Jean-Pierre Hugot
email: hugot@mnhn.fr

Violaine Nicolas

Jessica Martínez

Introduction

We recently published the diagnosis and the name of a new mammal species: Talpa aquitania Nicolas, Martínez-Vargas et Hugot 2015. Unfortunately, it happened that the editors of the Bulletin de l'Académie Vétérinaire de France, the selected journal, decided to stop the paper edition for their publication. An attentive examination of the corresponding articles of the International Code on Zoological Nomenclature (Art. 8) shows that, to be valid, a new name must be published on a paper support or electronically after being pre-registered in the Official Register of Zoological Nomenclature (ZooBank) before publication. Thus, in this situation we have a risk that our work will not be considered published, and therefore our new taxon considered not available. This is the reason why we publish the present article in a periodical printed on paper, distributed simultaneously to all subscribers and accessible online after its paper distribution, which makes our new name available under the traditional rules of zoological nomenclature. In the following we are giving the essentials of the diagnosis of the new taxon. For the details of the molecular phylogenetic, morphological and biogeographical information, we refer to our previous original works [START_REF] Nicolas | Talpa aquitania nov. sp. (Talpidae, Soricomorpha) a new mole species from southwest France and north Spain[END_REF][START_REF] Nicolas | Molecular data and ecological niche modelling reveal the evolutionary history of the common and Iberian moles (Talpidae) in Europe[END_REF].

Talpa aquitania

Holotype MNHN-ZM-2016-471 (VN1789). Collected in 2013. France-86280, Saint-Benoît, 46.546°N-0.348°W. Adult female: whole body preserved in ethanol.

Paratypes

Tissues preserved in ethanol and RnaLater; skulls extracted (national collection number, field number, date of collect, locality and district of collection, geographic coordinates, name of collector, age and sex). MNHN- ZM-2016-472 (YA0346). 06/10/2013, France-63320, Creste, Issoire, 45.550°N-3.043°W, Bernard Pradier, adult female. MNHN-ZM-2016-473 (YA0386). 13/04/2014, France-63190, Lezoux, alt. 833 m, 45.828°N-3.380°W, J-Michel Georgeon, adult female.

Diagnosis and distribution

Talpa aquitania can unambiguously be distinguished from its sister-related species, Talpa europaea Linnaeus 1758 and Talpa occidentalis Cabrera 1907, by a unique combination of characters:

The eyelids are fused together. As observed in Talpa occidentalis, the eye is completely covered by membranes. This characteristic differs from what is observed in Talpa europaea, which has open eyes.

Weight, head, body and hind-foot lengths are significantly greater in Talpa aquitania (weight: 89 ± 17 g, head and body: 149 ± 7 mm, foot: 21.5 ± 1.5 mm) than in Talpa europaea and Talpa occidentalis [START_REF] Nicolas | Talpa aquitania nov. sp. (Talpidae, Soricomorpha) a new mole species from southwest France and north Spain[END_REF].

The mesostyle of the upper first molar (M1) is simple in Talpa aquitania and Talpa europaea, while it is double in Talpa occidentalis. In T. occidentalis and T. europaea, the mesostyles of the upper second molar (M2) and the upper third molar (M3) are divided into two cusps. The two cusps are of subequal size, and they are aligned on a plane that extends parallel to the parastyle and the metastyle. Some T. aquitania specimens have a simple mesostyle in M2, and other specimens show an additional minute cusp. Unlike in T. europaea and T. occidentalis, this cusp is much smaller than the main cusp of the mesostyle and is located in the crest that connects the mesostyle to the metacone of M2 that is in a more lingual position than the mesostyle itself. In the M3 of some T. aquitania specimens, the mesostyle is composed of a main anterior cusp and a slightly smaller posterior cusp (see figure 4 in [START_REF] Nicolas | Talpa aquitania nov. sp. (Talpidae, Soricomorpha) a new mole species from southwest France and north Spain[END_REF], figure 6 in Nicolas et al. 2017). In other specimens, this posterior cusp is not clearly discernible because its posterior border is fused to the crest that runs from the mesostyle to the metacone of M3. Despite interindividual variability, the mesostyle condition of M2 and M3 of T. aquitania specimens differs from that found in T. europaea and T. occidentalis.

Base composition of 16 positions of the cytochrome b gene differ between Talpa aquitania and the two other species (based on 216 specimens of Talpa europaea, 118 specimens of T. aquitania and 26 specimens of Talpa occidentalis; [START_REF] Nicolas | Molecular data and ecological niche modelling reveal the evolutionary history of the common and Iberian moles (Talpidae) in Europe[END_REF]. Base composition at positions 87,171,176,282,309,328,351,369,465,492,745,813,828,981,1047 and 1074 is C, G, C, G, T, T, A, A, T, C, T, G, C, A, T, T in T. aquitania, and it is A, A, T, A, C, A, G, G, C, T, C, A, T, T, C, C in both T. europaea and T. occidentalis.

Talpa aquitania is present in France southward and westward of the Loire River, and in Northern Spain.

Acknowledgments:

We are grateful to Philippe Bouchet and Alain Dubois who drew our attention to this issue related to the code of nomenclature.

Commentary


Q Nénon

A Sicard

P Kollmann

H B Garrett

S P A Sauer

C Paranicas

A physical model of the proton radiation belts of Jupiter inside Europa's orbit

Key points

 A global physical model of the proton radiation belts of Jupiter inward of the orbit of Europa is presented  Observed two orders of magnitude flux depletions in MeV proton fluxes near Io are not from direct interactions with the moon or its torus  Resonant interaction with low frequency electromagnetic waves is modeled and likely to be dominant near Io's orbit

Introduction

Physics-based models of radiation belts are very useful tools to forecast trapped energetic charged particle fluxes at Earth, Saturn and Jupiter. Indeed, they can contribute to a data assimilation effort around Earth (Koller et al., 2007;[START_REF] Shprits | Reanalysis of relativistic radiation belt electron fluxes using CRRES satellite data, a radial diffusion model and a Kalman filter[END_REF][START_REF] Bourdarie | Electron radiation belt data assimilation with an Ensemble Kalman filter relying on the Salammbô code[END_REF], help to predict fluxes in unexplored regions of Saturn [START_REF] Kollmann | MeV proton flux predictions near Saturn's D ring[END_REF] or complement empirical models where in-situ measurements are limited to specify the harsh environment of Jupiter [START_REF] Sicard- | JOSE: A new Jovian specification environment model[END_REF]. At Jupiter, while physical models of the trapped electrons exist (Sicard et al., 2004;Santos-Costa and Bolton, 2008;[START_REF] Woodfield | The origin of Jupiter's outer radiation belt[END_REF][START_REF] Kita | Relation between the short-term variation of the Jovian radiation belt and thermosphere derived from radio and infrared observations[END_REF][START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], no physical model of the trapped protons has already been developed, even though this particle population represents a major threat to satellites (Garrett et al., 2017).

On the Space Science side, physical models enable to understand the origin, morphology and time-dynamics of the radiation belts. Regarding trapped protons around gas giants, [START_REF] Santos-Costa | Modeling the proton and electron radiation belts of Saturn[END_REF] and [START_REF] Kollmann | Processes forming and sustaining Saturn's proton radiation belts[END_REF] proposed models around Saturn and identified the following key processes: radial diffusion, absorption by the moons and dense rings, charge exchange and energy loss with neutral particles and small ring grains and proton source by Cosmic Ray Albedo Neutron Decay. Among the very important radiation belt physical processes, wave-particle interaction is a universal physical process shaping the electron radiation belts of Earth (see for e.g. [START_REF] Horne | Wave-driven diffusion in radiation belt dynamics[END_REF], Jupiter [START_REF] Woodfield | The origin of Jupiter's outer radiation belt[END_REF][START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], and maybe Saturn [START_REF] Menietti | Survey of Saturn Z-mode emission[END_REF], consistent with saturated electron belts for Earth and Jupiter in regard with the Kennel-Petschek limit [START_REF] Kennel | Limit on stably trapped particle fluxes[END_REF] discussed by [START_REF] Mauk | Electron radiation belts of the Solar system[END_REF]. One may wonder whether the resonant interaction also shapes the proton radiation belts of Jupiter, as expected in regard with the Kennel-Petschek limit [START_REF] Mauk | Comparative investigation of the energetic ion spectra comprising the magnetospheric ring currents of the Solar system[END_REF], and how similar or different the origin of the proton radiation belts of Jupiter is compared with the terrestrial and kronian ones.

A physical model of the proton radiation belts of Jupiter is proposed in this manuscript. It relies on the experience developed at ONERA through the model family named Salammbô [START_REF] Beutier | Salammbô: A three-dimensional simulation of the proton radiation belt[END_REF][START_REF] Santos-Costa | Modeling the inner Jovian electron radiation belt including non-equatorial particles[END_REF]Sicard and Bourdarie, 2004;[START_REF] Lorenzato | A physical model for electron radiation belts of Saturn[END_REF][START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] and will simply be referred as "Salammbô" hereafter. A focus is given in this study to protons with kinetic energies higher than 1 MeV, as is done in the empirical model proposed by Garrett et al. (2017). Lower energy protons are modeled in order to address the 1 MeV fluxes anywhere inside the orbit of Europa but not directly validated against in-situ observations. Future work may focus on the development of a lower energy Salammbô-Jupiter-proton model. The modeling principle is presented in section 2. In-situ measurements used to validate the model are then presented and discussed in section 3. The modeling of the effect of all the physical processes introduced in the Salammbô model is detailed in section 4 and the outer boundary condition imposed near the orbit of Europa (L=9.5) is mentioned in section 5. Predictions of the model are documented in section 6 and validated against observations in section 7, where the possible role of charge exchange with the Io gas torus and resonant interactions with Electromagnetic Ion Cyclotron waves are discussed. Finally, our findings are summarized in section 8.

