Hubert Piquet
email: hubert.piquet@laplace.univ-tlse.fr

Member, IEEE Sounil Bhosle
email: sounil.bhosle@led-development.fr

Rafael Diez
email: rdiez@javeriana.edu.co

Michael V Erofeev
email: michael@loi.hcei.tsc.ru

Pulsed Current-Mode Supply of Dielectric Barrier Discharge Excilamps for the Control of the Radiated Ultraviolet Power

Keywords: Dielectric barrier discharge (DBD), excilamps, pulsed current-mode supply, UV emission control

UV excimer lamps are efficient narrowband sources of UV radiation with applications in various domains. The issue of controlling the UV emission by means of the power supply associated with such lamps favors pulsed current-controlled generators. After having established the previous statements, we propose a dedicated power converter topology which implements the needed performances. The analysis of the degrees of freedom of this structure shows the capability of this pulsed supply to realize the control of both the pulses' current energy and of the mean power transferred to the lamp. Actual experimental realizations and measurement are presented and the feasibility and the performances of the proposed solutions are established.

I. INTRODUCTION

E XCILAMPS are electrodischarge sources of incoherent spontaneous UV and VUV radiation, which is emitted due to the decay of excimer and exciplex molecules. They have some distinctions which may be widely used in different fields of science and technology. The main distinguishing feature between the excilamps and traditional mercury lamps, as well as thermal sources of UV radiation, is the emission spectrum; up to 80% of radiant power may be concentrated in a narrow spectral band of transition of the corresponding molecule (a few nanometers at half maximum). It makes possible to use excilamps in applications where selective effect on complex systems induced by narrow band of UV and VUV radiation is needed. For example, in the stimulation of photobiologi-cal, photochemical, and photophysical processes, such as the inactivation of microorganisms [START_REF] Erofeev | UV excimer lamp irradiation of fibroblasts: The influence on antioxidant homeostasis[END_REF], [START_REF] Sosnin | A bactericidal barrier-discharge KrBr excilamp[END_REF], photolytic processing of metal, dielectric and semiconductor layers, surface cleaning and decomposition of harmful organics [START_REF] Sosnin | Applications of capacitive and barrier discharge excilamps in photoscience[END_REF]- [START_REF] Sokolova | Photo transformations of phenols in aqueous solutions under different excitation modes[END_REF]. The absence of mercury in working mixture is another advantage of excilamps which is very important from the ecological point of view. The most promising excilamps are those excited by dielectric barrier discharge (DBD) [START_REF] Kogelschatz | Dielectric-barrier discharges: Their history, discharge physics, and industrial applications[END_REF]- [START_REF] Rahmani | Dielectric-barrier-discharge excilamp in mixtures of Krypton and molecular chlorine[END_REF]. DBD are electric discharges between two metallic electrodes, with at least one of them covered by a dielectric material. Excilamps with two barriers have longer lifetimes due to the absence of direct contact between the working gas mixture and the metallic electrodes.

Previous researches have shown that DBD excilamps are particularly efficient when supplied in voltage pulsed mode [START_REF] Lomaev | Capacitive and barrier discharge excilamps and their applications (review)[END_REF]- [START_REF] Carman | Computer modelling of a short-pulse excited dielectric barrier discharge Xenon excimer lamp (172 nm)[END_REF]. With this supply mode, optimal conditions for supplying excilamps have been found with voltage pulses of some kilovolts applied at frequencies of some tens of kilohertz (around 100 kHz), with a duty cycle about 1%, featuring very narrow voltage pulses. Nevertheless, the voltage supply mode has appeared to be not really convenient with the intention of implementing an actual control of the UV radiation; this emission has been observed to be correlated with the stiffness of the flanks presented by the voltage pulses, being a property really difficult to control. Our studies are oriented toward disinfection and sterilization [START_REF] Erofeev | UV excimer lamp irradiation of fibroblasts: The influence on antioxidant homeostasis[END_REF], [START_REF] Laroussi | Decontamination of water by excimer UV radiation[END_REF], as well as dermatologic applications. Keeping this context in mind, a controllable UV emission is a highly desirable feature in these systems.

In this paper, a physical approach, based on finite element simulation, is proposed in Section II, where the correlation between gas current and UV emission is studied and the interest of implementing a pulsed current-source supply for DBD excilamps is established. Section III is devoted to the study of such a pulsed current source; innovative static converter topology, operating principle, design considerations, and actual implementation are presented. Section IV deals with the analysis of the performances obtained by means of this pulsed current source for the control of the UV emission; they confirm the very tight correlation between this emission and the pulsed current injected into the lamp, as well as the capability of the converter to control the UV output power, by means of its degrees of freedom (DOF).

