is due to the higher Jovicentric déclination during the inbound trajectory for V2 (S = 7.5°) compared with VI (£ = 3.2°). If one assumes a beamed émission centered near the magnetic equator, V2 exits the beam at its northern side earlier than VI because of its higher Jovicentric déclination. The reentry occurred later for V2 and vice versa for the magnetic Southern excursions at about 20°CML. This fact can easily be seen in the bottom panel of Figure A.l which shows a sketch of the two spacecraft trajectories in a Jovimagnetic coordinate System during one Jovian rotation and an émission beam fixed in magnetic latitude. The recordings at smaller radial distances from Jupiter show narrower émission gaps centered at « 200°but still wider for V2 than for VI. In fact, the relative HOM intensity (not normalized to a fixed distance) increased and we detected émission at the edge of the beam near to Jupiter which might not hâve been detected at larger distances at the same threshold.

  Crossing, while the corresponding Southern side exit was named the EARLY beam Southern exit. The reentry from the Southern side is named the LATE beam Southern entry, while the subséquent northern exit is named the LATE northern beam Crossing. These beam crossings are indicated in the bottom panel of Figure A.l. Note that the late beam exit occurs in general at

  Figure A.l: Recorded HOM émission for VI (top panel) and V2 (center panel) during one Jovian rotation before the respective encounters for the 3 frequencies indicated. The émission gap near 200°C ML is broader for V2 because of the higher Jovicentric déclination. Contrary, no émission gap near 20°C ML was seen from V2. The bottom panel sketches the VI and V2 trajectories before the respective encounters separated by a few degrees in Jovicentric latitude. By assuming an HOM émission beam fixed at magnetic latitude, the observations for VI and V2 Etre simulated very accurately.

Figure

  Figure A.3 summarizes the beaming results for aU sections defined in TableA.l by plotting magnetic decfination of the HOM northern beam Hmits (obtained from method a) for /=558 kHz (top panel) and /=1326 kHz (center panel) in terms of radial distance and the corresponding normalized détection threshold. The bottom panel shows the average beam width of HOM (average of the 3 frequencies studied). Linear interpolation has been performed between the obtained results. FuU Unes dénoté the early northern beam limit, and dashed Unes the late one.

  Figure A.2: VI (full Unes) and V2 (dashed Unes) émission occurrence as afunction of System III longitude observed during 40 Jovian rotations centered at the indicated distance, (a) displays preencounter, and (b) postencounter observations. Notice the high asymmetric shape of the émission gap centered at about 200°CML during nightside observations. The émission gap in (a) is wider for V2 because V2 observed from a higher Jovicentric déclination (7°) during the inbound trajectory compared to VI (3°).

  and A.4 (compare distances oF about 750 Rj on the day and nightside). The dayside beam calculated from V2 data is significantly larger than that observed by VI at the nightside.Further, we investigated low data-rate time periods at larger radial distances from Jupiter,(sections 8, 9, 15 in Table A.l). The corresponding beaming is shown in Figure A.3 (see arrows).

  Figure A.5: Schematic plot of the hectometer beam and the two spacecraft trajectories during one Jovian rotation in a Jovimagnetic coordinate System, a dénotés the différence between the Jovicentric latitude of VI and the magnetic déclination of the beam axis, 9 is the angular local time différence, 6 is the spacecraft latitude séparation, and /? is the beam half-width. In this Figure a = 9 = 0°, /? = 4°, and <5 = 5°. The CML range during which the beam could be detected by the respective spacecraft is accentuated by brackets. DV1 dénotés VI beam recording, DV2 the V2 beam recording, and during the period C, both spacecraft are within the beam. The degree of corrélation seen from the two spacecraft is different (C/DV1 ^C/DV2).

  Figure A.7), we had to introduce a beam half-width (3 « 2.45°. This beam width is smaller than the estimate of Alexander et al. (1979) {(3 = 5°), however. For comparison with our results, we determined a = 2°(VI Jovicentric decUnation before encounter « 3.5°, assumed beam axis « 1.5°), and 6 = 4.3°. Unfortunately, we hâve only a few observations where we could clearly compare VI and V2 before encounters, because of an extremely low data rate for V2 during early 1979. A typical case is shown in Figure A.8. VI data are plotted in the upper panel and V2 data in the lower one. The local time effect has been eUminated by shifting VI data with respect to the V2 data by the small local time différence. It can be seen that most of the émission is observed by both spacecraft which contradicts Alexander et al. (1979) results. On the other hand, it is shown from our calculated corrélations, that only for (3 > 5°both spacecraft observe most of the émission in common when 6 = 4.3°(Figure A.6c).

Figure A. 7 :

 7 Figure A.7: Comparison of the observed decorrelation of simultaneous HOM observations (VI and V2)by[START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] (full circles), and calculated decorrelation. In order to fit their observations best, we had to assume the beam half-width /? to be 2.45°(a = 0°, 9 = 2°). CV1 (full line) dénotés VI corrélations and CV2 (dashed line) those for V2. The total angular séparation (calculated from 9 = 2°) is also indicated at the top.

Figure A. 8 :

 8 Figure A.8: Typical simultaneous HOM observations of VI and V2 before the respective encounters. The local time différence is small and eliminated by shifting VI data with respect to the V2 data. The portions DV1 (for VI), DV2 (for V2) and C (common observations) are graphically pointed out (brackets) and the respective quantities CV1 and CV2 are corresponding to these in Figure A.6c which is calculatedfor P = 7°. In this case, we did not consider the weaker émission for V2 near 20°CML (dashed line in the lower panel) as émission gap. The angular latitudinal séparation (6) between the two spacecraft was 4.3°.

  Figure A.11 for VI (upper panel) and for V2 (lower panel). The lowest frequency limits down to 20 -40 kHz were observed within 200 Jovian rotations of the respective encounters. Here we detected events in the vicinity of Jupiter which might not hâve been detected farther away because of the natural decrease of intensity (not normalized) with increasing radial distance.

  Figure A. 10: Example of VI postencounter data where the HOM émission shows a low-frequency extension down to 40 kHz. The HOM émission can undoubtly be distinguished from bKOM which occurs mostly near 200°CML.

Figure A. 12

 12 Figure A.12, and for V2 in Figure A.13. Linear interpolated data replace original data gaps in ail of the quantities. The HOM intensity is obtained by integrating the intensity values over the HOM frequency range.

  Figure A. 12: VI solar wind density, HOM low-frequency limit, and HOM energy for the VI preencounter portion of 1979.

  Figure A.13: Same as Figure A.12 but for V2 data in the preencounter period.

  décades. The kilometric and hectometric components were discovered later on by the Voyager 1 and 2 spacecraft which both encountered Jupiter in 1979. This paper focuses exclusively on the HOM component. Most of the studies of HOM concern the phenomenology and the beaming of the émission, and its dependence on solar wind.[START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] found that HOM is strongly beamed in a curved thin sheet centered somewhat north at the magnetic dipole equator with a beam width of about 10°. During their investigation they show that HOM is well organized when it is considered as a function of the magnetic déclination of the observer. The periodic variations of HOM in terms of central meridian longitude (CML) are due to the varying Jovicentric déclination of the spacecraft within one Jovian rotation.[START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF] confirmed the HOM beaming model and found additionally a local time dependence of the radi ation. Furthermore, they investigated the spectral properties of the HOM and DAM émissions and found a slight change in the occurrence probability of the radiation when switching from the HOM to the DAM frequencies.[START_REF] Lecacheux | Some spectral characteristics of the hectometric Jovian émission[END_REF] also investigated HOM data and found spectral characteristics which could not be explained by the variation of the Jovicentric déclination of the observer.

  (hereafter Paper 1) reexamined the latitudinal beaming of HOM by using pre-and postencounter data of Voyager 1 (VI) and Voyager 2 (V2) in 1979. In general, the results of[START_REF] Alexander | Latitudinal beaming of Jupiter's low frequency radio émissions[END_REF] were confirmed,but the beam width was found to be larger (10°-20°) depending upon the détection threshold. In addition, a source extension in altitude from 2 to about 7 Jovian radii (Rj) from the center of Jupiter was derived based on a HOM low-frequency limit approximately equal to 40 kHz. It was also found that the solar wind ram pressure and the HOM energy correlate with the HOM beam width and the low-frequency extension of the émission. The corrélation works in such a way that an enhanced solar wind ram pressure increases the HOM energy, widens the HOM beam, and activâtes lower frequency HOM sources farther away from the planet.As far as the polarization of the émission is concerned,[START_REF] Kaiser | Voyager spacecraft radio observations of Jupiter: Initial cruise results[END_REF] reported that the source of circular polarization of the HOM (left-hand source) is opposite to that of the INTRODUCTION 79 DAM (right-hand source). On the other hand,[START_REF] Alexander | Synoptic obser vations of Jupiter's radio émissions: Average statistical properties observed by Voyager[END_REF] reported that the fundamental polarization sense of the HOM may hâve been reversed after the encounter. This polarization reversai was not understood and was attributed to local time variations. It has now been established, in Paper 1 and by Ortega-Molina andLecacheux (1990b) that right-hand (RH) polarization is associated with the northern hemisphere and left-hand polarization (LH)

  7. No Io control of the HOM has been observed so fax.

  Figure B.l: PRA observations during the Voyager 1 closest approach and (bottom) sketched plot of the spacecraft trajectory (from[START_REF] Lecacheux | Ray tracing in the Io plasma torus: Application to the PRA observations during Voyager l's closest approach[END_REF]. HOM émission was not observed along the part of the VI trajectory near closest approach (full thick line). The feature occurring near 1100-1200 spacercraft event time (SCET) at higher frequencies and drifting in time to lower frequencies has been interpreted as upper hybrid noise and n+1/2 gyroharmonic waves. The magnetic latitude of VI is near 0°which usually favours strong HOM activity.