Modeling principle and simulation

The modeling principle adopted in this study is the same as [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], where we modeled Jupiter's electron belts. Trapped protons gyrate around a guiding center (a motion that is associated with the first adiabatic invariant [START_REF] Schulz | Direct observation of the CRAND proton radiation belt source[END_REF]), which bounces along the magnetic field line between two mirror points (second invariant), and experiences an azimuthal drift (third invariant). The bounce and drift motions of the guiding center define a drift shell which is described by the McIlwain parameter 𝐿 and the equatorial pitch-angle 𝛼 𝑒𝑞 .

The radiation belt proton distribution may be described with three coordinates if the phases associated to the three adiabatic invariants are mixed [START_REF] Schulz | Direct observation of the CRAND proton radiation belt source[END_REF]. We use in this study the following set of three coordinates: kinetic energy 𝐸 𝑘 , sine of the equatorial pitch-angle 𝑦 = sin (𝛼 𝑒𝑞 ) and the McIlwain parameter 𝐿. The same magnetic field model as [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] is used: the internal field model O6 [START_REF] Connerney | Magnetic fields of the outer planets[END_REF] is combined with the current sheet model proposed by [START_REF] Khurana | Euler potential models of Jupiter's magnetospheric field[END_REF].

The proton distribution is then governed by a diffusion equation which is detailed in Appendix A of [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] for the trapped electrons. In their last equation, the friction, absorption and diffusion coefficients represent the physical processes acting on the trapped particles and violating the three adiabatic invariants, such as radial diffusion, moon sweeping, charge exchange, Coulomb collisions, or interactions with low-frequency electromagnetic waves (see section 4).

The diffusion equation is discretized following [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] with 88 linear steps in equatorial pitch-angle, 101 logarithmic steps in kinetic energy going from 25 keV to 250 MeV at the outer boundary at L=9.5, and 51 logarithmic steps for the McIlwain parameter ranging from 1.02 to 9.5. As in [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], the kinetic energy and equatorial pitch-angle grids defined at L=9.5 are transported inward by conserving the first and second adiabatic invariants. Figure 1 shows the minimum kinetic energy simulated by the Salammbô grid using the lower kinetic energy boundary of 25 keV at L=9.5. Our model is therefore not able to predict the distribution of 1 MeV trapped protons inside L=3 but can account for 15 MeV protons anywhere inside L=9.5.

The diffusion equation is finally solved with an explicit numerical scheme which imposes that the kinetic energy and equatorial pitch angle cross diffusion terms should be neglected, as in [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF].

In-situ measurements

The Pioneer 10 (Jupiter flyby in 1973), Pioneer 11 (1974) and Voyager 1 (1979) missions successfully measured in-situ fluxes of the radiation belt protons inside the orbit of Europa during their respective fly-bys. In addition to these snapshots, the Galileo mission entered the Jovian magnetosphere in December 1995 and released an atmospheric probe, hereafter referred as the "Galileo Probe". The "Galileo Orbiter" remained within the Jovian radiation belts for 35 more orbits and provides an extensive survey of the belts. The Galileo survey has a limited coverage inside the orbit of Europa as the spacecraft only passed rarely in this region. Also the used instrument suffered from contamination so that not all data is directly usable. More recently, Juno arrived in polar orbit around Jupiter in July 2016 [START_REF] Bolton | Juno's first glimpse of Jupiter's complexity[END_REF]. Figure 2 shows the trajectory in a magnetic frame of the previous missions. One can note that Pioneer 11 and Juno explore higher latitudes than the other spacecraft, and therefore sampled lower equatorial pitch-angle protons.

Proton measurements obtained in our region of interest and for kinetic energies greater than or close to 1 MeV are discussed hereafter. A particular attention is given to possible contamination issues. The goal of this section is to provide Salammbô with as-reliable aspossible proton measurements to validate the model for L<9.5.

The University of California -San Diego Trapped Radiation Detector (TRD) onboard Pioneer 10 and Pioneer 11 has been designed to measure integral fluxes of protons with kinetic energies higher than 80 MeV (>80 MeV hereafter) with its M3 channel.

The Pioneer 10 TRD M3 measurements are discussed by [START_REF] Fillius | Measurements of the Jovian radiation belts[END_REF]. The measurements suffered contamination by penetrating electrons but corrections of the M3 fluxes are proposed by [START_REF] Fillius | Measurements of the Jovian radiation belts[END_REF] to provide a reliable measurement of >80 MeV protons inside Io's orbit. The correction also provides an estimate of the counts or fluxes that can be attributed to electron contamination along the Pioneer 10 trajectory.

The Pioneer 11 TRD M3 measurements can be found in [START_REF] Fillius | Radiation belts of Jupiter: a second look[END_REF] but have not been corrected for electron contamination. The counts or fluxes which can be attributed to electron contamination in the Pioneer 10 TRD M3 measurements are close or a bit higher than the fluxes measured by Pioneer 11 TRD M3. In addition, [START_REF] Krimigis | Two-component proton spectra in the inner Saturnian magnetosphere[END_REF] have compared the Pioneer 11 TRD M3 measurements with those observed by Voyager 2 and propose that the fluxes measured by M3 at Saturn are overestimated by a factor of 3. The M3 Pioneer 11 channel is therefore considered in our study as severely contaminated by the electrons and we refrain from using it.

The University of Chicago Charged Particle Instrument (CPI) experiment includes a Fission Cell to measure >35 MeV proton fluxes. Fluxes measured by Pioneer 10 are available in [START_REF] Simpson | Protons and electrons in Jupiter's magnetosphere field: results from the University of Chicago experiment on Pioneer 10[END_REF] and those measured by Pioneer 11 in [START_REF] Simpson | Jupiter revisited: first results from the University of Chicago charged particle experiment on Pioneer 11[END_REF]. However, [START_REF] Simpson | Protons and electrons in Jupiter's magnetosphere field: results from the University of Chicago experiment on Pioneer 10[END_REF] have shown that the measurements might be contaminated by electrons and heavy ions. [START_REF] Krimigis | Two-component proton spectra in the inner Saturnian magnetosphere[END_REF] have shown that the Pioneer 11 CPI >35 MeV fluxes measured at Saturn are a factor 50 higher than the Voyager 2 measurements and suggest that this observation is highly contaminated and not reliable. We therefore do not use in the present study the Pioneer 10 and 11 CPI Fission Cell measurements, as a precaution.

The Pioneer 10 and 11 Cosmic Ray Telescope (CRT) developed by the NASA Goddard center and the New Hampshire University enables to measure two proton energy ranges: 1.2 to 2.1 MeV and 14.8 to 21.2 MeV. The Pioneer 10 CRT measurements considered here are from [START_REF] Trainor | Energetic particles in the Jovian magnetosphere[END_REF] and the Pioneer 11 ones from Trainor et al. (1975). These measurements have been corrected for the dead-time and contamination issues, so that they are considered as reliable in this study.

The Pioneer 11 Geiger Tube Telescope (GTT) experiment developed by the University of Iowa measured 0.5 to 3.6 MeV protons, can be found in [START_REF] Van Allen | Pioneer 11 observations of energetic particles in the Jovian magnetosphere[END_REF], and are considered as reliable.

Voyager 1 and the Low Energy Charged Particle (LECP) experiment [START_REF] Krimigis | The Low Energy Charged Particle experiment on the Voyager spacecraft[END_REF], channel PSA3, provides us with 15-minutes averaged measurements of protons with kinetic energies between 16.3 and 26.2 MeV. This energy pass-band is given by the website of the "Fundamental Technologies" (FTECS) company: http://voyager.ftecs.com/ and is considered as the best estimate of the energy passband of PSA3 available (private discussion with S. M. Krimigis, Principle Investigator of the LECP experiment). The count rates of PSA3 are from the NASA Planetary Data System and we use a geometric factor of 0.4935𝑐𝑚 2 . 𝑠𝑟, provided by the FTECS website, to convert the count rates to omnidirectional integral fluxes.