II. CORRELATION BETWEEN GAS CURRENT AND UV EMISSION

In order to analyze how the current controls the UV emission in an excilamp, we have developed a partial-differentialequation-based (PDE) model [START_REF] Bhosle | A new approach for boundary conditions in dielectric barrier discharge modeling[END_REF] for a planar double dielectric layer Xenon excilamp. The plasma is assumed homogeneous and side effects around the electrodes are neglected. The computation is consequently performed in one-dimensional, along the axis of the geometry similar to the one presented in [START_REF] Oda | One-dimensional modelling of low frequency and high-pressure Xe barrier discharges for the design of excimer lamps[END_REF]. In the modeled system, set up for the purpose of studying the correlation between gas current and UV emission, the thickness of the dielectric layers is 2 mm, the gas gap is 4 mm, and the Xenon filling pressure is 5.33 × 10 4 Pa (400 torr); the geometry of the bulb is symmetrical with respect to the two possible polarities. The model solves the drift-diffusion equations for the species considered in the model coupled to Poisson's equation.

A voltage-supplied DBD (which is the classical approach) is modeled imposing a potential on both outer sides of the dielectrics. This leads to two Dirichlet boundary conditions for Poisson's equation. Usually, one side is grounded and the other is held at the voltage chosen for the modeling.

A current-supplied DBD needs a different approach; it is modeled in grounding one side of the outer surface of a dielectric and imposing the electric field, which is proportional to the time integral of the current, on the outer surface of the other dielectric barrier

E(x 0 , t) = 1 ε t 0 j(x 0 , t)dt (1)
where E(x 0 , t) is the electric field on the outer dielectric surface, ε is the permittivity of the dielectric material, and j(x 0 , t) is the current density flowing through the dielectric.

This corresponds to a Neumann boundary condition for the Poisson's equation. The model relies on the local field approximation and consequently the transport coefficients and source terms depend on the electric field. These coefficients and source terms are computed by Bolsig [15]. Once solved, the model can display the evolution of the plasma species density, as well as the electric field, versus time and/or space [START_REF] Bhosle | Modeling of a dielectric barrier discharge lamp for UV production[END_REF]. From the modeling results, it appears that the mechanism which has the major impact on the development of the discharge is the propagation of the ionization wave, occurring in the neighborhood of the dielectrics in cathode phase. This ionization wave has a strong impact on the current waveform and leads to a massive production of charges, excited species, and particularly excimers [START_REF] Piquet | Innovative power supply concepts for DBD excilamps[END_REF]. As these latter are responsible for the UV emission, the current waveform is closely related to the time evolution of the UV flux.

When the excilamp is supplied in voltage mode [START_REF] Oda | Estimation of the light output power and efficiency of Xe barrier discharge excimer lamps using a one-dimensional fluid model for various voltage waveforms[END_REF], a large part of the voltage drop is transferred on the cathode sheath [START_REF] Bhosle | Implementation of an efficiency indicator in an electrical modeling of a Dielectric Barrier Discharge Lamp[END_REF]. As the applied voltage is monotonically evolving, the cathode sheath develops and stores energy. When the voltage drop at the sheath achieves a threshold value, electrons emitted at the cathode have enough energy to ionize the gas, leading to an avalanche and the development of the ionization wave toward the cathode. During this brief phase (some hundreds of nanoseconds), the energy stored in the sheath is released and a part is transferred to excimers, which relax and produce UV. The result is a UV emission peak correlated to a strong current peak in the external circuit due to the sudden collapse of the sheath voltage drop (note that this behavior is associated with a voltage supply; the details concerning the UV emissions can be found in [START_REF] Oda | Estimation of the light output power and efficiency of Xe barrier discharge excimer lamps using a one-dimensional fluid model for various voltage waveforms[END_REF]).

When the excilamp is supplied in current mode, the cathode sheath is formed like a current-charged capacitor. During this phase (called phase A, shown on Fig. 1), the imposed current flows mainly in the discharge as a displacement current. Then (phase B), the ionization wave appears (and the associated excimers are created) when the voltage drop at the sheath achieves the threshold. At this moment, the current in the discharge is mainly a conduction current due to the contributions of the imposed current and of the release of the sheath charges. However, if the total current is controlled and sustained (phase C), the ionization wave is then sustained and appears like a settled wave near the cathode. This zone could be considered similar to a negative glow.

The resulting UV flux waveform has a peak due to the release of the sheath energy, followed by a form similar to the imposed current form, if this latter is sustained longer than the peak time width. This can be observed on the simulation results for a 50 kHz square pulsed current wave supplying the modeled excilamp (Fig. 1).