Figure B. 3

 3 Figure B.3 shows the cône half angle 90 as a function of / and L. Several field Unes with L between 6 and 60 are displayed for frequencies between 40 and 1000 kHz. The shell parameters

Figure B. 4

 4 Figure B.4 gives an example of the émission intensity, which is incoherently calculated, versus magnetic latitude 6 for sources on field lines L= 40, 20, 6, and for the parameters a = 1°, fc = /=1000 kHz, and the cône half angle 9 = 60°. For this set of parameters, only field lines with L=20 would provide an intensity maximum near the magnetic equator. From Figure B.3 we can see that for X=20 and /=1000 kHz, 90 is about 60°; thus one edge of the émission cône is directed parallel to the magnetic équatorial plane in the magnetic meridian and produces an intensity maximum there. The second edge produces a local maximum at 6 = 60°(Figure B.4).On the other hand, field lines with L=6 produce the highest intensity maximum near 6 « 35°w hich is in disagreement with the observations. Again, we see that the Io torus cannot be the source of HOM émission hollow cônes in this simplified model. From Figure B.3 we see that 0O is

  direction approximately coincides with the direction of center of the HOM émission beam at 2°m agnetic latitude. Each source is located at the apex of the corresponding émission cône. The cônes exhibit different initial wave normal angles 9 depending predominantly on the L value of the spécifie source field Une. The sheU parameter L is calculated from the centered dipole which is tüted by 9.6°with respect to the rotation axis. The magnetic north pôle intersects the Jovian surface at CML « 200°(northem hemisphere). Since the hectometer sources with / < 1000 kHz Ue farther away than 3 Rj from the planet, the parameter L derived from the dipole represents the real magnetic configuration with sufficient accuracy. Some examples for sources with arbitrary L are plotted in FigureB.5. We additionaüy show the second wing of the émission cône which is symmetricaüy placed to the first wing with respect to the magnetic field in the magnetic meridian plane. Sources which Ue doser to the magnetic equator (low L) are

Figure B. 5 :

 5 Figure B.5: Ray-tracing (/=150 kHz) for sources located at ///c=1.05 in the northern and Southern hemispheres, and labeled by the shell parameter L. The wave normal angle at each source is chosen such that the wave finally propagates parallel to the magnetic équatorial plane. The second wing of the émission cône not directed toward the magnetic équatorial plane is also shown. Although rays 5 and 6 start with different wave normal angles 9 from the same source (L=8.2), they finally reach the same outward direction because ray 5 is highly refracted by the Io torus.

Figure

  Figure B.6 exhibits our findings for /=300 kHz (top panel) and /=500 kHz (bottom panel) for two spécifie source locations, respectively, in Jovimagnetic coordinates. The ray paths are projected onto the CML=200°meridian plane. For both frequencies the Io torus significantly

Figure B. 7

 7 Figure B.7 shows the same situation as Figure B.6 but now for field lines £=10 and £=8 for

  Figures B.6 and B.7, the Io torus produces a shadow zone near the magnetic equator at small radial distances; therefore HOM should be visible only above and below the magnetic equator but not in the proximity of 6 = 0°. In fact, VI PRA observations onMarch 4, 1979March 4, (ro tation 1918)), near the VI encounter (r « 15 Rj) exhibit HOM émission centered at CML=200°w

  Figure B.6 near the magnetic équatorial plane. That is exactly what is observed for HOM in Paper 1 (Figure 9) although a higher frequency HOM component (942 kHz) was studied there. As was done similarly in Figures B.6 and B.7, we investigated source locations for the hectometric frequencies / =40, 150, 300, 500, 800, and 1000 kHz and searched for the critical angle 0«.,•* as a function of the £ parameter of the source field line for each frequency. The results are displayed in a frequency-0^,* diagram as shown in Figure B.8. The £ parameters of the source field lines are plotted corresponding to the calculated 0^,* dépendent on the frequency of the émission.

  Figure B.6: (left panels) Variation of the cône half angle 9 frora 90 to higher cône half angles including Ocrit for sources at L=22 and L=15. The rays for which 9 « 9crit are accentuated and reach nearly 90°f or £=22. For cône half angles greater than 9crn, the final ray direction falls out of the direction of the observed beaming near the magnetic equator. Examples are shown for (top) /=300 kHz and (bottom) /=500 kHz in the magnetic frame of reference at CML=200°.

Figure B. 7 :

 7 Figure B.7: (right panels) Same as Figure B.6 but for sources at field Unes L=8 and £=10. Rays originally emitted with a 9 nearly perpendicular to the local magnetic field are diverted away from the magnetic equator.

  For £=15 and £=30 we identified the foot points on the Jovian surface starting from 3 Rj (fc « 1000 kHz). The resuit is shown in Figure B.9 for the north and south polar régions, respectively. The dashed lines indicate the projection of the field lines £=15 and £=30 onto the surface. The hatched area indicates the location of foot points linked with possible HOM source field lines

  Figure B.10: Foot point locations which link the non-Io DAM (21.86 MHz) sources to the Jovian ionosphère in the northem hemisphere (from Maeda and Carr, 1988). The foot points at the start and end of a non-Io DAM storm are shown by the open and solid circles labeled with the same letter, respectively. The results are displayed for three cases: (a) 9 (cône half angle)=45°, (6) 9 = 55°, and (c)

Figure

  Figure C.l displays PRA observations for the indicated frequencies as seen by Voyager 1. Figure C.la was recorded during one Jovian rotation approximately 1 month (70 Jovian rotations) before the VI encounter (therefore labeled Rotation # -70) and represents a typical HOM profile as measured far from the planet (The spacecraft-Jupiter distance is indicated at the top). The émission peaks twice within one Jovian rotation at System III longitudes (or CML) ~60°-110°and CML « 300°-350°. The peaks are quite symmetrically placed with respect to CML ae 202°, where the northern magnetic pôle is tilted toward the spacecraft by 9.6°with respect to the rotation axis. At that longitude, a wide émission gap occurred where no significant HOM activity arised. The lower panel (Figure C.lb) was recorded 1 Jovian rotation before the encounter, and the émission topology has completely changed. First of ail, the émission gap seen in Figure C.la is mostly fllled by strong activity around CML= 200°, which is flanked by low activity zones centered on CML « 120°and CML « 270°, respectively. Finally, a range of activity also occurred around CML « 45°and CML « 330°.

Figure

  Figure C.l: Voyager 1 PRA observations in the hectometric frequency range as a function of System III longitude, radial distance, and Jovimagnetic déclination. The rotation numbers are counted with respect to the encounter. The vertical dashed Unes indicate magnetic equator crossings of the spacecraft. RH-polarization is indicated by dotted Unes and LH-polarization by full Unes, (a) Observations at large distances from Jupiter. Note the absence of émission at higher magnetic latitudes, (b) Observations just before the VI encounter. Note the absence of radiation near the magnetic equator.

  Figure C.2 where we display the évolution of the HOM hollow cônes calculated by ray-tracing. For HOM, the Io torus behaves like a divergent lens which prevents the rays from entering low magnetic latitude régions near the planet but, in turn, focusses the radiation near the magnetic équatorial plane farther away from Jupiter. We analysed this phenomenon in more detail by plotting the extension of the shadow zone (as determined in Figure C.2) projected onto a meridian plane in Figure C.3. Two different wave normal angles are considered, namely 9 = 80°(full line) and 9 = 70°(dashed dotted line).

  ofBagenai and Sullivan, 1981). The Divine and Garrett model is therefore the best analytical model available at présent time. However, a new Io torus model is in progress(Bagenal, private communication) which is possibly somewhat larger in vertical extension. This new model may therefore improve our fit without assuming a somewhat enhanced torus density.