The Energetic Particle Investigation (EPI) onboard the Galileo Probe [START_REF] Fischer | Energetic Particles Investigation (EPI)[END_REF] provides a unique dataset of electron, proton, and heavy ions measurements in the innermost part of the Jovian radiation belts. Three channels are of interest for our proton model, namely the channels P1, P2 and P3. However, as pointed out by [START_REF] Fischer | Highenergy charged particles in the innermost Jovian magnetosphere[END_REF], these channels do not discriminate very well particle species. We use in this study the geometric factors derived in the Ph.D. thesis of Eckhard Pehlke [START_REF] Pehlke | Teilchenpopulationen in der inneren Jupitermagnetosphäre. Untersuchung der EPI-daten von der Galileo Probe[END_REF], which were computed after the first publication of [START_REF] Fischer | Highenergy charged particles in the innermost Jovian magnetosphere[END_REF] and are the best estimates of the detector responses we have (private discussion with L. J. Lanzerotti, Principle Investigator of EPI). Appendix A gives the geometric factors of P1, P2, and P3 in response to electrons, protons, and alpha particles (𝐻𝑒 2+ ), scanned from [START_REF] Pehlke | Teilchenpopulationen in der inneren Jupitermagnetosphäre. Untersuchung der EPI-daten von der Galileo Probe[END_REF]. We also give in Appendix A a method to estimate the counts which might be attributed to alpha particles in P1, P2, and P3 from the measurements obtained by the channel HE of EPI. Finally, the electron model of [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] is used to compute the count rates of P1, P2, and P3 which might be attributed to trapped electrons. Appendix A also details how predicted counts are proposed from our electron and proton models taking into account the energy-dependent geometric factors.

Measurements of trapped protons by the Galileo Orbiter mission come from the Energetic Particle Detector experiment (EPD) [START_REF] Williams | The Galileo Energetic Particles Detector[END_REF]. It comprises two bi-directional detectors, respectively named the Low Energy Magnetospheric Measurement System (LEMMS) and the Composition Measurement System (CMS). Only two channels of EPD actually observe protons with kinetic energies higher than 1 MeV (Mauk et al., 2004, table A1) and are therefore of interest for our study: LEMMS/B0 which observes protons with kinetic energies from 3.2 to 10.1 MeV [START_REF] Jun | Monte Carlo simulations of the Galileo energetic particle detector[END_REF] and CMS/TP3 which measures 0.54-1.14 MeV protons [START_REF] Mauk | Energetic ion characteristics and neutral gas interactions in Jupiter's magnetosphere[END_REF].

Onboard the Juno spacecraft, the Jupiter Energetic particle Detector Instrument (JEDI) investigation observes trapped protons with kinetic energies up to around 2 MeV [START_REF] Mauk | The Jupiter Energetic Particle Detector Instrument (JEDI) investigation for the Juno mission[END_REF]. [START_REF] Kollmann | A heavy ion and proton radiation belt inside of Jupiter's rings[END_REF] give measurements of 1.1 MeV protons observed during Perijove 1 on the 27 th of August 2016. The trajectory of Juno is provided by the university of Iowa website: http://www-pw.physics.uiowa.edu/~jbg/juno.html. Salammbô will not be validated against the JEDI measurements in this study as the equatorial pitch-angle grid of the model is not sufficiently refined for the Juno trajectory. Indeed, according to the magnetic field model we use, Juno measures a few degrees in equatorial pitch angle away from the loss cone in our region of interest, what is not resolved by the currently used grid. Future work will propose a refined computation grid for the Salammbô-electron and proton models in order to address the Juno measurements. However, one can note from the Figure 2 of [START_REF] Kollmann | A heavy ion and proton radiation belt inside of Jupiter's rings[END_REF] that the 1.1 MeV proton fluxes suffer of a depletion of around a factor 100 near the field lines with L=6, consistent with what has been observed at this energy by Pioneer 10, Pioneer 11, and Galileo (see section 6).

Table 1 summarizes the proton in-situ measurements used to validate Salammbô.

Modeling the effect of the physical processes

4.1.Radial diffusion

Radial diffusion in the inner magnetosphere of Jupiter might be driven by neutral winds in the ionosphere of the planet [START_REF] Brice | Jupiter's radiation belts[END_REF][START_REF] Miyoshi | Observation of short-term variation of Jupiter's synchrotron radiation[END_REF]Santos-Costa et al., 2008;[START_REF] Tsuchiya | Short-term changes in Jupiter's synchrotron radiation at 325 MHz: Enhanced radial diffusion in Jupiter's radiation belt driven by solar UV/EUV heating[END_REF][START_REF] Kita | Relation between the short-term variation of the Jovian radiation belt and thermosphere derived from radio and infrared observations[END_REF] or by electric fields in the Io torus [START_REF] Bespalov | Features of the radial diffusion of energetic electrons in the middle Jovian magnetosphere[END_REF][START_REF] Murakami | Response of Jupiter's inner magnetosphere to the solar wind derived from extreme ultraviolet monitoring of the Io plasma torus[END_REF].

As discussed in [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], the radial diffusion coefficient of trapped particles inside Europa's orbit is poorly known. We use in this study a simple parametric form that does not depend on the particle kinetic energy or equatorial pitch-angle:

𝐷 𝐿𝐿 = 10 -10 𝐿 4 𝑠 -1
The adopted radial diffusion coefficient will be validated in section 7 and possible kinetic energy dependencies discussed in section 8. One can note that our radial diffusion coefficient is close to the one used by [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] for the trapped electrons. This is reasonable since at Saturn, which has a similar magnetosphere as Jupiter, proton and electron radial diffusion coefficients were found to be similar [START_REF] Kollmann | Processes forming and sustaining Saturn's proton radiation belts[END_REF].

Cosmic Ray Albedo Neutron Decay (CRAND)

At Earth, CRAND due to Galactic Cosmic Ray (GCR) protons nuclear interactions with the atmosphere is the main source of >10 MeV protons in the inner terrestrial radiation belt [START_REF] Hess | Van Allen belt protons from Cosmic Ray Neutron Leakage[END_REF][START_REF] Schulz | Direct observation of the CRAND proton radiation belt source[END_REF]. At Saturn, CRAND from nuclear interactions with the rings is the main source of >5 MeV trapped protons [START_REF] Cooper | Nuclear cascades in Saturn's rings -Cosmic ray albedo neutron decay and origins of trapped protons in the inner magnetosphere[END_REF][START_REF] Kollmann | Processes forming and sustaining Saturn's proton radiation belts[END_REF]. CRAND from the Jovian atmosphere or rings might therefore be a source of trapped protons at Jupiter. However, this source is neglected in this study, for three main reasons:

 Section 6 will show that there is no evidence of CRAND in the proton measurements close to the planet. [START_REF] Simpson | Jupiter revisited: first results from the University of Chicago charged particle experiment on Pioneer 11[END_REF] and [START_REF] Kollmann | A heavy ion and proton radiation belt inside of Jupiter's rings[END_REF] also do not find any evidence of CRAND, and therefore argue that the process is expected to be weak at Jupiter.  The magnetic field of Jupiter has a dipole moment respectively 20000 times and 34

times larger than the one of Earth and Saturn and is therefore a stronger deflecting shield against GCR protons. Indeed, for instance, a GCR proton requires a kinetic energy of at least 1000 GeV to access the Jovian atmosphere near the magnetic equator, as computed under the magnetic dipole approximation with the formula derived by [START_REF] Störmer | The polar aurora[END_REF]. The GCR flux on the Jovian atmosphere would therefore be way less important than what is found near Earth or Saturn where GCR protons need an energy of 17 GeV to get close to the planets, so that we may speculate that the CRAND source at Jupiter is way smaller.  Very energetic trapped protons near Earth (typically >10 MeV) may only be supplied by CRAND because inward adiabatic transport does not energize them to the observed energies. However, Jupiter's field is strong enough and its magnetosphere extended enough that radial diffusion of protons with energies as low as 300 keV from the orbit of Europa to L=2 is a source of 80 MeV protons there. Neglecting CRAND in our study therefore means that the GCR induced source is neglected against the radial diffusion source. At Saturn, the only way to produce energetic protons inward of the strongly absorbing moons and rings is CRAND. At Jupiter, there are no absorbers that work that efficiently because of the tilt of the magnetic field, so that there is no need for CRAND to explain the presence of MeV protons inward of the Jovian moons orbits.

Our assumption of neglecting CRAND is justified by the fact that the model intensities either are in agreement with the observations or tend to overestimate the proton fluxes, even in the regions closest to Jupiter (see section 7). Therefore, there is no need for an additional source like CRAND that would increase the intensities even more.

Sweeping effect of the moons

The trapped protons may impact the volcanic moon Io, which orbits at 5.9 Rj (1 Rj = 71492 km) from the center of Jupiter or the inner moons Thebe (3.1 Rj), Amalthea (2.5 Rj), Adrastea (1.8 Rj), and Metis (1.8 Rj). We assume that these moons are insulated bodies and simply absorb the impacting proton that is therefore lost from the radiation belts. The sweeping effect of the moons is modeled with a loss term 1 𝛤 in 𝑠 -1 numerically calculated following the method detailed by Santos-Costa and Bourdarie (2001). However, their method assumes that the gyroradius of the trapped particle is small compared to the size of the moons, which have a diameter of 3630 km (Io), 116 km (Thebe), 250 km (Amalthea), 20km (Adrastea) and 60 km (Metis). This is not true anymore for trapped protons, so that the gyroradius effect is taken into account in this study, following [START_REF] Paonessa | A theory of satellite sweeping[END_REF].

Figure 3 shows the absorption area of a moon when taking into account the proton gyroradius.

From Figure 3, we approximate the absorption area by a sphere with a diameter 𝐷 given by:

{ 𝐷 = 𝐷 𝑚𝑜𝑜𝑛 + 2 * 𝑟 𝑔 𝑖𝑓𝑟 𝑔 ≤ 𝐷 𝑚𝑜𝑜𝑛 2 𝐷 = 2 * √ 2 * 𝐷 𝑚𝑜𝑜𝑛 * 𝑟 𝑔 𝑖𝑓𝑟 𝑔 ≥ 𝐷 𝑚𝑜𝑜𝑛 2
For instance, the moon Thebe which has a geometric radius of around 55 km is seen by a 15

MeV proton with a gyroradius of 39km as an absorber body with a radius of 94km.