As a result, the UV flux is directly related to the conduction current form. Except during the sheath formation and energy release phases (A and B), the conduction current corresponds to the total imposed current. Note that the UV peak (phase B) is associated with a current peak that is internal to the DBD structure; the latter, as a result, does not appear as a current peak in the supply current waveform in Fig. 1.

Consequently, a power supply which is able to execute a current control on an excilamp is also able to achieve a control on its UV flux waveform.

Concerning the lamp voltage waveform of Fig. 1, it should be noted that the gas breakdown occurs when the gas voltage rises to 1800 V. Nonetheless, the lamp voltage is higher at the same moment (as shown in model in Fig. 2, lamp voltage is the sum of gas voltage and dielectric walls voltages). After gas breakdown happens, lamp voltage continues increasing linearly as the dielectric capacitance is supplied by a current source. This is the reason why voltage across the lamp rises to almost 20 kV in Fig. 1.

The aim of the following section is to study a pulsed currentmode supply which will be used to validate the previous reasoning.

III. PULSED CURRENT-MODE POWER SUPPLY

The following experiments are accomplished with an axisymmetrical DBD lamp (see Fig. 2). The lamp geometry is approximately 130 mm in length, with internal and external cylinder radius of 10 mm and 20 mm, respectively, and barrier thickness of around 1.5 mm. Fused silica is used as the dielectric material and the confined volume is filled with Xenon and Cl 2 to produce the XeCl exciplex (308 nm). The external electrode, connected to the electrical ground, is conformed by a metallic mesh that wraps the exterior wall, allowing the UV radiation. The internal electrode is a metallic cylinder, which is connected to the power supply output.

A. Specifications for the Pulsed Current-Mode Power Supply

The waveform of the imposed current, shown in Fig. 1, flowing into the test lamp has been defined a priori. We propose here a reasoned approach for the definition of its characteristics. Concerning the fundamental electrical characteristic of the DBD lamp, the classical equivalent circuit of dielectric barrier discharges is shown in Fig. 2. C diel is the equivalent series capacitances of the dielectric walls of the lamp; C gas is the capacitance of the gas gap, which mainly describes the behavior of the latter when the gas voltage v gas remains under the threshold. When the discharge current appears, the conduction current in the gas is defined by means of the gas conductance G gas .

A complete approach of the modeling of DBD by means of such an equivalent circuit, as well as the delicate issue of the identification of its parameters, is presented in [START_REF] Díez | Predictive model of a DBD lamp for power supply design and method for the automatic identification of its parameters[END_REF]. One of the major benefits of such a predictive model is its ability to calculate the waveforms of nonmeasurable quantities, such as Ggas, igas, vgas, as will be shown later (Section III-D).

Owing to the mainly capacitive nature of the DBD equivalent circuit, a mandatory property of a current source supply will be an average value equal to zero for the lamp "i lamp " current. This average value has to be evaluated over an interval equal to the operating period of the considered pulsed source. To enable comparisons with the results obtained with a voltage supply, the frequency range of the pulsed current source is chosen similar to the one which is usually selected (fs between 50 kHz and 150 kHz).

The pattern of the current waveform (Fig. 3) is chosen similar to the one shown in the simulation of Fig. 1; three parameters are used to define it:

1) the magnitude of the current pulses I a ; 2) the duration of the current pulses tdech; 3) the duration of the relaxing time interval trel during which the lamp current remains zero (this quantity, in conjunction with the previous one defines the value of the operating period Tlamp).

Finally, the power transferred to the lamp by the pulsed current supply is taken from a dc voltage stage (typically 100 V).

B. Power Supply Topology, Operating Principle, and Degrees of Freedom 1) Topology:

A static converter circuit that complies with the current-mode idea and the specifications detailed in Section I was developed in [START_REF] Piquet | Innovative power supply concepts for DBD excilamps[END_REF], [START_REF] Diez | Current mode converter for dielectric barrier discharge lamp[END_REF]. This topology is synthesized starting from a buck-boost converter operating in discontinuous current mode (DCM), cascaded with an H-bridge and a stepup transformer. The H-bridge is inserted to achieve the periodic inversion of the lamp current direction. The transformer is used to adjust the voltage in the lamp to the semiconductor devices range. After the simplification of the structure (elimination of redundant switches), the final topology is shown in Fig. 4.