  ) around the source magnetic field line.Contrary to the study of Gulkis and Carr who elaborated a straight line propagation from the radio source to the spacecraft, we performed a ray-tracing study since the ray paths are considerably altered when passing in the vicinity of the Io-torus. For one given subsource, we traced 120 rays, 40 for each of the three cône half opening angles (9 = 70°, 75°, 80°). For a given 9y the whole émission cône generally appears as a distorted trace when projected onto a sphere surrounding Jupiter at a given distance of observation. If the point of observation lies within the trace calculated for 9 = 75°and one of those calculated for 9 = 70°or 9 -80°, the actual cône half angle of the ray which intersects the point of observation is determined by linear interpolation from the angles 9 of the corresponding traces. The interpolated 9 is then used for the calculation of f(9) via Equation (C.l). If the observer is located outside the région defined by the three traces on the sphere, Equation (C.l) becomes zéro. Since the subsources are supposed to radiate independently, the calculated intensity profile for a given point in space consists of the algebraic sum of the contributions of the subsources, corrections being made for the varying spacecraft-subsource distance. For the intensity calculation, we took 9 equally spaced subsources in longitude (40 degrees séparation !) at each hemisphere instead of a continuous distribution. To overcome the error which arises from this assumption we calculated the average intensity along 40 degrees in magnetic longitude centered around the C.5. MODELING OF THE HOM-PROFILE actual point of observation. Furthermore, ail effects of focussing and diffraction of radiation are included throughout the détermination of the final intensity profile. The assumption of equal activity along the entire radio ring in the auroral zones does not require detailed knowledge concerning the question of whether the sources rotate with the planet or are fixed in local time.

  Paper 1. The modeled conical émission pattern that Voyager would hâve observed during its trip through the Jovian magnetosphere is shown in Figure C.4 for two représentative rotations. In the upper panels of Figures C.4a and C.4b are displayed the traces of the HOM émission cônes on a sphere surrounding Jupiter at the actual Voyager 1 distance. The Voyager trajectory occurs as a sinusoidal curve when plotted against magnetic latitude. The plot sequence for Rotation # +1 shows the shadow zone which causes the émission gaps when Voyager 1 was very close to the planet. The calculated intensity profile is plotted below and will be compared with the observations in the next section.

Figure C .

 C Figure C.4b exhibits the situation for Rotation # -6 which is représentative for observations far from the planet. The area where the shadow zone is apparent during Rotation # +1 is replaced by a sharply beamed, strong émission in the vicinity of the magnetic equator arising from the superposition of many émission cônes. The variation of the beam with respect to the magnetic dipole equator is predominantly due to the slight offset of the Io torus with respect to the magnetic équatorial plane. The close correspondent of our modeled results to those obtained by earlier statistical studies can be demonstrated by comparison of Figure C.4b with Figure 1 (occurrence probability vs. CML for VI observations) and Figure 6 (sketched plot of HOM beam) of Alexander et al. (1979) and also with Figure 1 of Paper 1. Thus, our model unambiguously accounts for the beaming at hectometer wavelengths. Assuming that the rays emanating from the northern hemisphere exhibit RH-polarization and those from the Southern hemisphere LH-polarization, the HOM beam should show a rather complicated and puzzling polarization behaviour, which is exactly what was observed (see e.g. Alexander et al., 1981). When considering the observations near the encounter (Figure C.lb), RH-polarization is associated with positive magnetic latitudes and LH-polarization with négative magnetic latitudes, and this is predicted as shown in Figure C.4a. However, we note that a polarization reversai often occurred at low frequencies (Figure C.lb). This polarization reversaihas not yet been understood.

  Figure C.5c) at DOY 64.5 is not interpreted as HOM. Shortly after CA (Figure C.5d), the first observed lack of émission (around DOY 64.8) is accurately predicted. The other lack of émission near DOY 65 occurred about 90 minutes before the modeled one. We notice the symmetric behaviour of the radiation pattern with respect to the encounter by comparing Rotations # -1 and # -f 1. Because of the high temporal variability of HOM mainly due to external control, the profiles are normalized for each rotation separately. This is justified by the fact that our model can, of course, only simulate stationary émission.Although the overall simulation is fax from being perfect (we do not expect otherwise, because of the simplifications made in our assumptions) the major structures are explained very well, suggesting that the modulation of HOM can be associated with a source located at high latitude auroral zones.The results in Figures C.3, C.4 and C.5 were calculated for a set of parameters ///c, 0, A0, the torus density model p(r), and the value L of the source locations. The first three parameters were selected to be in agreement with the cyclotron maser mechanism which is now the most promising theory for radio émission. The Io torus density model was determined by in situ observations, but it is an average model, and it suffers (very likely) temporal fluctuations. Therefore, we hâve verified how that parameter may influence the results. The only free parameter is the L shell of the source field fines. In Paper 2 we hâve shown, that 15 < L < 30 accounts for the observations for nearly perpendicular 0. On the contrary, as found in Paper 2, for sources at lower magnetic latitudes (e.g. £=10) the observations could no more be fitted for nearly perpendicular 0. Thus, when maintaining large wave normal angles (consistent with the CMI) the accurate fits in Figures C.4 and C.5 would vanish. Here we hâve used £=20 and shown that the modeled émission is

  Figure D.4: Semimajor axis b and d (distance of the center of the ellipse from origin in velocity space) for values f/fc and fp/fe inside the separatrix. Note the change in scaling for 0 = 80°.

3.

  No refraction of the propagating wave 4. fp/fc -constant along ray path near the source 5. The instability (dF/dv± > 0) is caused by a loss cône superposed by a parallel electric field 6. No wave absorption after phase of amplification 7. u>i is taken to be constant when the corresponding résonant ellipse is lying within the space of instability 8. l\ is the point where the résonant ellipse of the corresponding wave enters the unstable région and is the point where the semimajor axis b exceeds that région (Figure D.5, ellipses 1 and 2).

  Figure D.5: Loss cône instability used throughout our analysis. The loss cône angle a is typical for a source located between 2 and 3 planetary radii. Positive growth is assumed for waves whose résonant ellipses hâve access to the unstable région. The two ellipses mark entrance (1) and leave (2) from the instability (corresponding to Yi and Yi in Figure D.6). For AV (potential différence between the radio

  Figure D.6: Part of the f/fe-fp/fc space extracted from Figure D.3. The curves represent the sépara trices Sg=7o and Sg=go, respectively. An example of the ray path in this space serving for the calculation of T is visualized for fp/fc =0.1. At the point Y\ which corresponds to l\ in real space, the respective résonant ellipse entera the range of instability (corresponding to ellipse 1 in Figure D.5). Then the semimajor axis b increases while the wave travels from the separatrix into régions of decreasing B (increasing f/fc) and at a given point Y2, b exceeds the région of instability (see ellipse 2 in Figure D.5). For each value fp/fc, two régions for possible amplification exist near Sg which are denoted &i (branch 1) and 62 (branch 2). The wave particle interaction time T is largest for a given 9 at plasma conditions within the shaded areas just below the vertices of Sg (discussed later on in Figures D.8a, D.9a).

Figure D. 7 :

 7 Figure D.7: Geometry used for the dérivation of the interaction time T. / deviates from r by the angle 9, B is assumed to be a function of r, and gradB\\B.

Figure D. 8 :

 8 Figure D.8: Normalized interaction time T (a), interaction length L (b), and refractive index at li (full line) and at I2 (dashed line) for 9 = 70°(c) at ail possible values fp/fc along the separatrix Sg=70-The peak values for T and L are found for fp/fc just below the vertex of S9-70 (compare Figure D.6).

  Figures D.8a and D.9a that the values /p/fc most favourable for amplification (maximum of T)

  occurs below the gyrofrequency. Propagation effects when leaving the auroral arc and entering the neighboring cold plasma may therefore cause a change of the behaviour of the radiation. y = un /<= = -Z7T 771 e /p: électron plasma frequency, /c: électron gyrofrequency, e: unit charge, Ne: électron number density, B: magnetic flux density, me: électron mass, e0: permittivity constant. For a wave with frequency /, n is a function of JVe, B, and the direction t? of the wave normal with respect to B. The direction of the wave normal and the associated ray (direction of energy flow) are in general different, because the refractive index n dépends on the direction of the wave normal with respect to B.

E

  Figure E.l: Cross-Section of refractive index surface by a plane containing the direction of the magnetic field. CX and CA are the normal and tangent, respectively, at the point C. The ray direction is therefore perpendicular to the refractive index surface.

  Figure E.2: Cross section in the magnetic meridian plane of (a) the refractive index surface, and (b) the ray surface, for whistler mode waves. Note the reciprocal properties of these surfaces.

  ) is again the light velocity c and we obtain nx(E.19) Equations (E.16) and (E.19) mathematically describe that the ray direction is parallel to the normal to the refractive index surface G, and that the wave normal direction is parallel to the normal to the ray surface for a given point x,y,x in space. The refractive index surface G may be obtained by using the Appleton-Hartree formula (Equation E.l). The construction of F (Equation E.18) is more complicated. It is therefore convenient to express the ray surface F in terms of G.