Effect of the dust rings

Jupiter has four very tenuous dust rings. They are believed to be populated by silicon dioxide grains created by micro-meteoroids impacts on the four inner moons Metis, Adrastea, Amalthea and Thebe [START_REF] Burns | The Formation of Jupiter's Faint Rings[END_REF]. The grains then drift inward under the Pointyng-Robertson drag effect to create the rings. The two innermost rings are the Halo (1.25 to 1.72 Rj) and the main ring (from 1.72 to 1.82 Rj) which is the brightest one. The two external Gossamer rings produced by meteoroid impacts on Amalthea and Thebe extend respectively from 1.72 to 2.54 Rj and 1.72 to 3.11 Rj in the equatorial plane.

The effect of the rings is not included in the present model and will be the object of a future study which will discuss the effect of the rings against proton measurements (using the Salammbô model presented here) and electron in-situ measurements and synchrotron observations (using the model of [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF]). However, the validation of the proposed proton model against Galileo Probe EPI measurements in section 7 shows that the main ring may have a predominant effect on >60 MeV protons close to Jupiter. We give hereafter a first calculation to further test this hypothesis.

Following [START_REF] Brooks | The size distribution of Jupiter's main ring from Galileo imaging and spectroscopy[END_REF], we assume that the main ring is composed of uniformly distributed spherical grains with a radius of 15𝜇𝑚. >60 MeV protons easily go through these grains and only suffer of a kinetic energy friction 𝑑𝐸 𝑑𝑡

. The stopping power of the main ring is then scaled from the stopping power of the silicon dioxide with the ratio between the molecular density in the ring and the molecular density of silicon dioxide [START_REF] Kollmann | MeV proton flux predictions near Saturn's D ring[END_REF]:

𝑑𝐸 𝑑𝑥 | 𝑟𝑖𝑛𝑔 = 𝑑𝐸 𝑑𝑥 | 𝑆 𝑖 𝑂 2 * 𝑛 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒-𝑟𝑖𝑛𝑔 𝑛 𝑚𝑜𝑙𝑒𝑐𝑢𝑙𝑒-𝑆 𝑖 𝑂 2
Following the method of [START_REF] Kollmann | MeV proton flux predictions near Saturn's D ring[END_REF] to compute the molecular density in the ring, we finally have:

𝑑𝐸 𝑑𝑡 = -𝑣 * 𝑑𝐸 𝑑𝑥 | 𝑟𝑖𝑛𝑔 = -𝑣 * 4 3 𝜋𝑟 3 𝑛 * 𝑑𝐸 𝑑𝑥 | 𝑆 𝑖 𝑂 2
Where 𝑟 is the radius of the grains, assumed to be 15𝜇𝑚, 𝑣 the speed of the proton and 𝑛 the grain density within the ring. This density is computed by assuming an optical depth at visible wavelength of 5.910 -6 [START_REF] Brooks | The size distribution of Jupiter's main ring from Galileo imaging and spectroscopy[END_REF]) and a thickness of the ring of 200𝑘𝑚 [START_REF] Brooks | The size distribution of Jupiter's main ring from Galileo imaging and spectroscopy[END_REF]. The stopping power of silicon dioxide is given by the NIST database. The kinetic energy friction term for 60 MeV protons staying within the ring during their full drift period is finally of -

1 𝐸 𝑑𝐸 𝑑𝑡 = 210 -6 𝑠 -1
, what is three orders of magnitude higher than the local radial diffusion coefficient at 𝐿 = 1.8 of 𝐷 𝐿𝐿 = 10 -9 𝑠 -1 . This first calculation shows that the main ring may clearly have a strong effect on the protons observed by Galileo Probe-EPI.

Coulomb collisions with cold plasma and neutral gas torus

Trapped protons inside Europa's orbit experience elastic Coulomb collisions with:

 The free electrons of the cold plasma of the inner magnetosphere of Jupiter  The bound electrons of the cold plasma ions  The bound electrons of the neutral particles of the Jovian hydrogen corona and Io and Europa gas torus

The equatorial pitch-angle diffusion, i.e. the trajectory deflection, is negligible for trapped protons [START_REF] Schulz | Direct observation of the CRAND proton radiation belt source[END_REF]. However, trapped protons suffer of subsequent kinetic energy losses that are represented with the kinetic energy loss rate 𝑑𝐸 𝑑𝑡 computed as follow:

- 𝑑𝐸 𝑑𝑡 = 4𝜋 𝑚 0𝑒 𝑣 ( 𝑞 2 4𝜋𝜀 0 ) * [𝜒 𝑓𝑟𝑒𝑒 + 𝜒 𝑏𝑜𝑢𝑛𝑑 ]
Where 𝑣 is the proton velocity, 𝑚 0𝑒 the rest mass of the electron and the 𝜒 𝑓𝑟𝑒𝑒 and 𝜒 𝑏𝑜𝑢𝑛𝑑 terms give the contribution from free and bound electrons and are computed following [START_REF] Schulz | Direct observation of the CRAND proton radiation belt source[END_REF] by:

𝜒 𝑓𝑟𝑒𝑒 = 〈𝑛 𝑒 〉 [1 - 1 𝛾 2 -𝑙𝑛 ( 𝜆 𝐷 𝑚 0𝑒 𝑣 ℏ )] 𝜒 𝑏𝑜𝑢𝑛𝑑 = ∑ 𝑍 𝑖 〈𝑛 𝑖 〉 [1 - 1 𝛾 2 -ln( 2𝑚 0𝑒 𝑐 2 (𝛾 2 -1) 𝐼 𝑖 )] 𝑖
With 𝜆 𝐷 the Debye length evaluated at the magnetic equator, 〈𝑛 𝑒 〉 the free electron number density averaged over the drift shell and 𝛾 the Lorentz factor. The sum in 𝜒 𝑏𝑜𝑢𝑛𝑑 is evaluated over the different ions and neutral particles with drift shell averaged number densities 〈𝑛 𝑖 〉 and mean excitation energies 𝐼 𝑖 .

The atmosphere model is the same as [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF]. The cold plasma free electron and ion densities are provided by the model of [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF], which is consistent with more recent models of the magnetodisc by [START_REF] Bagenal | Empirical model of the Io plasma torus: Voyager measurements[END_REF], [START_REF] Bagenal | Flow of mass and energy in the magnetospheres of Jupiter and Saturn[END_REF], or [START_REF] Bagenal | Survey of Galileo plasma observations in Jupiter's plasma sheet[END_REF]. [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF]) also provides us with the plasma temperatures to compute the Debye length.

As in [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], the Coulomb collisions with the neutral particles of the Io gas torus are neglected against the elastic collisions with the cold plasma ions, as their densities are one order of magnitude lower than the ion ones and that the mean excitation energies are similar. However, it is not true anymore near Europa, where ion densities range from 1 to 20 𝑐𝑚 -3 while neutral densities may range from 1.6 to 410 𝑐𝑚 -3 [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF], depending on the assumptions. Coulomb collisions with the neutral gas torus of Europa is still neglected in our study, and section 4.9 will show that this assumption does not impact the Salammbô results, as Coulomb collisions will remain negligible against local radial diffusion near Europa's orbit. Sicard and Bourdarie (2004) and [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] did not take into account the Coulomb collisions with the oxygen and sulfur ions of the magnetodisc 𝑂 + , 𝑂 ++ , 𝑆 + , 𝑆 ++ , and 𝑆 +++ . To do so, one needs the mean excitation energies 𝐼 𝑖 of the oxygen and sulfur ions. [START_REF] Sauer | The mean excitation energy of atomic ions[END_REF] computed the mean excitation energies of various atomic ions. Mean excitation energies of oxygen and sulfur ions have been computed for this study following the method detailed by [START_REF] Sauer | The mean excitation energy of atomic ions[END_REF] or [START_REF] Jensen | Mean excitation energies for molecular ions[END_REF] and are reported in Table 2.

Charge exchange with the Jovian atmosphere

Trapped protons 𝐻 + may experience a charge exchange or a charge transfer with the neutral particles 𝐴 of the Jovian atmosphere following:

𝐻 + + 𝐴 → 𝐻 + 𝐴 +
The proton is therefore lost from the radiation belts, and the loss term is computed as:

1 𝛤 = 𝑣 * 𝜎 * 〈𝑛(𝐴)〉
Where 𝑣 is the speed of the proton, 〈𝑛(𝐴)〉 the density of neutral particles averaged on the bounce and drift motions of the trapped proton and 𝜎 the charge exchange cross section associated to the previous reaction.

For the Jovian atmosphere, only charge exchange with hydrogen atoms, the main constituent in the upper atmosphere, is taken into account in Salammbô. The density model is the same as [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] and the charge exchange cross section is given by [START_REF] Claflin | Charge-exchange cross sections for hydrogen and helium ions incident on atomic hydrogen: 1 to 1000 keV[END_REF].