2) Operating Sequences: Fig. 5 shows the idealized expected waveforms (current in the L inductance i L and current in the lamp i lamp ). These plots are obtained with a circuit simulation program [START_REF]PSIM User's Guide[END_REF], [START_REF]Saber MAST Language Reference[END_REF]; the step-up transformer is supposed ideal (1:n ratio) and the lamp is sketched, according to the characteristic which will be presented in Fig 8, as a ±V th (the threshold voltage V th is around 1800 V) voltage source in series with the dielectric capacitor C diel .

The operating sequences, according to the states of the switches of the converter are shown in Fig. 6.

During sequences (A) and (C), the energy is stored in the L inductance; as the current in the inductance starts from 0 at the beginning of the sequences (in agreement with DCM mode), this energy is controlled by the duration of these sequences (see [START_REF] Sosnin | Applications of capacitive and barrier discharge excilamps in photoscience[END_REF]

below).

This stored energy is transferred through the transformer into the lamp during the oscillating sequences (B) and (D), involving L and Cdiel.

3) Degrees of Freedom (DOF): A very important feature of this converter is shown in Fig. 5; as stated in ( 2) and (4), t charge , the duration of sequences (A) and (C)-energy stored in the L inductance-permits to control the amount of energy E pulse which is injected into the lamp during each half period during sequences (B) or (D). In ( 2) and ( 3), E denotes the DC voltage source (see Fig. 4) and I L0 denotes the current in the L inductor at the end of sequences (A) and (C).

The duration of the sequences (B) and (D) t discharge is defined by the values of C diel , L, n (step-up ratio of the transformer), and I L0 [START_REF] Díez | Design of a current converter for the study of the UV emission in DBD excilamps[END_REF]; they naturally finish when the i L current matches a zero value (spontaneous turn-off of the thyristors-like switches, as will be detailed in next section-see Section III-C1).

A blanking time interval (t blanking ), added once, between sequences (B) and (C) and then between (D) and (A), is introduced to adjust the relaxation time interval between two current pulses in the lamp [as stated with ( 5)].

The pulse energy E pulse , combined with the operating frequency f s , defines the average power P lamp transferred to the lamp [see [START_REF] Sosnin | Development and applications of novel UV and VUV excimer and exciplex lamps for the experiments in photochemistry[END_REF]].

I L0 = E.t charge /L
(2)

E pulse = 1/2 • L • I 2 L0 = E 2 .t 2 charge /2L ( 3
)
P lamp = 2.f s .E pulse = 2 • f s • 1 2 L • I 2 L0 (4) T = (t charge + t discharge + t blanking ).2 = 1/f s (5)
As a conclusion, concerning the control of the pulsed currentmode supply, different variables are available for this purpose; they all rely on an accurate time management of the sequences: 1) two independent quantities (pulse energy E pulse and operating frequency) can be used to define the average power transferred to the lamp; 2) the pulse energy E pulse is directly controllable by means of the duration of sequences (A) and (C) t charge ; 3) the operating period is defined by t charge together with t blanking . Note that the control stated above is valid for E pulse large enough to breakdown the gas during each polarity change. Consequently, the voltage across the lamp must comply with (6) during the most part of sequences (B) and (D).

|v lamp | > V th • C gas + C diel C diel (6)

C. Design of the Pulsed Current-Mode Power Supply

Concerning the design of such a pulsed current mode supply, one should mention three important issues which are considered below:

1) dedicated power switches; 2) design of the step up transformer; 3) time management. 1) Thyristor-Like Switches: The three switches of the converter (Fig. 4) require thyristor-like operating characteristics: unidirectional current in ON state and bidirectional voltage in OFF state, with controlled turn-on under positive voltage and spontaneous turn-off at zero current crossing. The usual operating frequencies of classical thyristor devices are not compatible with the frequency expected in the considered application (some kilohertz).

Thus, a synthesized function based on a power MOSFET, in series with a high voltage fast diode, associated with an electronic management circuit (Fig. 7) has been particularly studied and designed [START_REF] Diez | Current mode converter for dielectric barrier discharge lamp[END_REF].

2)

Step-Up Transformer: The design of the step-up transformer, which is a critical point for the setup of such a supply, is a very important issue; indeed, the parasitic parameters of the windings (particularly the high voltage one) have a critical effect on the quality of the waveforms and of the operating conditions.

The magnetizing inductance must have a value large enough to avoid current flow through the lamp during sequences (A) and (C). As for the capacitance of the secondary winding, it derives a percentage of the current in the lamp and should be minimized as well.

3) Accurate Management of the Firing Events: In the experimental setup, the previously mentioned DOF, available for the control of the power transfers (Section III-B3), are managed by means of a DSP-FPGA-based control unit. This equipment accurately defines all the events through the firing orders of each power switch and offers possible transient analysis and time domain measurements.