  16) and (E.23) are called together the "ray équations". These are the relevant équations which détermine the propagation of rays in a medium. Before discussing them in detail, we shall find some important relations between the refractive index surface G and the ray surface F. We add Equations (E.21) and (E.2224) vanishes because xnx + ÿny + znz=Vr • n= c/(n cos a) n cos a -c-con3téquations are derived when setting dF/dy = dG/dy = dF/dz = dG/dz = 0. Now let us combine Equations (E.25), (E.23) and (E

  (r,0,0,nr,nfl,n^) = \Jnr + n2e + n\ n(r,^,<^,nrîn^,n^) (£.31) nr, n$, and n# refer to a polar coordinate System A,<p which is centered on the point r,9,<f>. The components of n are nr = ncosy? ng = n sin <p cos A = n sin ip sin À (E.32) Equations (E.29) and (E.30) are the ray équations in spherical polar coordinates. They are the basic équations for our purpose i.e. to show how to find the ray path for any given modeled magnetosphere where the magnetic flux density B and the électron number density Ne are known at each point in space. Equations (E.29) are used to détermine the ray direction given by f, 9, (f> for a given point Po(ro,0o,0o) in space and a given wave normal direction nr0,ng0yn^,0. These two ingrédients are initially required to calculate the refractive index surface G via Equation (E.31). By taking an incrémental step At in time in the obtained ray direction, a new point in space P\(ri = r0 + rAt, 9\ = 90 + 9At, <t>\ -(f>0 + <j>At) is found. According to Snell's law, the wave normal direction has generally changed when the wave propagates from PQ to

  équations contain the dérivatives dn/dr, dn/dd (do not confuse with dn/dti), and dn/d<f> which need further investigation. They can be written

Table A

 A the first section is centered at 630 Rj (Rot. number 1812) and the extension of the section is represented by 60 rotations centered on Rot. number 1812. The results obtained from this first section are représentative of the beaming at 630 Rj before encounter for VI. Similarly, we defined 8 sections for VI and 7 for V2. Sections close to the encounters were chosen to be shorter because of the rapid variation of the distance to Jupiter near the encounter. AU of the 15 sections are summarized in TableA.l. Sections 8, 9, and 15 represent data recorded at larger distances from Jupiter; they are discussed later on in the text.

	Voyager 1/section			1	2	3	4	5	6	7	8
	Voyager 2/section	9	10	11	12	13	14				15
	Dist. to Jupiter (Rj)	-1120	-756	-630	-420	-210	210	420	630	756	1120
	Extension (Jov. rot.)	200	20	60	60	40	40	60	60	20	200

.l: Distance and extension of the 15 investigated sections mentioned in the text.

A.2.3 Results

Hectometer latitudinal beaming

  ). The components of the refractive index occur only in the combination ni + + ni = n2. The refractive index surface may then be writtenIt can be shown that the constant of proportionality in Equation (E.14) is the light velocity c[START_REF] Budden | Radio Waves in the Ionosphère[END_REF]. Thus, Equation (E.14) becomes

	Vi	Tlxi Hyi ^z) -	n(x,y,z,nx,ny,nz) yjn2+n2 + n2	(E.15)
		dG	ÔG	.	ÔG
		Cdnx y °dny Z Cdnz	(E.16)

  Let us study now the dérivatives dn/dnry dn/dng, dn/dnj,: They can be written Finally, the quantities dp/dnT, dp/dng, dp/dn#, dX/dng, and dX/dn$ are obtained by différ entiation of Equations (E.32) using n2 = n2 + n2e +

	dti	1
	d\ = ^isin<^sin^sin(^-^)]
	dtp	1	n2-n2
	dnr	sin p	n3
	dtp	1	n2 -n g
	dng	cos p cos A	n3
	dtp	1	n2 -n2d
	nj,	cos p sin A	n3
	dX		1	n2 -ng
	dng	sin p sin A	n3
	tary magnetospheres
	dX	1	ri2 -n2d
	By performing différentiations with respect to nr, n$, and n<j, in Equations (E.29) we get n^sin p cos A n3
	r	\ (	dn\
	Z ~VT ~n~far)	(E.33)
	è	1 /	dn \
	ê = ^r-n^)
		1		dn
				-n-
	c	r sin On2 \	dn$ I
		dn	dn dd dtp	(E.34)
		dnr	di) d<f> dnr
	dn _ dn / dd d<p	d'd d\ \
	dng dd \d(pdng ^dXdng)
	dn _ dn ( dd dip	dd d\ \
	dnj, dd \d1pdn4 dXdn4 J

CHAPTER 3. RAY-TRACING IN THE JOVIAN MAGNETOSPHERE: HOM SOURCES

Acknowledgments

First of ali I must express my thanks to my superviseurs Dr. Yolande Leblanc (Observatoire de Paris) and UD Dr. Helmut 0. Rucker (Space Research Institute of the Austrian Academy of Sciences) for their overall support and for contributing useful ideas during the development of this work. I am also grateful to my colleagues of the "groupe decametrique" at the Observatoire de Paris for their generous hospitality and many discussions on the subject of radio astronomy.

In particular, I am grateful to Philippe Zarka, Alain Lecacheux, Sophie Dubus, Jean-Luc Anton, Mohammed Boudjada, and Patrick Galopeau for the kind introduction in the "French way of life".

Appendix A

Jovian hect omet rie radiation -Beaming, polarization, source extension, and solar wind control Abstract From observations of the Jovian radio émission at hectometric wavelength (HOM) obtained by Voyager 1 (VI) and Voyager 2 (V2) in 1979, the beaming at three selected frequencies /=1326 kHz, 942 kHz, and 558 kHz is determined. We find that the total beam width is between 10°and 20°depending on the normalized (to earth) détection threshold. The beam center is found to be situated at about +1.6°magnetic (dipole) déclination. On the nightside the beam width is a few degrees (« 4°) narrower compared to the dayside. We further provide evidence that the émission is not uniform in System III longitude (CML). We establish that right-hand polarization is associated with the northern hemisphere and left-hand polarization with the Southern hemisphere, without reversai from dayside to nightside observations. From the analysis of the frequency limits of HOM, we détermine a source extension from 2 Jovian radii (Rj) out to more than 6 AEj, by assuming an émission close to the R-X cutoff frequency. The beaming results, and the HOM low-frequency limits are compared with the solar wind parameters. We find that increases in the solar wind density and/or pressure are well correlated in time with the lowest frequency limits of HOM and the largest beam widths. A strong corrélation is also obtained between those two parameters and the HOM energy. This supports the idea that a high density solar wind stream at Jupiter enhances the HOM energy output, extends the source régions to higher altitudes on auroral field Unes, and widens the HOM beam to higher latitudes.

A.l Introduction

Observations obtained from the Planetary Radio Astronomy (PRA) experiment [START_REF] Warwick | Planetary radio astronomy experiment for Voyager missions[END_REF] show that the Jovian radio spectrum consists of 4 distinct components: a decameter wavelength component (DAM), a hectometer wavelength émission (HOM), and two kilometer wavelength components (KOM), namely the broadband (bKOM) and the narrowband (nKOM)

Appendix B

Source location of the Jovian hectometric radiation via ray-tracing technique Abstract Ray-tracing using realistic magnetic field and plasma models has been performed to locate the Jovian hectometric radiation (HOM) sources. To consider only a few possible source locations, we hâve assumed that the radiation mechanism is the Cyclotron Maser Instability (CMI), and taken into account the characteristics of the HOM including the recent results by [START_REF] Ladreiter | Jovian hectometric radiation -Beaming, polarization, source extension, and solar wind control[END_REF] (hereafter Paper 1). The émission is assumed to escape from the planet in the extraordinary wave mode within a thin beam of hollow cônes whose apexes are distributed uniformly in longitude at the northern and Southern hemispheres at altitudes where the gyrofrequency fc is iess but nearly equal to the observed wave frequency. The rays are traced from possible sources located at f/fc=1.05 and labeled by the dipole shell parameter L. For each source, we hâve determined the emergence wave normal angle dcrit above which the rays no longer travel within the HOM émission beam nearby the magnetic equator (Paper 1). We show that the HOM sources cannot be located on field fines within the Io flux tube. However, wave refraction due to the Io torus plays a crucial rôle for the propagation and beaming of the waves toward the magnetic equator. It is found that HOM sources located at field fines 15 < L < 30 agréé best with the observations when assuming that the cône half angle of émission is about 70°-90°with respect to the local magnetic field. Thus, the source is associated with the tail field aurora where the magnetic field fines connect the polar région to the Jovian magnetic tail and is extended in altitude from 2 to 7 Jovian radii (Rj). Our results explain in detail the radio phenomenology of the hectometric radiation, in particular the strong latitudinal beaming, the lowest observed frequencies (ae 40 kHz), the solar wind control, the absence of HOM émission when Voyager 1 was within the Io torus, and the absence of Io control on the HOM. The results are discussed in the context of the other Jovian radio sources, namely the sources of the non-Io decametric (DAM) and kilometric (KOM) émissions.