Charge exchange with the neutral gas torus of Io and Europa

The intense volcanic activity of Io releases sulfur dioxide molecules 𝑆𝑂 2 into space, creating a neutral gas torus mainly composed of oxygen and sulfur particles [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF]. A gas torus is also found near the moon Europa, created by sputtering and potentially plumes [START_REF] Sparks | Probing for evidence of plumes on Europa with HST/STIS[END_REF] and composed of oxygen atoms and dihydrogen molecules. Charge exchange with these neutral populations may remove trapped protons from the radiation belts. In order to evaluate this loss process, one needs to know the neutral densities and associated charge exchange cross sections.

The kinetic model of [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF] predicts the radial extension of the Io and Europa gas torus. In our region of interest, the Io torus extends from 1 Rj to 9.5 Rj and the Europa torus from 6 Rj to 9.5 Rj, the outer boundary of our model. Figure 4 shows the geometric configuration of the two gas tori used in this study, with a constant thickness of respectively 1.4 Rj for the Io torus [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF] and 2 Rj for the Europa torus [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF]. The assumption of a thickness is also necessary to derive densities from the column densities provided by [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF]. [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF] predict that the oxygen atom number densities dominate over the sulfur atoms ones in the Io torus. The effect of the sulfur atoms is neglected against the effect of the oxygen atoms, as the charge exchange cross sections of 𝐻 + on 𝑂 and 𝑆 are similar [START_REF] Varghese | Atomic total electroncapture cross sections from C-,O-,F-and S-bearing molecular gases for MeV/u H+ and He+ projectiles[END_REF]. We therefore only focus on oxygen atoms in the Io torus and their density is supposed to be uniform along a vertical axis with a radial distribution given by:

{ 𝑛(𝜌) = 𝑛 𝑚𝑎𝑥 * 𝐴 𝑂 1 * 𝑒𝑥𝑝(𝐵 𝑂 1 * 𝜌)𝑓𝑜𝑟1 ≤ 𝜌 ≤ 6 𝑛(𝜌) = 𝑛 𝑚𝑎𝑥 * 𝐴 𝑂 2 * 𝑒𝑥𝑝(𝐵 𝑂 2 * 𝜌)𝑓𝑜𝑟6 ≤ 𝜌 ≤ 9.5
Constants 𝐴 𝑂 1 , 𝐴 𝑂 2 , 𝐵 𝑂 1 , 𝐵 𝑂 2 are approximating the column densities given by [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF] and the maximum density 𝑛 𝑚𝑎𝑥 is let free in our simulations. UV observations of the Io torus propose a value of 𝑛 𝑚𝑎𝑥 ≈ 30𝑐𝑚 -3 , as summarized by [START_REF] Lagg | Determination of the neutral number density in the Io torus from Galileo-EPD measurements[END_REF]. Observations of the pitch-angle distribution of energetic heavy ions suggest values of 𝑛 𝑚𝑎𝑥 ≈ 30𝑐𝑚 -3 [START_REF] Lagg | Determination of the neutral number density in the Io torus from Galileo-EPD measurements[END_REF] or 𝑛 𝑚𝑎𝑥 ≈ 10𝑐𝑚 -3 [START_REF] Mauk | Galileo-measured depletion of near-Io hot ring current plasmas since the Voyager epoch[END_REF].

In the Europas torus, the densities of 𝐻 2 dominate the densities of 𝑂 [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF]. We therefore neglect the contribution of the oxygen atoms against the dihydrogen molecules, as is done by [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF]. The radial distribution of dihydrogen molecules is fitted to the column densities given by [START_REF] Smyth | Europa's atmosphere, gas tori, and magnetospheric implications[END_REF], as we did for the oxygen of the Io torus. The maximum density of 𝐻 2 is let free, and may vary from 1.6 to 410𝑐𝑚 -3 [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF].

Charge exchange cross sections of trapped protons with dihydrogen molecules of the Europa torus are found in [START_REF] Barnett | Collisions of H, H2, He and Li atoms and ions with atoms and molecules[END_REF]. For the cross section of protons on neutral oxygen, we use the values given by [START_REF] Lindsay | Charge transfer cross sections for energetic neutral atom data analysis[END_REF] for kinetic energies lower than 100 keV. [START_REF] Varghese | Atomic total electroncapture cross sections from C-,O-,F-and S-bearing molecular gases for MeV/u H+ and He+ projectiles[END_REF] provide values of the cross section above 800 keV. In between 100 keV and 800 keV, we extrapolate the results of [START_REF] Lindsay | Charge transfer cross sections for energetic neutral atom data analysis[END_REF] to fit the value reported by [START_REF] Varghese | Atomic total electroncapture cross sections from C-,O-,F-and S-bearing molecular gases for MeV/u H+ and He+ projectiles[END_REF] at 800 keV. Figure 5 shows the adopted cross section. The proposed extrapolation fits very well the values reported by [START_REF] Varghese | Atomic total electroncapture cross sections from C-,O-,F-and S-bearing molecular gases for MeV/u H+ and He+ projectiles[END_REF].

Finally, charge exchange with the ions of the magnetodisc (𝑂 + , 𝑂 ++ , 𝑆 + , 𝑆 ++ , 𝑆 +++ ) is neglected in this study against charge exchange with the neutral atoms and molecules. This assumption is supported by the charge exchange cross sections of 𝐻 + on the oxygen ions computed by [START_REF] Fujiwara | Coulomb-born calculation of charge transfer cross sections of highlyionized atoms[END_REF], where these are two to three orders of magnitude lower than the cross sections of 𝐻 + on neutral oxygen.

Wave-particle interaction

Low-frequency electromagnetic waves, with frequencies under the local proton gyrofrequency, may resonate with the gyromotion of trapped protons and diffuse their equatorial pitch-angle and kinetic energy [START_REF] Kennel | Velocity space diffusion from weak plasma turbulence in a magnetic field[END_REF]. These waves propagate at frequencies close to ion cyclotron frequencies and are therefore named Electromagnetic Ion Cyclotron waves, or EMIC waves. A first modeling of the effect of the EMIC waves on Jovian protons is proposed in this study. To do so, the WAve-Particle Interaction software (WAPI), which relies on the quasi-linear theory and is developed by ONERA [START_REF] Sicard-Piet | Effect of plasma density on diffusion rates due to wave particle interactions with chorus and plasmaspheric hiss: extreme event analysis[END_REF], has been used.

EMIC waves can form as a result of corotating neutral molecules from the Io torus being ionized and picked up. Strong EMIC waves were observed by the Ulysses/URAP (Unified Radio And Plasma wave) experiment near Io in 1992 [START_REF]ULF waves in the Io torus: Ulysses observations[END_REF] and by Galileo/MAG during four passes over Io [START_REF] Kivelson | Io's interaction with the plasma torus: magnetometer report[END_REF][START_REF] Warnecke | Ion cyclotron waves observed at Galileo's Io encounter: Implications for neutral cloud distribution and plasma composition[END_REF][START_REF] Bianco-Cano | The Io-mass loading disk: wave dispersion analysis[END_REF]Russell et al., 2001). Following these observations, we assume that the EMIC waves propagate along magnetic field lines with 5.95 ≤ 𝐿 ≤ 6.22, which represent one interval near Io in the L-grid of Salammbô, and their effect is neglected outside this area.

The waves have been observed to have a left-handed polarization and to propagate parallel to the magnetic field lines near the magnetic equator. It is therefore assumed in this study that the propagation angles of the EMIC waves follow a Gaussian law with a mean propagation angle of 𝜃 𝑚 = 0°, a full width at half of the maximum 𝛿𝜃 = 30° and low and high cutoff angles of 0° and 70°.

It is also assumed, as in [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF], that wave-particle interaction in the magnetodisc, i. e. for magnetic latitudes around [-10°,+10°], dominates over the resonant interaction at higher latitudes.

Figure 1 of [START_REF] Bianco-Cano | The Io-mass loading disk: wave dispersion analysis[END_REF] shows EMIC waves spectral magnetic densities measured by Galileo/MAG. Very strong EMIC waves have been observed with frequencies in between the gyrofrequencies of the 𝑆𝑂 2 + and 𝑆𝑂 + ions. These waves have two to three orders of magnitude stronger spectral densities than the other observed frequencies. It is therefore assumed here that the effect of EMIC waves with frequencies between 0.4 and 0.7 Hz dominates over the effect of the other frequencies. The spectral magnetic density of the simulated EMIC waves is assumed to follow a Gaussian function, with low and high cutoff frequencies of 0.4 and 0.7 Hz, a mean frequency of 0.6 Hz and a large full width at half of the maximum of 10000 Hz. The last width enables to simulate a constant spectral magnetic density between the two frequencies of interest. The value of this constant should represent the drift-averaged density seen by trapped protons, that we tune in this study between 0 and the values observed by Galileo/MAG near Io as the occurrence rate and longitude distribution of EMIC waves in the Io torus are unknown. Galileo/MAG observations suggest that the constant should be capped by 10 2 to 10 4 𝑛𝑇 2 . 𝐻𝑧 -1 . In our model, a value of 2𝑛𝑇 2 . 𝐻𝑧 -1 is adopted to discuss the possible effect of EMIC waves on trapped protons. This value does not seem to be unrealistic in regard with Galileo/MAG observations. Harmonic numbers of -5 to +5 are considered. This harmonic number range is found to be sufficient to compute the diffusion rates, as wider ranges give similar results. Finally, the cold plasma electron and ion densities are given by the model of [START_REF] Bagenal | Empirical model of the Io plasma torus: Voyager measurements[END_REF] based on Voyager measurements at the orbit of Io.