D. Implementation and Experimental Results

A prototype of the pulsed current-mode supply has been implemented; the main electric characteristics are summarized in Table I.

Fig. 8 shows the current measured in the L inductance and the current in the lamp i lamp . These waveforms appear to be very similar to the theoretical ones; higher frequency oscillations, which appear on the i lamp signal, are caused by the mentioned parasitic elements of the step-up transformer.

Using the model described in Section I, nonmeasurable quantities are also calculable; the computed current flowing through the gas i gas is presented. The latter appears to be very similar to the i lamp current, except at the beginning of the energy transfer sequence, when the current injected into the lamp flows mainly in the discharge as a displacement current and is used to modify the charge of the C gas capacitor, according to the polarity of the discharge. The instantaneous power transferred to the gas P gas is also shown. One can notice that the waveforms of i gas and P gas are very similar, indicating that the gas voltage is almost constant. This last point confirms the hypothesis which has been stated in previous sections (see Section III-B2), concerning the behavior of the discharge in ON state, and defines the used value of the V th voltage (V th ± 1800 V).

IV. UV RADIATION CONTROL

Associated to the power supply, an optical apparatus has been developed, which offers time-resolved (with synchronization on the control signals of the switches of the power supply) and averaged measurements of the produced light, both in the visible and UV domains. The experimental system used in Fig. 9 is based on a high-speed CCD Roper Scientific PI-MAX camera, with a bandpass UV filter. For Fig. 10, a H25 Jobin-Yvon monochromator was used instead of the filter. The controller of the camera handles the synchronization of the 30 ns acquisitions with the firing logical signals of the excilamp power supply. For Fig. 12, a UV photodiode with a fast amplifier was used. The rising time of the system is lower than 100 ns. The photodiode method is simpler for realtime measurement. Nevertheless, it presents electromagnetic interference perturbations in the waveform due to the switching of the converter. For this reason, the pure optical system is used in Fig. 9.

A. Correlation Between Gas Current and UV Radiation

The comparison between the shapes of the instantaneous UV power and the computed i gas current is proposed on Fig. 9.

Due to the synchronization between the power supply and the optical measurements apparatus, the similarity of the waveforms is undoubtedly stated. This point confirms the physical reasoning which has been developed in Section II.

Several similar measurements, with different i gas pulses durations, have been realized and have given identical conclusions: the shape of the UV emission is very tightly correlated to the i gas current in the gas. One should remember that the latter is not directly controllable; the DOFs of the supply allow the control of the i lamp current in the lamp, which appears to be identical to i gas as soon as the discharge is in ON state and the voltage across the gap capacitor C gas has reached the V th threshold voltage. Note that the gas current is computed with the model of Fig. 2 using the experimental lamp current as input. That explains the pulse-to-pulse fluctuation in the gas current in Fig. 9.

B. Stability of the UV Emission

The quality of the produced UV has been checked with different levels of energy injection (controlled by means of the t charge duration); Fig. 10 proves that the spectral quality of the radiation of the lamp is not affected by the transferred power.

The power distribution remains clearly centered on 308 nm (which is the specific wavelength for XeCl lamps), whatever the pulse energy level is.

C. Time Domain Behavior of the Whole System

By means of the t charge DOF of the supply, which controls the energy of the current pulses, a current step has been realized [see [START_REF] Sosnin | A bactericidal barrier-discharge KrBr excilamp[END_REF]]. This event, as shown in Fig. 11, is immediately followed by a similar current step in the i lamp current.

Concerning the produced UV, any change in the pulse current is immediately followed by the same change on the UV emission; as it appears in Fig. 12, the magnitude of the UV emission is directly controlled by the injected lamp current (in Fig. 12, the step response of the system is highlighted). The timescale range concerned by this last statement starts from at least half the period of the supply.

D. Output Characteristics of the Pulsed Current-Source Supply

Considering the mean values of the UV power (measured with a 308-nm radiometer), the DOFs of the supply have been used to study the correlation between the relative UV power and the pulses energy for several operating frequencies.

The plots of Fig. 13 show both electrical power injected into the lamp and UV emission power, versus the current pulses energy, for different operating frequencies. According to (4), for a given pulses energy, the transferred electrical power should increase linearly with the operating frequency; the plots of Fig. 13(a) should be homothetically spaced. The actual organization of these plots let us conclude that the electrical efficiency of the supply decreases when the frequency reaches a 65 kHz value (the design of the latter has been realized for a nominal 50 kHz frequency). This reduction of electrical efficiency can be explained as the switching losses and the transformer losses increase with the frequency. Particular care must be taken for lower frequencies if the same average power is desired, as the inductance core could saturate for high energy levels.