Distance {Rj) Sources at field Unes L < 10 hâve a very small cône half angle Q0 which even approaches 0°for the lowest HOM frequencies (40 kHz).

only a small varying function of / for high L parameters when excluding the lowest frequencies.

Therefore a variation of the value / in Figure B.4 would not dramatically change the topology except for the lowest frequencies (/ < 400 kHz). Furthermore, when varying the sheet half thickness a, the intensity peaks are nearly unchanged in magnetic déclination S. At last, when changing 6 to higher values, field Unes with higher L will successively fulüll the requirements (intensity peak near 6 = 0°). We hâve further demonstrated that the intensity maxima of the radiation in terms of magnetic decUnation coincide with the directions of the wings of the émission cônes in the meridian plane which contains the radio source. Therefore the subséquent ray-tracing will consider only rays in the meridian plane. We notice that the shapes of the three curves corresponding to the respective émission cônes are different because a uniform intensity distribution along the émission cônes does not translate into a uniform distribution in terms of magnetic latitude.

B.3.2 Discussion of results

Although we started with oversimpüfied assumptions (no wave refraction along its propagation, no refraction at the source), we can eUminate the field Unes with L < 10 as possible source study including alI effects of refraction which a ray suffers during its propagation from the source into free space. The computer program is based on the [START_REF] Stix | The Theory of Plasma Waves[END_REF] cold plasma formulation of the refraction index. The [START_REF] Haselgrove | Ray theory and a new method for ray tracing[END_REF] first-order differential équations (canonical ray équations, see [START_REF] Budden | Radio Waves in the Ionosphère[END_REF] are solved numerically. At a given point in space, the program calculâtes a refraction index surface for R-X mode waves based on a B-field model and a realistic plasma model. Next, the program takes an incrémental step perpendicular to the surface of refraction index; this dénotés the direction of the group velocity and energy flow, and is identical to the ray direction. Then, a new point in space is found where the refraction index surface eau be calculated and the steps ace repeated. The wave normal direction changes according to Snell's law when the wave travels through the magnetoplasma. The directions of the ray (energy flow) and of the wave normal (perpendicular to planes of constant phase) are very similar when the refractive index n does not differ very much from unity, but a substantial différence occurs when n approaches 0 (at the R-X cutoff frequency).

B.4.2 Magnetic field and plasma models

The computed ray paths in the program are dépendent on the involved magnetic field and plasma models. For the description of the Jovian magnetic field, we hâve taken the 0-4 model [START_REF] Acuna | The main magnetic field of Jupiter[END_REF]) which provides spherical harmonie coefficients which correspond to the dipole, quadrupole and octopole terms. The influence of the Jovian current sheet on the magnetic field, described by [START_REF] Connerney | Modeling the Jovian current sheet and inner magnetosphere[END_REF], is also included, but the effect on waves at hectometric wavelengths remains, although it is very small. A realistic plasma model given in analytical expressions is taken from [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]. In their analysis they give density and energy models not only for charged particles in the Io torus, but also for the remaining magnetospheric régions up to 170 Rj. As we ray trace radiation at hectometric wavelengths we do not need to include an ionospheric model and the oblateness of Jupiter as was done by [START_REF] Hashimoto | A theory of the Io phase asymmetry of the Jovian decametric radiation[END_REF]. It is further assumed that the density and magnetic field gradients are small compared to the wavelength, so that no partial reflection occurs. Moreover, the électron température is assumed to be sufficiently low to allow for the cold plasma dispersion relation.

B.4.3 Génération mechanism of the radiation

Before starting our ray-tracing calculations, one must introduce some restrictions for the wave propagation at its source due to a distinct génération mechanism. We hâve considered the Cyclotron Maser Instability (CMI) by [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF]. This theory is able to explain in detail most of the properties of auroral radio émissions from the earth (AKR), Jupiter (DAM), Saturn (SKR), and also possibly from Uranus (UKR). [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] assumed that AKR is generated by the résonance of upgoing loss cône particles with the upper frequency branch of the extraordinary (R-X) mode. For simplified conditions, they were able to dérivé an expression for the growth rates of R-X and also L-0 waves and found that R-X waves are favoured over L-0 waves. Moreover, the theory predicts an initial wave normal angle 9 with respect to the magnetic field which is primarily dépendent upon the distribution of suprathermal électrons precipitating in the auroral zones. This angle 6 is roughly perpendicular as confirmed by in situ measurements in the earth's magnetosphere. Since the pioneer work by Wu and Lee, many B.3. In contrast, assuming that 9»9crit, we do not need to introduce a substantial decrease of 9 when / decreases to the lowest hectometric frequencies (Figure B.8). For 9»9crit the rays axe not initially parallel to the magnetic équatorial plane. It is the passage near the Io torus that refracts the rays in the required direction and produces the sharp latitudinal beaming for HOM.

Moreover, the assumption 9%9crit is strongly supported by the fact that HOM was detected near the torus when the Voyager 1 -Jupiter distance was larger than 6-7 Rj. This is also shown in In contrast, an émission with 9 -90 for which the waves axe not influenced by the torus could not be observed by VI within a large period near the closest approach.

During our ray-tracing analysis, we could see that for / « 600 -700 kHz, the waves axe not entirely refracted parallel to the magnetic équatorial plane for 9^9^. This is caused by the fact that in the Io torus model, the peak density is not higher than a corresponding plasma frequency of « 600 kHz. However, it has also been reported that VI probably did not pass through the région of peak density, and that V2 did encounter higher densities outside the torus than did VI; it is not inconceivable that the plasma frequencies in the torus could exceed 1 MHz (cf. [START_REF] Jones | Radio wave émission from the Io torus[END_REF]. This is further supported by the fact that bKOM (which is probably generated at the torus) is sometimes active up to 1 MHz. If this is the case, HOM frequencies of the order of 1 MHz are also highly refracted when traveling in the proximity of the torus.

We were able to verify that the results obtained for 90 in Our source location for a given HOM frequency on a distinct field line labeled L is now only dépendent on the cône half angle 9. When assuming a distinct 9, the shell parameter L for which 9^is greater but neaxly equal to 9 can be derived from Figure B.8. The cône half angle 9 therefore plays a key rôle in determining the source location. It dépends predominantly on the energy of the suprathermal électrons which axe responsible for the génération of the auroral radio émissions and on the ratio /p//c at the source. [START_REF] Staelin | Character of the Jovian decametric arcs[END_REF] reported that électrons with a longitudinal (with respect to the magnetic field) velocity vjj of 0.1 c (c = speed of light) and a total velocity v of 0.25 c (« 15 keV) may provide an émission cône half angle of 9 -71°. He estimated V|| from the drift of a sériés of Jovian millisecond S-bursts downward in frequency.

More recently, [START_REF] Horanyi | The précipitation of energetic heavy ions into the upper atmosphère of Jupiter[END_REF] pointed out that energetic électrons with energies in excess of 10 keV precipitate into the upper atmosphère of Jupiter to explain the observed Lyman band émissions. These energies would also provide cône half angles somewhere between 70°and 80°.

In order to model Jovian decametric radiation arcs, [START_REF] Menietti | Jovian decametric arcs: An estimate of the required wave normal angles from three-dimensional ray tracing[END_REF] found that hollow émission cônes axe able to describe the spécifie arc pattern provided that the cône half angle 9 is vaxied with frequency. They found 9 to be « 80°for the arc vertex frequency which is situated at about 10 MHz, and 9 decreases down to about 70°at the high-frequency (« 30

MHz) and at the low-frequency (« 2 MHz) extension of an arc. They further showed that 9 performed by [START_REF] Maeda | Auroral origin of a component of Jupiter's decametric radiation[END_REF] in their analysis is used. The authors suggest the source région to be situated at field lines connecting the UV auroral zone which is distinct from the tail field aurora except for a short interval in System III longitude centered at « 140°CML. Despite the fact that it is difficult to provide électron energies sufficiently high to account for cône half angles of about 45°when /p//c at the source is very low, it is interesting to note that the authors dérivé the source to be at the tail field aurora when they take 9 to be 55°. From our results we therefore cannot exclude the possibility that HOM is the low-frequency extension of non-Io DAM as suggested by [START_REF] Genova | Voyager and Nancay observations of the Jovian radio émission at different frequencies: Solar wind effect and source extent[END_REF]. However, HOM shows a spectral émission peak near 1 MHz [START_REF] Brown | Spectral behaviour of Jupiter near 1 MHz[END_REF], a fact that should also be kept in mind to make the link between non-Io DAM and HOM.

A further interesting question concerns a possible link between broadband kilometric radiation (bKOM) and HOM. From our investigations, we are able to state that bKOM cannot be the lowfrequency extension of HOM, since bKOM occurs statistically in the CML range of 170°-300°a

nd HOM in the remaining CML range. Moreover bKOM activity tends to cover a larger CML interval at the lower frequencies, in contrast to the HOM observations. Therefore bKOM sources at the Io torus as suggested by [START_REF] Jones | Radio wave émission from the Io torus[END_REF][START_REF] Jones | Io plasma torus and the source of Jovian kilometric radiation (bKOM)[END_REF] and [START_REF] Jones | Source of broadband kilometric radiation[END_REF] are favoured over an auroral source région.