Balance of the physical processes

The balance of the physical processes introduced in Salammbô is discussed here, in order to point out the predominant effects shaping the Jovian proton belts for kinetic energies higher than 1 MeV. A first way to estimate this balance is to have a look at the values of the absorption, friction and diffusion coefficients, normalized in 𝑠 -1 . Figure 6 documents these coefficients and one can say, at first order, that a process is important if its coefficient is close or greater than the local radial diffusion. Conversely, a physical process with a diffusion coefficient one or two orders of magnitude lower than the local radial diffusion is not very effective.

A first result of our study is about the kinetic energies of the protons with which 0.4-0.7 Hz EMIC waves may resonate. Figure 6 panel a) shows that the strongest equatorial pitch-angle diffusion coefficients near Io are found for low equatorial pitch-angle 1 MeV protons, while higher energies may be affected at higher equatorial pitch angles. The assumed spectral magnetic density of 2𝑛𝑇 2 . 𝐻𝑧 -1 makes the 0.4-0.7 Hz EMIC waves very effective in diffusing the equatorial pitch-angle of the trapped protons, so that strong proton precipitations in the Jovian atmosphere might be expected. Kinetic energy diffusion is found to be negligible against local radial diffusion.

As seen in Figure 6, charge exchange with the neutral gas torus of Europa is a strong loss process of 100 keV protons near the icy moon, as the associated coefficient is higher than local radial diffusion, what is consistent with the data analysis of [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF]. At this energy, charge exchange with neutral oxygen of the Io torus might be important near the volcanic moon but does not seem to be effective near Europa. For 1 MeV protons, charge exchange is a negligible process with the assumed maximum neutral densities, but a density in the Io torus a factor 100 higher than what has been used might change this conclusion (see section 7).

Coulomb collisions at 0.1 MeV is not affected by whether we take into account or not the elastic collisions with the ions of the magnetodisc, as the dashed blue line is superimposed with the thick blue line in Figure 6. A difference however appears at higher energies. Coulomb collisions are found to be negligible at >1 MeV against local radial diffusion. Near Europa, the Coulomb collisions coefficients are for all considered energies a few order of magnitudes lower than the local radial diffusion, what makes them negligible near the icy moon, even if Coulomb collisions with neutral particles were added. This justifies our assumption of section 4.5 on neglecting elastic collisions with neutral particles.

The strong absorption effect of the Jovian moons is noted, which gets more and more effective as the kinetic energy of the considered proton increases. It comes from the proton gyroradius, which is proportional to the square root of the energy and increases the absorption area of the moon, as discussed in section 4.3, but also from the drift period of the protons being faster at high energies, making the moon sweeping process more effective.

Outer boundary condition

The outer boundary condition should represent the kinetic energy spectrum and equatorial pitch-angle distribution of trapped protons at L=9.5. The equatorial omnidirectional differential kinetic energy spectrum is from the GIRE3 model (Garrett et al., 2017), which reproduces the Galileo/EPD/CMS spectra published by [START_REF] Mauk | Energetic ion characteristics and neutral gas interactions in Jupiter's magnetosphere[END_REF] under 1 MeV and fits the Pioneer measurements above. This spectrum is shown in Figure 7 b-d.

The equatorial pitch-angles are supposed to have near Europa's orbit a "pancake" distribution, peaked at 90°, reproduced by a sine function:

𝑓(𝐸 𝑘 , 𝑦 = sin(𝛼 𝑒𝑞 ) , 𝐿 = 9.5) = 𝑓(𝐸 𝑘 , 𝑦 = 1, 𝐿 = 9.5) * sin (𝛼 𝑒𝑞 )

Section 7 will validate the adopted outer boundary condition against in-situ measurements.

Salammbô predictions

Figure 7 panel a) shows predictions of the integral omnidirectional fluxes of protons by the Salammbô model in a magnetic meridian plane, using a maximum neutral density in the Io gas torus of 35𝑐𝑚 -3 and a maximum neutral density in the Europa gas torus of 410𝑐𝑚 -3 . These assumptions are not critical for the shown model output at >1 MeV. Outside of the equator, Figure 7 panel a) shows that the predicted fluxes strongly decrease near L=6.

Validations in section 7 will discuss the origin of this decrease in our model, whether it is an absorption effect of Io, charge exchange with neutral particles or resonant interactions with EMIC waves.

Kinetic energy spectra predicted at the magnetic equator for various L values are then documented in panels b, c and d. For the energy spectra, several simulation results are shown, with a model which does not take into account neither charge exchange with the Io and Europa gas torus or resonant interactions with EMIC waves (panel b), one model without EMIC waves but with charge exchange with the gas torus (panel c) and the last model with charge exchange and EMIC waves (panel d).

Sharp flux drops at low energies seen in panel b-d are artifacts resulting from the minimum kinetic energy boundary condition, as discussed by [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF]. Real spectra are expected instead to gradually decrease to low energies due to charge exchange losses, as we discuss below. Intensities above the sharp drop-off are unaffected by the artifact.

Panel b enables to appreciate the adiabatic transport of protons: this process essentially shifts spectra at large L towards higher energy when moving inwards to smaller L. It also shows the absorption effect of Io between L=6.65 and L=5.56. No clear absorption effect of the inner moons Thebe (between L=2.98 to L=2.38) or Metis and Adrastea (between L=2.08 to L=1.59) is seen in the equatorial and omnidirectional flux. This is a major difference to the trapped electrons that comes from the fact that protons do not experience pitch-angle diffusion by Coulomb collisions or pitch-angle frictions by synchrotron radiation. Indeed, the previous diffusion and friction would help to move equatorial protons to higher mirror latitudes where they can be swept more efficiently by the moons, making the absorption effect of the moon observable in the omnidirectional equatorial flux. The model therefore predicts that equatorial protons do not suffer of moon absorptions, what creates the elongated equatorial flux seen near the magnetic equator close to Jupiter in the >80 MeV meridian plot.

Figure 7 panel c) shows losses by charge exchange with the Io and Europa gas torus, effective for kinetic energies lower than a few hundreds keV. Strong losses due to the interaction with EMIC waves near Io can be seen in Figure 7 panel d), with a wavy pattern similar to what wave-particle interaction does on trapped electrons [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF].

Validation of the model against in-situ observations

The validation of the Salammbô proton model that takes into account charge exchange with the Io and Europa torus and resonant interaction with EMIC waves near Io is discussed here.

Table 1 shows that in-situ flux measurements are available in three energy ranges: 1 to 3 MeV, around 15 MeV and then around >60 MeV to >80 MeV (what we call hereafter "very energetic protons"). This section presents the comparison of the proton fluxes predicted by the Salammbô model with the observations in these three energy ranges.

Predictions of the model in which the effect of EMIC waves is switched off are also shown, to discuss the effect of these waves on our predictions. A discussion on the effect of the charge exchange process is also included, in order to discuss the origin of the intense flux depletion observed near Io in 1 MeV measurements.

Validation against 1 to 3 MeV observations

Figure 8 shows the comparison of predicted fluxes with 1 to 3 MeV observations. The outer boundary condition imposed near the orbit of Europa can either be seen at L=9.5 for the Galileo plots, or at the beginning and end of our model of the Pioneer fly-bys. One can note that the Salammbô outer boundary condition understimates the 1 MeV fluxes by a factor 2 to 10 near Europa. However, the slope of the intensity change between the orbit of Europa and Io (that results mostly from adiabatic acceleration) is consistent with the measurement. Then, near Io, a two-order of magnitude flux depletion is seen in the five channels. One can note that the Salammbô model without EMIC waves do not predict this intense depletion at all, even when assuming the maximum reasonable densities in the Io and Europa tori. This means that our model clearly dismisses the absorption effect of Io or its torus as the origin of the observed flux depletion. Only when additional losses due to EMIC waves scattering protons in Jupiter's atmosphere are taken into account, the amplitude of the depletion is better reproduced, with a maximum to minimum ratio near Io of around 50. The flux depletion is therefore still underestimated but our modeling shows that EMIC waves with the frequencies and spectral magnetic densities discussed in section 4.8 might be the origin of it.

Our modeling effort shows that charge exchange near Europa is very effective to remove protons in the energy range of hundreds of keV from the proton belts, consistent with the conclusions of [START_REF] Kollmann | The vertical thickness of Jupiter's Europa torus from charged particle measurements[END_REF]. In principle, this depletion at relatively low energies and large distances translates into a depletion in the MeV range when the protons are transported inward towards the orbit of Io. However, our simulations reveal that this charge exchange depletion is negligible against the sweeping effect of Io on MeV protons.