Concerning the light emission, Fig. 13(b) shows the UV power increase:

1) with the pulse energy controlled by means of the t charge duration, see (3); 2) for a given level of pulse energy, with the operating frequency, see (4). One can notice that the lower curve at 50 kHz remains very near to the one at 55 kHz. This can be interpreted as better conversion from electrical to optical power (higher efficiency) of the lamp at 50 kHz. Actually, at 50 kHz the electrical to optical power efficiency is nearly 15% better than for the other frequencies (55, 60, and 65 kHz).

These facts also suggest using the pulsed current-mode power supply to identify the optimal operating frequency of the lamp.

V. CONCLUSION

The concept of a pulsed current-mode power supply for DBD excilamps has been introduced on the basis of physical considerations concerning the correlation between the UV emission and the electrical quantities associated with the lamp.

According to the conclusions of this first step, specific topologies for static converters implementing the pulsed current mode principle have been proposed and experimental setup has been designed.

A UV optical measurement apparatus, synchronized with the power supply, has been associated with the experimental setup; it has highlighted the fact that the UV production is directly controlled by the current which actually flows into the gas-this non-observable current is controllable by means of the current which is injected in the lamp.

The proposed solutions have shown the capability to control, by means of its DOFs, the energy of each current pulse injected into the lamp (at each half operating period), as well as the mean value of the power transferred from the supply to the lamp.

Fig. 1 .

 1 Fig. 1. Time evolution of current and voltage of the lamp (current supply mode) and UV flux of the excilamp at 50 kHz.

Fig. 2 .

 2 Fig. 2. Geometry and equivalent circuit model of the DBD lamp.

Fig. 3 .

 3 Fig. 3. Idealized current to be injected into the lamp.

Fig. 4 .

 4 Fig. 4. Pulsed current-mode power converter.

Fig. 5 .

 5 Fig.5. Main waveforms of the pulsed current-mode power converter. Each sequence is represented with its corresponding ON state switch (see Fig.6).

Fig. 6 .

 6 Fig. 6. Operating sequences of the pulsed current-mode supply (as seen from the secondary winding of the transformer).

Fig. 7 .

 7 Fig. 7. High frequency thyristor-like structure.TABLE I ELECTRIC CHARACTERISTICS OF THE SUPPLY

Fig. 8 .

 8 Fig. 8. Measured currents: (brown) i L and (red) i lamp -computed current (blue) igas and power (black) Pgas.

Fig. 9 .

 9 Fig. 9. Measured instantaneous UV power (blue) compared to the (black) computed igas current.

Fig. 10 .

 10 Fig. 10. Power distribution of the UV emission for different levels of pulse energy (operating frequency of the supply: 50 kHz).

Fig. 11 .

 11 Fig. 11. Instantaneous control of the i lamp current following a pulse energy step (i L is the current of the inductance which controls the pulses energy).

Fig. 12 .

 12 Fig. 12. UV production controlled by the power supply.

Fig. 13 .

 13 Fig. 13. (a) Electrical power transferred to the lamp and (b) UV emission power, both versus pulse energy.

ACKNOWLEDGMENT

The authors would like to thank Dermoptics (Quantel Group) for providing their patented lamp.

Hubert Piquet received the degree in applied physics from the Ecole Normale Supérieure de Cachan, Cachan, France, in 1984 and the Ph.D. degree in electrical engineering from the Institut National Polytechnique de Toulouse, Toulouse, France, in 1990.

He is currently a Professor at the ENSEEIHT Ing. School, Toulouse, where he teaches Power Electronics. His research activity takes place in the LAPLACE laboratory (Energy Conversion and Plasma Lab., Toulouse, France). His main research interests include quality and stability in embedded networks and power supplies for the electrical discharge applications. He is currently an Assistant Professor with the Department of Electronics at the Pontificia Universidad Javeriana. His main research interest is the development of power converters for electric discharges.