Finally, one should compare the Jovian hectometric émission with the other planetary auroral émissions. In a way similar to HOM, a solar wind control was established for the Saturnian kilometric radiation (SKR) [START_REF] Desch | Evidence for solar wind control of Satura radio émission[END_REF][START_REF] Desch | The relationship between Satura kilometric radiation and the solar wind[END_REF]) and for the terrestrial kilo metric radiation [START_REF] Gallagher | Corrélations between solar wind parameters and auroral kilometric radiation intensity[END_REF]; moreover, for both Saturn and the earth, the solar wind influence is stronger than for the Jovian HOM. Furthermore, ail of these planetary émission components exhibit a local time dependence.

The exact source locations of SKR axe well established [START_REF] Kaiser | Voyager détection of nonthermal radio émission from Saturn[END_REF][START_REF] Kaiser | Saturnian kilometric radiation: Statistical properties and beam geometry[END_REF][START_REF] Kaiser | Saturnian kilometric radiation: Source locations[END_REF][START_REF] Lecacheux | Source location of Saturn kilometric radio émission[END_REF] to be situated at magnetic field lines connected with the UV aurorae [START_REF] Sandel | P p pf ylG/j_ 3o 6 154 and S. Linick, Extrême ultraviolet observations from the Voyager 2 encounter with Saturn[END_REF] and polar cusp [START_REF] Behannon | Saturn's magnetic tail: structure and dynamics[END_REF]; thus the solar wind has direct access to the radio source. For the earth, it is also well-known that the source is located in the auroral zones [START_REF] Gurnett | The earth as a radio source: Terrestrial kilometric radiation[END_REF][START_REF] Gurnett | On the polarization and origin of auroral kilometric radiation[END_REF]. The source locations of HOM in the Jovian tail field auroral régions complété the analogy to TKR and SKR.

Like these émissions, HOM sources are active along a large range of altitudes on auroral field To model the Jovian hectometric radiation (HOM), we performed three-dimensional ray-tracing at a frequency of /=500 kHz. The source locations are assumed to lie along magnetic field lines L-20 as determined by Ladreiter and Leblanc (1990a). Furthermore, they axe distributed uniformly in longitude at magnetospheric heights, where the cyclotron frequency is less but nearly equal to the wave frequency. The émission is beamed at large angles (70°-80°) with respect to the magnetic field and propagates in the extraordinary (R-X) mode. Our study can account for the major characteristics of the HOM radiation as observed by the Planetary Radio Astronomy (PRA) experiment aboard Voyager 1 and Voyager 2 during the encounter period and at large distances from the planet. Thus, geometrical effects are taken into account.

The modeled radiation pattern reveals the existence of a shadow zone at the magnetic (dipole) équatorial plane extending to about 20 Jovian radii (Rj), which was actually observed by both

Voyagers. The results from our ray-tracing analysis account for the strong latitudinal beaming of the radiation, observed at large radial distances from Jupiter, as well as for the polarization properties. Moreover, the modeled intensity profiles, compared with observations in the vicinity and far from Jupiter, show a remarkable agreement. However, a better fit to the observations is obtained when the Io torus électron density (from [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]) is enhanced by 15 %. This study confirms that the HOM source locations are located along open magnetic field lines with footprints in the tailfield auroral ovals in both hemispheres. We suggest that HOM is the low-frequency extension of non-Io DAM, since the observed spectral peak of HOM near 1 MHz could be produced by the focussing of the radiation due to refractory effects of the Io a few words about the ray-tracing procedure used throughout this paper. The procedure of raytracing was described in detail in Paper 2, so only a short review is given here. The program is based on the numerical intégration of Haselgrove's first order differential équations [START_REF] Haselgrove | Ray theory and a new method for ray tracing[END_REF][START_REF] Budden | Radio Waves in the Ionosphère[END_REF] in order to détermine, step by step, the final ray path from the radio source throughout the Jovian magnetosphere. The ray équations require analytical magnetic field and plasma models which are provided by [START_REF] Acuna | The main magnetic field of Jupiter[END_REF] (O4 model), Connerney et al.

(1981) (distortion of magnetic field by plasma sheet currents), and [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF] (plasma model, including Io torus).

C.3.2 HOM source location and émission mechanism

The HOM sources and propagation properties used in our présentation were determined in Paper 2. Thus, we assume that the sources are located on L-20 (to take an intermediate value between L=15 and L=30) and are distributed uniformly in longitude at both hemispheres. For L=15 (T=30) somewhat smaller (larger) wave normal angles would be required than for L-20 in order to successfully simulate the HOM latitudinal beaming (Paper 2, Figure 8). For the sake of simplification, we hâve restricted ourselves to the detailed investigation of radiation at /=500 kHz, but the trends for other frequencies will also be shortly discussed. For L=20 and /=500 kHz, the critical emergence angle above which the HOM observations are no longer accounted for, is about 86°(see Paper 2, section 4.4 and Figure 8). Our selected value for 0 should therefore be less than 86°. We hâve used an emergence angle 6 = 75°, and a cône half-width AO = 5°.

The two values are justified if we consider the cyclotron maser mechanism which predicts nearly perpendicular emergence angles [START_REF] Wong | Electromagnetic cyclotronloss-cone instability associated with weakly relativistic électrons[END_REF], and a small cône half-width (Le Queau, 1988) when the source is at a level where /p//c is very small, which is the case for HOM (/p/ fc < 0.01, see Paper 2). Finally one has to introduce the ratio ///c at the radio source (/c being the électron gyrofrequency). We select f/fc = 1.02 in accordance with the CMI which predicts ratios ///c nearly equal but slightly greater than 1. The réfraction of rays near the source dépends on the assumed ratio f/fc and cône half angle 0. In our case, réfraction of the rays at the source does not occur down to f/fc « 1.01 for an R-X mode wave; therefore the results are not crucial to variations of f/fc provided that f/fc > 1.01. This can also be seen in Paper 2 were we used f ! fc-1-05. However, the actual value for HOM is not known and may be anywhere between ///c=l-01 and ///c=1.05. In addition, the major features of the results are found to be not considerably affected by the spécifie choice of A0 if 1°< AO < 10°.

On this point, we should emphasize that we do not perform a parameter study by varying source parameters in order to fit the observations. Instead, we selected a set of parameters from Paper This is remarkably good if we know that the modeling of the shadow zone is a joint conséquence of the beaming properties, the source locations and the refractive effects of the Io torus.

It is noteworthy that these conclusions can be extended to the higher frequency HOM component.

Several tests (not shown) for higher frequencies yield similar results, but the torus density had to be enhanced more substantially. To match the observations at /=1000 kHz, the actual Io torus density model [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]) must be multiplied by a factor of 2-3. In fact, it suffices to enhance the density only in the inner région of the torus, since the higher frequencies are able to enter deeper in the Io torus. Furthermore, the shadow zone is found to be narrower for the higher frequency range of HOM which also agréés with the observations.

Since Voyager 2 encountered higher densities outside the Io torus than did Voyager 1 [START_REF] Jones | Analysis of Jovian kilometric radiation simultaneously observed by Voyager 1 and Voyager 2[END_REF]), the plasma model by Divine and Garrett (obtained from VI observations) may represent a low limit of the actual torus density. This is further supported by the fact that the broadband kilometric radiation (bKOM) which is most probably produced at the Io torus may by active up to 1 MHz at times [START_REF] Jones | Radio wave émission from the Io torus[END_REF][START_REF] Jones | Io plasma torus and the source of Jovian kilometric radiation (bKOM)[END_REF][START_REF] Jones | Source of broadband kilometric radiation[END_REF] suggesting a torus peak density that is enhanced by a factor of three to the présent one.

We selected VI data for a detailed analysis because it approached Jupiter much doser than did V2. However, also the V2 observations (espedally on the dayside) also reveal the existence of a shadow zone as found for VI. For /=500 kHz, the shadow zone for V2 extends at least to 20Rj

in the magnetic équatorial plane, but we are not able to State unambiguously that the shadow zone for V2 is larger than that for VI.

In our analysis, we introduced the torus density model by [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF] who used assumptions about the ion températures reported by [START_REF] Bagenal | Direct plasma measurements in the Io torus and innner magne tosphere of Jupiter[END_REF]. These ion températures were revised later on by [START_REF] Bagenal | Revised ion températures for Voyager plasma measurements in the Io plasma torus[END_REF] because of an error made in the earlier analysis. Consequently, the Divine and Garrett model should also be revised. However, by the ratio ///c at the source to the normalized (to c) parallel bulk velocity /3\\0 of the insta bility (characteristic for an électron distribution function) via the équations cos(0) = /3||0 and ///c = (1 -/?||0)"1/2. During this investigation we considered the loss cône and holelike in stability to be responsible for amplification. Both of these régions exhibit a relatively small perpendicular energy. We found that for (3\\0 corresponding to 1-10 keV, 9 is found to be nearly perpendicular with respect to the magnetic field and is decreasing when /?||0 increases. The wave frequency is slightly above the gyrofrequency, but is substantially away from the R-X cutoff; thus, the refractive index is near unity at the radio source. No strong refraction along the ray path is therefore expected for /p//c << 1. The résulta are highly relevant for the lower frequency auroral émissions of Jupiter (low frequency DAM and HOM) and of Satum (lower frequency SKR) where very low density magnetoplasmas (fp/fc < 0.01) do in fact exist at the respective source régions.