Regarding the Io gas torus, the maximum density of neutral oxygen is not known with certainty but has been reported to be around 35𝑐𝑚 -3 (see section 4.7). Even a maximum density of 350𝑐𝑚 -3 has no observable effect in our simulations, while Figure 9 shows the effect of a maximum density of 3500𝑐𝑚 -3 on the 1 MeV prediction along the trajectory of Pioneer 10. One can note that this enhanced charge exchange process does not help to reproduce the observed flux depletion near Io. However, it completely empties the 100 keV proton belts at Io's orbit, what is seen inward of the volcanic moon in our predictions. Using the charge exchange cross sections detailed in section 4.7, we therefore dismiss charge transfer with the Io gas torus as a possible explanation of the observed flux depletions in 1 MeV measurements near the moon, independently of the neutral number density. The intensity increase of trapped protons from Europa to Io is consistent with the measurements. Near Io, flux depletions predicted along the Pioneer 10 outbound, Voyager 1 outbound, and Pioneer 11 trajectories are not affected by whether EMIC waves are introduced in the model or not and are realistically predicted. These cases where the prediction is independent of the effect of EMIC waves validate the adopted radial diffusion coefficient, as the good match obtained between model and data only comes from the adopted boundary condition (constrained by many in-situ measurements), the sweeping effect of Io (that is a geometric calculation in which we trust) and the radial diffusion coefficient (the assumption we validate). Pioneer 10 inbound and Voyager 1 inbound predictions are however strongly affected by EMIC waves with the assumed magnetic densities (see section 4. Above a distance to the center of Jupiter of 2.3 Rj, our simulations suggest that the channel P1 of Galileo Probe EPI only measures trapped electrons. The proton model correctly reproduces the counts observed there by P2 and P3. Our study of the contamination by alpha particles (see Appendix A) shows that P2 and P3 are very likely to be contaminated between 1.8 and 2.3 Rj, while a different assumption on the response of P1 to alpha particles might lead to the same conclusion for this channel. We therefore consider that the "bump" seen in Galileo Probe EPI proton channels is a contamination by alpha particles. Inside 1.8 Rj, a major discrepancy between Salammbô and the observed counts, of a factor 100 to 1000, is noted. We infer this discrepancy to the main ring, which has been shown to be able to play a major role there in section 4.4 and is not included in the present model.

Validation against 15 MeV observations

Summary and discussion

A physical model, named Salammbô, of the trapped protons with kinetic energies greater than 1 MeV inside Europa's orbit has been presented. It is the first physics-based model of the proton radiation belts of Jupiter ever proposed, what gives for the first time a tool to not only predict the radiative environment near Jupiter but to also study the physical processes balance in the Jovian proton radiation belts. It relies on an outer boundary condition at L=9.5 provided by the empirical model GIRE3 developed by Garrett et al. (2017) that correctly reproduces the observations used to validate Salammbô.

All physical processes able to shape the proton belts have been introduced, among which is radial diffusion. The assumption on the radial diffusion rate has been validated against >15 MeV observations and Galileo Probe measurements in section 7. We note that the radial diffusion rate used in this study is very similar to what has been proposed by [START_REF] Nénon | A new physical model of the electron radiation belts of Jupiter inside Europa's orbit[END_REF] for the trapped electrons. As it is generally assumed around Earth and Saturn that the radial diffusion is the same for electrons and protons [START_REF] Lejosne | Bounce-averaged approach to radial diffusion modeling: from a new derivation of the instantaneous rate of change of the third adiabatic invariant to the characterization of the radial diffusion process[END_REF][START_REF] Kollmann | Processes forming and sustaining Saturn's proton radiation belts[END_REF], the previous note tends to show that the present proton model somewhat validates the radial diffusion rate of the electron model and vice-versa. The adopted radial diffusion coefficient in our physical models is consistent with what has been proposed by [START_REF] Bespalov | Features of the radial diffusion of energetic electrons in the middle Jovian magnetosphere[END_REF], and therefore supports the hypothesis that electric fields in the Io torus might be the origin of the radial transport of radiation belt particles in the inner Jovian magnetosphere. A dependence of the radial diffusion coefficient with kinetic energy might exist, but it would give a rate decreasing with increasing kinetic energies if similar to what is found around Earth [START_REF] Lejosne | Deriving electromagnetic radial diffusion coefficients of radiation belt equatorial particles for different levels of magnetic activity based on magnetic field measurements at geostationary orbit[END_REF], what goes in the opposite direction of what would be needed in our model to reproduce intense MeV flux drops near Io's orbit with a radial coefficient validated against 15 MeV measurements.

Coulomb collisions with the plasma ions and free electrons of the magnetodisc have been modeled. Our simulations show that, according to the density model of [START_REF] Divine | Charged particle distributions in Jupiter's magnetosphere[END_REF], these elastic collisions play a minor role. Charge exchange with the neutral gas torus of Io and Europa has also been shown to be negligible for a model which intends to reproduce >1MeV fluxes, independently of the neutral densities near Io or Europa.

Absorption by the moons clearly plays a major role in the proton belts of Jupiter. Interactions with the Jovian atmosphere, including absorption in the loss cone, Coulomb collisions and charge exchange with atmospheric atoms and particles, also have a predominant effect in our model as they remove field-aligned protons bouncing within or close to the atmosphere.

Equatorial pitch-angle diffusion by 0.4-0.7 Hz EMIC waves have been simulated near Io. As reported in section 4, this frequency range has been assumed to dominate over other frequencies. Our wave-particle simulations have shown that, according to the electron and ion densities given by [START_REF] Bagenal | Empirical model of the Io plasma torus: Voyager measurements[END_REF], 0.4-0.7 Hz EMIC waves resonate with 1 MeV low equatorial pitch angle protons and higher energy higher equatorial pitch-angle protons (see Figure 6). The intensity of the waves, or spectral magnetic densities, is only known in the vicinity of Io (see section 4), so that the drift averaged magnetic spectral density has been tuned between 0 and the values measured by the Galileo/MAG experiment. Validations with an adopted value of 2𝑛𝑇 2 . 𝐻𝑧 -1 have been presented. This demonstrated that scattering by EMIC waves is of major importance since it dominates over moon absorption and charge exchange losses near Io on all kinetic energies above 1 MeV, as was suspected by [START_REF] Thomsen | On determining magnetospheric diffusion coefficients from the observed effects of Jupiter's satellite Io[END_REF].

Then, the validations presented in section 7 try to explain the flux depletions observed near the orbit of Io. Salammbô tries puts a scientific context on what future equatorial observations might see with the Europa-Clipper and JUICE missions, but does not fully close the following questions: what physical process may sweep near Io equatorial protons in the MeV to tens of MeV range ? What is the origin of the two orders of magnitude flux depletion seen at 1 MeV by Pioneer 10, Pioneer 11, Galileo, and Juno ? Wave-particle interaction with EMIC waves has been proposed in this study but does the magnetic field configuration observed by Galileo in the wake of Io influence the drift trajectory of protons, as it may do for trapped electrons [START_REF] Thorne | Energetic electron butterfly distributions near Io[END_REF] ? If so, is the absorption cross section of Io enhanced or reduced ?

The refinement of the Salammbô equatorial pitch angle grid will enable to feed the Salammbô model with on-going Juno/JEDI observations. In addition, a revisited magnetic field model might change our results in the future, especially very close to the planet where currently available models fail to reproduce the magnetic field observed by Juno [START_REF] Connerney | Jupiter's magnetosphere and aurorae observed by the Juno spacecraft during its first polar orbits[END_REF].

Finally, the Salammbô-proton model is able to predict fluxes anywhere inside L=9.5, making it a powerful tool to assess the Jovian radiation belts environment. It may complement empirical models, as is done in the hybrid electron JOSE model [START_REF] Sicard- | JOSE: A new Jovian specification environment model[END_REF]. The outer boundary condition which is consistent with the GIRE3 model makes GIRE3 and Salammbô easy to plug together, so that a common model might be developed in order to predict the harsh radiative environment Juno, Europa-Clipper and JUICE will be confronted to.

be approximated with step functions. In our study, the response of the HE channel to alpha particles is approximated by a step function starting at 350 MeV with a constant geometric factor of 𝐺(𝐻𝐸) = 3.10 -2 𝑐𝑚 2 . 𝑠𝑟. P1, P2 and P3 have the same minimum kinetic energy of 350 MeV and constant geometric factors of respectively 1𝑐𝑚 2 . 𝑠𝑟, 1.510 -1 𝑐𝑚 2 . 𝑠𝑟 and 1.510 -1 𝑐𝑚 2 . 𝑠𝑟.

Assuming that the four previous EPI channels respond to >350 MeV alpha particles means that we assume that they all respond to the same external omnidirectionnal integral flux of alpha particles. This integral flux can be estimated by: 𝐽(> 350𝑀𝑒𝑉) = 4𝜋 𝑐𝑜𝑢𝑛𝑡𝑠(𝐻𝐸) 𝐺(𝐻𝐸)

Then, the counts which may be attributed to alpha particles in P1, P2 or P3 (𝑃𝑖) may be estimated with:

𝑐𝑜𝑢𝑛𝑡𝑠(𝑃𝑖) = 𝐺(𝑃𝑖) 4𝜋 * 𝐽(> 350𝑀𝑒𝑉) = 𝐺(𝑃𝑖) 𝐺(𝐻𝐸) * 𝑐𝑜𝑢𝑛𝑡𝑠(𝐻𝐸)

Figure 11 shows counts which might be attributed, from this method, to alpha particles in the P1, P2 and P3 channels.