Jean-Jacques Daudin

Pierre P Vallois

Marie-Pierre Etienne

Asymptotic behavior of the local score of independent and identically distributed random sequences


Christophe Coillot
email: christophe.coillot@lpp.polytechnique.fr

Joël Moutoussamy

Richard Lebourgeois

Sébastien Ruocco

Gérard Chanteur

Principle and Performance of a Dual-Band Search Coil Magnetometer: A New Instrument to Investigate Fluctuating Magnetic Fields in Space

Keywords: Magnetometers, magnetic analysis, mutual coupling, frequency response. I

come   L'archive ouverte pluridisciplinaire

INTRODUCTION

Sensitive and accurate measurements of DC and fluctuating magnetic fields are mandatory to characterize plasma phenomena occurring in the interplanetary medium pervaded by the solar wind or in the vicinity of solar system objects (i.e. planets and their natural satellites, comets, asteroids, …) 1, 2. Usually, two kinds of magnetometers are embarked onboard scientific spacecraft aiming at measuring magnetic fields in space 3 : (i) fluxgates well adapted for weak magnetic fields from DC to a few Hz, (ii) search coils covering the frequency band from around 1 00 mHz up to a few kHz. The frequency dependent sensitivity of a magnetometer is characterized by the Noise Equivalent Magnetic Induction (NEMI) which is the smallest amplitude of an external harmonic magnetic induction at a frequency f which produces a detectable output signal above the noise level of the instrument at that frequency. For a fluxgate the NEMI is almost constant from DC up to a few tens of Hz, while it is V-shaped for a search coil as demonstrated in section IV. The two NEMI curves intersect at the crossover frequency fco, with the fluxgate being more sensitive than the search coil below fco, and the search coil performing better above fco. Moreover, due to its decreasing NEMI the search coil is better adapted to detect natural electromagnetic waves as their power spectrum generally varies like f --a with 1<a<5. As typical fluxgates used in space physics have a NEMI on the order of 10000fT/√Hz, the objective of this project was to design a search coil achieving a better NEMI above 1Hz.

For exploratory space missions of poorly known environments it is desirable to design instruments having large enough dynamics and frequency bands, meanwhile being compliant with allowed mass and energy budgets and various constraints due to the thermal or radiation conditions prevailing in the targeted environment. For the BepiColombo mission expected physical phenomena encompass electromagnetic waves of various origins. Magnetospheric electromagnetic waves are expected to be observed from very low frequencies below 1Hz, associated with heavy planetary ions (O+, Na+, K+ …), up to 10-20 kHz associated to auroral electron cyclotron radiation.

Despite the fact that high frequency synchrotron radiation by magnetospheric electrons at Mercury seems to be unlikely, considering the present understanding of the Hermean environment, there are electromagnetic waves up to a few 100kHz associated with solar bursts and planetary foreshock phenomena worth to investigate. These scientific objectives have motivated us to design a wide-band searchcoil. 2 The increased complexity of its design is worth the effort considering the saving of mass and volume it allows compared to the use of two traditional sensors covering two overlapping frequency bands. This is an important issue for space applications.

II. BASICS OF SEARCH COIL

A regular search-coil consists of a conductor coiled around a magnetic core: Faraday's law of induction relates the voltage across the terminals of the coil to the rate of change of the magnetic flux through the coil. The magnetic flux through the coil is augmented by the presence of the magnetic core (4, 5), usually a cylinder: it has been shown in 6 that a drastic improvement of the magnetic amplification is achieved by using an optimized shape with flaring ends illustrated by 1. The sensor is connected to a very low noise preamplifier 7. In the case of voltage amplification a feedback loop is used in addition to flatten the natural resonance of the sensor 8. Current amplification is a possible alternative which does not require any feedback but slightly increases the power consumption. Let us first consider a sensor designed to reach 2000fT/√Hz at 10Hz with the following characteristics : optimized core with a relative permeability r µ =2500, 100mm length, 4mm diameter, and 14000 turns. The transfer function of this low frequency (LF) search coil is depicted on 2. as well as its NEMI which first decreases with frequency, up to the resonance frequency fLF around 2kHz, where it reaches its minimum of 40fT/√Hz, and increases beyond. This sensor is well fitted for magnetic measurements in the low and intermediate frequency ranges below 20kHz, but a priori not enough sensitive for detecting weak magnetic fluctuations in the 100kHz frequency domain.

III. ROUGH MODELING OF THE MAGNETIC CORE

First, we propose the following way to estimate the magnetic amplification of a cylinder with flaring ends, as represented on 1.