D.l Introduction

Among the théories proposed to explain the génération mechanism of the auroral kilometric radiation (AKR) and its analogies at Jupiter (DAM, HOM) and at Satura (SKR), the Cyclotron Maser Instability (CMI) [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] agréés best with wave and particle observations in the source région of AKR. Since this pioneer work, many investigators picked up this topic and performed improvements on this theory. Shortly speaking, the CMI theory demonstrates that weakly relativistic électrons which axe precipitating along auroral field lines are able to amplify in particular electromagnetic R-X mode waves near the R-X cutoff frequency via the cyclotron maser mechanism. [START_REF] Wu | A theory of the terrestrial kilometric radiation[END_REF] derived the growth rate of the wave in terms of the imaginary part of the angular frequency U{ of the wave. They assume that the background électrons of ionospheric origin (relatively cold électrons) are responsible for the propagation of the wave, and that the unstable energetic électrons, which are anticipated to form a loss cône feature in the distribution function, are responsible solely for the amplification. During this investigation, they additionally found that R-X waves are favoured over L-0 waves. Later on, [START_REF] Wong | Electromagnetic cyclotronloss-cone instability associated with weakly relativistic électrons[END_REF] and [START_REF] Wu | Génération of auroral kilometric radiation[END_REF] solved the dispersion relation with the inclusion of the effects of the hot électrons. They pointed out that the angular dependence with respect to the magnetic field of the most amplified wave is a strong function of the ratio /p//c (denoting the électron plasma and cyclotron frequency, respectively) and of the ratio ne/n&, ne being the density of the energetic électrons and ru, that of the background (cold) électrons. One of their main conclusions was that, if the source of AKR shows a density cavity for cold électrons which is confirmed by recent satellite measurements [START_REF] Louarn | Trapped électrons as a free energy source for the AKR[END_REF] due to a strong parallel electric field, the possibility of amplification is restricted to waves lying in a relatively small range of 9 near 7r/2 provided that /p//c is low (in the order of 0.005). Moreover, the R-X cutoff frequency is then situated slightly below the électron gyrofrequency which is in strong contrast to the cold plasma dispersion relation. [START_REF] Dusenbery | General concepts on the génération of auroral kilometric radiation[END_REF] studied the relativistic résonance condition and found that the interaction length between the amplified waves and the résonant particles is very small and they provided evidence that also the "hole" région which represents an instability excited by downgoing électrons may give rise for amplification of initially downward propagating waves. This fact was approved by Le Queau et al. (1984a,b) who performed a fully analytical treatment of the CMI. They concluded that initial upward propagating waves (destabilized by the loss cône feature) would be heavily damped when penetrating through régions of decreasing magnetic field magnitude. Contrary, initially downgoing waves could be amplified nearly until they are reflected as a conséquence of the increasing magnetic field to finally travel upwards and escape into free space.

In recent years, researchers started to treat the CMI in an inhomogenious medium. Omidi and Gurnett (1984) performed ray-tracing in a medium with varying magnetic field magnitude. They concluded that the électron distribution function as measured by the S3-3 satellite is not able to produce AKR in the requested intensity. By steepening the slopes of the loss cône instability région in the distribution function they could easily compose the observed wave amplitudes. This work is very comprehensive since it shows that initially high amplification may be quenched or even compensated by heavy damping that the waves suffer throughout the further propagation in free space. During their investigation they showed evidence that it is the loss cône feature which is most likely the unstable région in the électron distribution, but did not refuse the possibility of amplification of downgoing waves by the holelike feature. Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF] developed an analytical inhomogeneous treatment of the CMI and obtained expressions for the wave emergence angle 9 as a function of c = (/p//c)2 and gave a maximum value ec above which no amplification is possible. A similar inhomogeneous treatment of the CMI lead [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF] to dérivé the spectrum of terrestrial kilometric radiation and [START_REF] Galopeau | Theoretical model of Saturn's kilometric radiation spectrum[END_REF] that of the Saturnian kilometric radiation. [START_REF] Pritchett | A simulation study of kilometric radiation génération along an auroral field line[END_REF] and [START_REF] Pritchett | A simulation study of kilometric radiation génération along an auroral field line[END_REF] thoroughly studied the effect of hot électrons on the dispersion relation and discovered significant changes compared to the cold plasma theory. Similar to [START_REF] Wong | Electromagnetic cyclotronloss-cone instability associated with weakly relativistic électrons[END_REF], [START_REF] Pritchett | A simulation study of kilometric radiation génération along an auroral field line[END_REF] acquired the highest net gain for waves with nearly perpendicular emergence angle 9 at the source in case région (upward side), 2) holelike feature (downward side), 3) trapped électrons (near t>j_-axis).

in Figure D.l; Firstly, the loss cône région associated with the upward side of the distribution function (ascending électrons), secondly, the accelerated downgoing électrons (forming a holelike feature), and thirdly, the trapped électrons near the üj_-axis. The latter are suggested to be trapped throughout a time-varying (or space-varying) parallel electric field [START_REF] Louarn | Trapped électrons as a free energy source for the AKR[END_REF] between their magnetic mirror point above the ionosphère and a second mirror point due to the parallel electric field along auroral field fines. The corresponding electric potential has been reported to be about 3 kV over a distance of several earth radii [START_REF] Croley | Signature of a parallel electric field in ion and électron distributions in velocity space[END_REF]. Although a common conclusion has not yet been drawn, it is generally accepted that AKR is likely to be excited by the two former instabifities, the loss cône and/or holelike région. These two régions are characterized by a relatively small /3j_0 which leads to some simplification when studying the résonance condition.

D.2.2 Dispersion relation and growth rate

Under several conditions (0 « 90°, n (refractive index) « 1, / « /c, fp « fc, the dispersion relation A (iu, k) can be significantly simplified (Wu and Lee, 1985) A(w, k) = 1 -c2k2 , dF + knü^v ±j'i2{k±vi/ujc) _ {u -ujJT -fc||V||) " (D.l) where u = 2nf, k\\,k± are the components of the wave vector paraJlel/perpendicular with respect to the magnetic field f?, F dénotés the électron distribution function in the velocity space (ü||,v_l), J\ is the Bessel function, and T = 1/\/l -v2/c2 = l/y/l -/32.

It is further assumed that the cold (ionospheric) électrons support solely the wave propagation, whereas the hot precipitating électrons forming the instabilities in the distribution function are only responsible for the amplification of the wave.

The growth rate for the CMI is expressed in terms of the imaginary part uof the angular frequency u = ur + iw». An approximate formula for the R-X mode wave is given by [START_REF] Wu | Kinetic cyclotron and synchrotron maser instabilités: Radio émission processes by direct amplification of radiation[END_REF]: when n w 1 and dF/dv\\ w dF/dvj_

Although some of the assumptions made for the dérivation of the dispersion relation and the growth rate are very questionable after the recent Viking measurements in the AKR source région [START_REF] Louarn | Trapped électrons as a free energy source for the AKR[END_REF], it is sufficient for our purpose because our aim in particular is the discussion of the résonance condition occurring in the denominator of Equation (D.l) and as argument of the 6 function in Equation (D.2). More accurate formulae for Equations (D.l) and D.2, in particular the introduction of the hot électrons for the wave's propagation axe given by [START_REF] Wong | Electromagnetic cyclotronloss-cone instability associated with weakly relativistic électrons[END_REF].

D.2.3 Résonance condition

By inspection of Equation (D.2), we see that a necessary condition for wave growth (w,-> 0) is the existence of an inversion of population dF/dv± > 0 in velocity space along régions where the argument of the ^-function is 0. In other words we hâve to study the quantity dF/dv± along the résonance contour in velocity space defined by U -u>c/T -fc||U|| = 0 (D.4)

For a given wave (k, /) this résonance contour can be found in the velocity space by solving the cold plasma dispersion relation [START_REF] Budden | Radio Waves in the Ionosphère[END_REF][START_REF] Stix | The Theory of Plasma Waves[END_REF]. For the fast extraordinary (R-X) mode these contours are ellipses entirely placed at either the upward or downward side of the Figure D.2: Extension of an instability (dF/dv± > 0, dashed area) in the velocity space. Ellipses 1 and 3 are not intersecting this unstable région along their curves, which leads to damping of the corresponding waves. Ellipse 2 encounters also the unstable area, and the corresponding wave may be amplified; the net gain dépends on the balance of growth and damping along the ellipse (Equation D.2). Note that the growth can be optimized when d (Equation D.6) equals /?||0 (Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF]. P dénotés the point where dF/dvj_ = max, with the coordinates /?||0, distribution function [START_REF] Dusenbery | General concepts on the génération of auroral kilometric radiation[END_REF]. This is visualized in Equation (D.4) where u must be greater than uJY because the R-X cutofF frequency Jrx is always higher than fc.