Figure 10

 10 Figure 10 is similar to Figure 8 and shows the comparison between the in-situ measurements around 15 MeV by Pioneer 10, Pioneer 11 and Voyager 1 and the fluxes predicted by the Salammbô model in this energy range. One can note that the adopted outer boundary condition is in agreement with the Pioneer 10 and Pioneer 11 measurements, what tends to validate the chosen equatorial pitch-angle dependency detailed in section 5. However, the outer boundary condition overestimates the Voyager 1 fluxes by a factor of 3, what might be inferred to time variability or to an underestimated geometric factor of the PSA3 channel of LECP.The intensity increase of trapped protons from Europa to Io is consistent with the measurements. Near Io, flux depletions predicted along the Pioneer 10 outbound, Voyager 1 outbound, and Pioneer 11 trajectories are not affected by whether EMIC waves are introduced in the model or not and are realistically predicted. These cases where the prediction is independent of the effect of EMIC waves validate the adopted radial diffusion coefficient, as the good match obtained between model and data only comes from the adopted boundary condition (constrained by many in-situ measurements), the sweeping effect of Io (that is a geometric calculation in which we trust) and the radial diffusion coefficient (the assumption we validate). Pioneer 10 inbound and Voyager 1 inbound predictions are however strongly affected by EMIC waves with the assumed magnetic densities (see section 4.8) and reduce the intensities by about one order of magnitude relative to our model without EMIC waves. For the Pioneer 10 prediction, the flux depletion with EMIC waves is overestimated, what then tends to have fluxes underestimated of around of a factor 20 near perijove. While the absolute values of the predicted Voyager intensities deviate from the observations, the relative intensity change across Io's sweeping zone is properly predicted by the model including EMIC waves. Finally, on the Pioneer 10 outbound trajectory, a flux depletion is predicted near the orbit of Thebe and consistent with the observation. On Pioneer 11, effect of the EMIC waves is only seen for McIlwain parameters lower than 3. The model, with or without

  Figure 10 is similar to Figure 8 and shows the comparison between the in-situ measurements around 15 MeV by Pioneer 10, Pioneer 11 and Voyager 1 and the fluxes predicted by the Salammbô model in this energy range. One can note that the adopted outer boundary condition is in agreement with the Pioneer 10 and Pioneer 11 measurements, what tends to validate the chosen equatorial pitch-angle dependency detailed in section 5. However, the outer boundary condition overestimates the Voyager 1 fluxes by a factor of 3, what might be inferred to time variability or to an underestimated geometric factor of the PSA3 channel of LECP.The intensity increase of trapped protons from Europa to Io is consistent with the measurements. Near Io, flux depletions predicted along the Pioneer 10 outbound, Voyager 1 outbound, and Pioneer 11 trajectories are not affected by whether EMIC waves are introduced in the model or not and are realistically predicted. These cases where the prediction is independent of the effect of EMIC waves validate the adopted radial diffusion coefficient, as the good match obtained between model and data only comes from the adopted boundary condition (constrained by many in-situ measurements), the sweeping effect of Io (that is a geometric calculation in which we trust) and the radial diffusion coefficient (the assumption we validate). Pioneer 10 inbound and Voyager 1 inbound predictions are however strongly affected by EMIC waves with the assumed magnetic densities (see section 4.8) and reduce the intensities by about one order of magnitude relative to our model without EMIC waves. For the Pioneer 10 prediction, the flux depletion with EMIC waves is overestimated, what then tends to have fluxes underestimated of around of a factor 20 near perijove. While the absolute values of the predicted Voyager intensities deviate from the observations, the relative intensity change across Io's sweeping zone is properly predicted by the model including EMIC waves. Finally, on the Pioneer 10 outbound trajectory, a flux depletion is predicted near the orbit of Thebe and consistent with the observation. On Pioneer 11, effect of the EMIC waves is only seen for McIlwain parameters lower than 3. The model, with or without

Figure 1 Figure 2

 12 Figure 1 Minimum kinetic energy of equatorially mirroring particles simulated by the Salammbô-electron (Nénon et al., 2017) and Salammbô-proton models using a lower kinetic energy boundary of 25 keV at L=9.5.

Figure

  Figure Absorption cross section of a moon when the proton gyroradius is smaller than the moon radius (left) or bigger than the moon radius (right). Purple circles represent limit trajectories of protons impacting the moon. When the proton gyroradius is biggerthan the moon radius, a guiding-center zone within the moon exists where protons would turn around the moon and not be absorbed.

Figure 6

 6 Figure 6 Panel a) Equatorial pitch-angle and kinetic energy diffusion coefficients associated to EMIC waves near Io. Panel b) Absorption and friction coefficients associated to the other physical processes. When a coefficient is not on the plot, it means that its value is under the minimum value of the vertical axis.

Figure 7

 7 Figure 7 Panel a) Omnidirectional integral flux of trapped protons in a magnetic meridian plan. The yellow dashed line shows the Galileo Probe trajectory. The grey area in the >1 MeV plot reminds that Salammbô cannot predict 1 MeV protons inside L=3 (see section 2). Panels b), c) and d) show the kinetic energy spectra of the predicted omnidirectional differential fluxes at the magnetic equator, taking into account or not charge exchange with the Io and Europa gas torus and resonant interactions with EMIC waves near Io. Sharp flux drops at low energies are an artifact.

Figure 8 Figure 9 Figure 10

 8910 Figure 8 Validation of the Salammbô model with (in red) or without (in purple) taking into account wave-particle interaction with EMIC waves against 1 to 3 MeV in-situ measurements (in blue). For the Galileo validation, only the prediction at the magnetic equator is shown. Orange areas show the Mc Ilwain parameters intercepted by Io. The grey area shows the Mc Ilwain parameters intercepted by Thebe.

Figure 11

 11 Figure 11 Validation of the Salammbô model against very energetic proton in-situ measurements. Orange areas show the Mc Ilwain parameters intercepted by Io and the grey areas the ones intercepted by Thebe. Note that the Galileo/EPI panels are in counts. The model count rates were calculated by applying the instrument response to the modeled intensities (see Appendix A).

Figure

  Figure A1 Geometric factors of HE, P1, P2, and P3 channels in response to electrons, protons and alpha particles, scanned from Pehlke (2000). The dotted lines in the geometric factors in response to alpha particles give the approximated step function used in our study. The response of P2 to alpha particles is assumed to be the same as P3 to alpha particles.

Table 1 In-situ proton measurements used in this study to validate the Salammbô model

 1

	Mission-Instrument-Channel Energy range	L-coverage
	Pioneer 10-TRD-M3	>80 MeV	3 -9.5
	Pioneer 10-CRT	1.2-2.1 MeV	3 -9.5
		14.8-21.2 MeV
	Pioneer 11-CRT	1.2-2.1 MeV	1.4 -9.5
		14.8-21.2 MeV
	Pioneer 11 -GTT	0.5 to 3.6 MeV	1.4 -9.5
	Voyager 1 -LECP -PSA3	16.3 to 26.2 MeV	5 -9.5
	Galileo Probe -EPI -P1, P2,	See appendix A	1 -5
	P3
	Galileo Orbiter -	3.2 to 10.1 MeV	≈ 3 -9.5
	EPD/LEMMS -B0
	Galileo Orbiter -EPD/CMS	0.54 to 1.25 MeV	≈ 3 -9.5
	-TP3

Table 2 Mean excitation energies of oxygen and sulfur neutral atoms and ions.

 2

	Atomic particle or ion	Mean excitation energy 𝐼 𝑖
	𝑂	95.0 eV
	𝑂 +	125.2 eV
	𝑂 ++	157.2 eV
	𝑆	180 eV
	𝑆 +	195.5 eV
	𝑆 ++	232.5 eV

Acknowledgements

The authors are thankful for fruitful discussions with Voyager 1 LECP and Galileo Probe EPI Principle Investigators S. M. Krimigis and L. J. Lanzerotti.

We thank I. Rabadan for discussions on charge exchange cross sections.

We are also thankful to S. M. Brooks, H. Throop and M. Showalter for discussions on the Jovian rings.

The research described in this paper by H. Garrett was carried out at the Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA, USA under a contract with the National Aeronautics and Space Administration.

Voyager 1 15 minutes averaged LECP count rates can be found on the NASA planetary data system (PDS) website in the volume VG1-J-LECP-4-SUMM-SECTOR-15MIN-V1.1. Galileo/EPD data not archived in the PDS are available upon request by contacting EPD researchers, see the team contacts available on the EPD website sdwww.jhuapl.edu/Galileo_EPD.

Appendix A Galileo Probe Energetic Particle Investigation

Figure A1 shows the energy-dependent geometric factors 𝐺(𝐸) of the channels HE, P1, P2, and P3 in response to impacting electrons, protons and alpha particles. They were scanned from the thesis of Eckhard Pehlke [START_REF] Pehlke | Teilchenpopulationen in der inneren Jupitermagnetosphäre. Untersuchung der EPI-daten von der Galileo Probe[END_REF].

From there, it is possible to integrate over the distribution function of Salammbô to predict counts (in 𝑠 -1 ) by:

With 𝑝 the proton relativistic momentum, 𝑓(𝐸, 𝑦, 𝐿) the distribution function of Salammbô, 𝛼 and 𝛼 𝑒𝑞 the local and equatorial pitch angles. The factor 2𝜋 comes from the integration over the gyration angle, and the factor 2 from the pitch-angle integral being evaluated between 0 and 𝜋 2 while pitch angle values range from 0 to 𝜋.

In order to be able to use the count rates measured by the channel HE to study the contamination by alpha particles in P1, P2, and P3, the geometric factors of Figure A1 should