This can only be achieved when /;||V|| > 0, therefore it is requested that fc|| and ü|| point in the same direction. Upgoing waves can therefore only be amplified by ascending électrons and downward propagating waves only by descending électrons.

A qualitative estimation of the growth can be acquired by studying the location of the résonant ellipse for a given wave (k, /) with respect to the instabilités in the distribution function. An example is sketched in Figure D.2 (adapted from Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF]. The hatched région dénotés dF/dv± > 0. The innermost and outermost ellipses are not Crossing this unstable area and the corresponding waves therefore do not give rise for amplification. The ellipse in the middle is largely embodied in the unstable région and may lead to amplification. The net gain dépends on the balance of growth and damping when integrating along the résonant contour (Equation D.2). The growth is optimized when the distance d of the ellipse from the origin of the velocity space equals /3||0 (Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF]. Using the résonance condition (Equation D.4) and the cold plasma dispersion relation Ac(u;,£) (e.g. [START_REF] Budden | Radio Waves in the Ionosphère[END_REF] the coordinates of the center d, the semimajor axis 6, and semiminor axis a of the ellipse can be calculated for a given 9 and for plasma parameters /p//c, ///c [START_REF] Dusenbery | General concepts on the génération of auroral kilometric radiation[END_REF].

(/3|| -df h _ where hy = k\\c/uc, Arj| = fcy(/p//c,///c, 0) via Ac(w,E), P\\, P.l, a, 6, d in units of the velocity of light c.

From Equations (D.7) and (D.8) it can easily be seen that the ellipses are elongated in the (3±-direction (6 > a). For 0 nearly perpendicular (hy << 1) the ellipses are well approximated by circles a ae 6.

Now let us systematically study the résonant contours for any arbitrary wave (fc, /) in a given plasma (/p, fc) to see which waves are adapted for growth in a given instability (characterized by P\\oiP.Lo)-The findings can be visualized in a f/fc-fP/fc diagram (Figure D.3). For a given 0, we can distinguish three areas in the diagram; first the région above the curve / = fpjc where no propagation is possible (/ < /rx), second, the région outside the curve labeled Se and within the curve / = /rx where no résonant ellipses can be found for the respective value of 0. The third région lies within the ^-contour. In this space which we call the résonant space, résonant ellipses exist and it dépends on the électron distribution function, whether they encounter a space with dF/dv± > 0 or not. The curve Se encircling the résonance space represents the so-called separatrix (Le [START_REF] Zarka | The maser synchrotron instability in an inhomogeneous medium: Détermination of the spectral intensity of the auroral kilometric radiation[END_REF] where the résonant ellipses shrink to a point. The away from the separatrix we find conditions for which the résonant contours lie favourably within the space of instability. In general, a large (3±0 is needed to hâve conditions located considerably away from the separatrix. K therefore /?j_o is not too large, the location of the separatrix Se itself is a good approximation for plasma parameters /p, /c, // fc to be adapted for amplification of waves with emergence angle 9. Assuming a ratio /p//c for a given 9 there exist in general two small ranges of values f/fc situated slightly inside the separatrix for which small résonant ellipses are possible. We will corne back again to this fact later on. Provided that /3±0 is small, Equation (D.ll) relates /3\\0 to ///c, so that the Doppler shifted frequency of the amplified wave is a function of the parallel energy of the unstable électrons.

Further, the product of the refractive index and the cosine of the wave normal angle is equal to the parallel bulk velocity (Equation D.10). Thus, the angle 9 cannot yet be determined from /?l|c. To solve this problem, we will perform an investigation in section D.3 in order to détermine for which n the largest growth is expected, when keeping 0 constant.

To give a short review of the findings in this section, we analyzed the résonant ellipses for waves (k, /) in a plasma with given /p, /c. It is found that for a given 0, the possibility of existence of résonant contours is restricted to a région enclosed by Sg. When 9 decreases, the corresponding Sg expands to higher values of ///p and /c//p. Out of Sg there exist either no électrons which can resonate with the wave or wave propagation is inhibited because / < /rx For plasma parameters lying within the separatrix Sg, we hâve studied the properties of the résonant contours for varying /p//c and ///c. The resuit is that ellipses with small extensions which are required for waves to be possibly amplified via the loss cône or the holelike feature, are produced for plasma conditions which are confined along the separatrix Sg and slightly inside of it. Allowing for these conditions, Equations (D.10) and (D.ll) could be determined. Equation (D.ll) already relates f3\\0 to f/fc and is independent from /p//c, n and 9. Equation (D.10) requires further analysis to dérivé 9 soley from /3\\0 which is the purpose of the next section.

D.3 Amplification of the radiation D.3.1 The exponential gain factor

In section D.2 we used an approximate expression for the growth (Equation D.2). Omidi and Gurnett (1984) demonstrated that it is not sufficient to calculate the growth only at the source région because subséquent damping along the further ray path may occur and quench or even overcome the initial growth. To see whether or not there remains a net gain, one must calculate the exponential gain factor g (Omidi and Gurnett, 1984) 9 = r,2<o

Jll dl (D.12)

where vg dénotés the group velocity.

To obtain a large net gain it is not only necessary to hâve a positive value of u;,-along the ray path dl, but also to hâve small group velocities to maintain the amplification process for a

D.3.3 Analysis

We hâve to make the link between the coordinates /i and I2 in real space and Y\ and Y2 in the Appendix E Ray tracing of electromagnetic waves in a magnetoplasma

E.l Fundajnentals

In the appendices B and C we used the ray tracing technique to localize the hectometric émission radio sources. In this appendix we will evaluate the mathematical tools which are used in the ray tracing program. Before the dérivation of the ray differential équations which describe the characteristics of the ray paths throughout the wave propagation, it is necessary to develop some basic équations in the magnetoionic theory. This includes in particular the définition of the " refractive index surface" and the so-called "ray surface" in order to show the relationship between the ray (direction of energy flow and the wave normal direction. Then, the ray équations are determined and we demonstrate, how to proceed ray tracing in a magnetoplasma such as planetary magnetospheres. Since dn/df is generally greater than 1, Vr > U. Similar to n = c/V we can define a refractive index which belongs to the ray velocity Vr. We will call it the ray refractive index nray nray = c/Vr (E.13)

Now we are able to define a "ray surface" in a similar way as we did it for the refractive index surface. Again, we introduce spherical polar coordinates r, d,<p and let the magnetic field be parallel to the w-axis. The direction of a given ray is then -a. Consider a surface in which the radius r to each point is equal to V^t?,.). There are two such surfaces for any medium, one for each of the two characteristic waves (O or X mode). These are the ray surfaces. Each is a surface of révolution about the tn-axis, and has the plane t? = 7r/2 as a plane of symmetry.

The ray surface can be visualized as the wave front reached after unit time for a point source at the origin. Thus, the normal to the ray surface at any point is the wave normal. where p and A axe the polar coordinates of nr, ng n$ (Equations E.32) and d is the angle between the wave normal and the magnetic field.

The quantity dn/dd can be easily calculated by différentiation of the refractive index (Equation E.l). To calculate dd/dp and dd/dX we hâve to détermine $(<,0, A). The situation is displayed in Figure E.3. The coordinate System is centered at a given point r, 0,0 in space. nr, ng and n4 coincide with the r, 9 and (f> directions, respectively. The direction of n is determined by p and A using Equations (E.32).

Let the magnetic field direction hâve the polar angles ps and A#. where the dérivatives dn/dX and dn/dY can be obtained by différentiation of the Appleton-Hartree formula (Equation E.l). dX/dNe and dY/dB are derived via Equations (E.2). Finally, the dérivatives dNe/dr, dNe/de, dNe/d<j>, and dB/dr, dB/de, dB/d<f> must be calculated from an analytical plasma density model iVe(r, e, <p) and magnetic field model B(r, e, <f>). We substitute

Equations (E.39) in Equations (E.38) and calculate the variation of the wave normal direction nr, h$, 71$ based on the given magnetic field and plasma models.

In this section we showed how to handle the ray équations (E.33) and (E.38) in order to calculate ray paths in a magnetoplasma which is determined by an électron density model iVe(r, 0, <f>) and a magnetic field model B(r, e, 4>). Since one needs also the dérivatives of B and Ne with respect to r, e, 4> these models should be provided in analytical form. In ail aspects of the ray tracing procedure, the wavelength should by small compared with any characteristic scales in the plasma.

In other words the électron density and the magnetic flux density should not vary much within one wavelength.