When a magnetic body is immersed into a magnetic field Hext a magnetization appears and the internal field is given by Hint = Hext -NM where N is the demagnetizing factor and M the magnetization. The demagnetizing factor N depends upon the shape and orientation of the magnetic body with respect to the external field. With a few exceptions like the ellipsoid 4, the cylinder ( [START_REF] Bozorth | Demagnetizing factor of rods[END_REF], [START_REF] Chen | Demagnetizing Factors for Cylinders[END_REF] and the rectangular prism 10, N is generally a tensor depending upon coordinates and numerical computations are necessary to estimate the demagnetizing field Hd = -NM even when the external field Hext is uniform as supposed in the present study. The magnetic flux density, or magnetic induction, B inside the body is linked to the magnetic field by B=µr Hint, where µr denotes the relative permeability of the magnetic material, related to the magnetic susceptibility χr by χr = µr -1. The ratio B/µ0Hext, called the apparent permeability µapp, can be computed from the relative permeability µr of the magnetic material and the demagnetizing factor N. We make two rough assumptions: the demagnetizing factor N reduces to a scalar, its component NZ along the measurement axis z, which is constant throughout the whole core (cf. Fig. 1). That leads to the following apparent permeability µapp:

z r r ext app N µ µ H µ B µ ) 1 ( 1 0     (1)
A long cylinder of length L and diameter d however, made of a high permeability material, can be roughly approximated by an oblate ellipsoid, leading to the following approximate demagnetizing factor along the z axis:

              1 ) 1 ln( 1 1 1 ) ( 2 2 2 m m m m m m N Z (2)
where m=L/d>>1 denotes the aspect ratio of the cylinder.

Let us now express the demagnetizing field for the magnetic core of length L with flaring ends of diameter D ("diabolo" core) and the one of a cylinder of length L and diameter D as:

-Cylinder:

M D L N H Z d ) / (   and H M   -Diabolo: ' ) / ( ' ' M D L N H Z d   and ' ' H M  
By noticing that the cylinder and the diabolo have the same surface density of magnetic poles at their ends, we deduce that their related demagnetizing magnetic fields are identical at the ends of the core:

d d H H  ' ( 3
) Then, we compute the magnetic field at the centre of the diabolo core (H') of diameter d' by means of the flux conservation between the ends and the centre of the diabolo core as:

' ' 2 2 H D d H  (4)
and,

d ext d ext H H H H H     ' ' (5)
By replacing, Hd in (5) we express:

H D L N H H Z ext  ) / ( '   (6)
By replacing H from ( 4) in ( 6) we obtain :

' ' ) / ( ' 2 2 H D d D L N H H Z ext    (7)
This leads to:

1 2 2 ' ) / ( 1 '            D d D L N H H Z ext  (8)
Finally, we obtain:

2 2 0 ' ) / ( ) 1 ( 1 ' D d D L N µ µ H µ B µ Z r r ext app     (9)
The accuracy of this formula has been compared with simulations carried out with the finite element software Flux2D. This model fits with simulations within 10% for diameter ratios 1<D/d'<5. The diabolo shape increases considerably the apparent permeability µapp at the center of the magnetic core 6.

IV. DISCUSSION OF THE FREQUENCY BEHAVIOR

A harmonic external magnetic induction Be jt of amplitude B and pulsation  induces a voltage V(t) of amplitude V between the terminals of the winding:

B Sµ N V dt t d t V app   1 , ) ( ) (    (10)
where (t) is the magnetic flux through the N1 turns of the coil, S is the sectional area of the core, µapp is the apparent permeability of the core approximated by [START_REF] Chen | Demagnetizing Factors for Cylinders[END_REF].

We assume that the sensor is equivalent to the RLC circuit displayed by Fig. 3, where L1 is the inductance of the winding, R1 its electrical resistance, and C1 its capacitance. Thus, the transfer function between the output voltage VOUT and the external magnetic field is equal to:

    1 1 2 1 1 1 ) 1 ( ) ( C jR C L Sµ N j B V j T app ext OUT      Fig. 3
Equivalent electrical circuit of the search coil: e(t) is the voltage induced by the varying external magnetic induction, L1 is the inductance of the coil, R1 its resistance , and C1 its capacitance. The output voltage VOUT of the sensor is applied to a preamplifier having a high input impedance.

The detection threshold per Hertz of the output voltage is equal to the square root of the variance per Hertz v 2 noise of the noise voltage of the sensor given by:

1 2 2 4kTR v v PA noise   (11)
where v 2 PA is the variance per Hertz of the noise voltage at the entry of the preamplifier, and 4kTR1 is the variance per Hertz of the thermal noise voltage of the resistance, where k=1,38×10 -23 J.K -1 is the Boltzmann constant and T the temperature.

Hence the NEMI, defined as the smallest magnetic induction B which can be detected due to the noise of the sensor, is the following V-shaped function of  :

2 1 1 2 2 1 1 1 1 2 ) ( ) 1 ( 4    C R C L Sµ N kTR v NEMI app PA     (12)
At low frequencies, the NEMI decreases with frequency and is approximated by the following formula, which does not involve the resonance frequency:

 app PA Sµ N kTR v NEMI 1 1 2 4   (13)
This simple expression can be used to estimate the number of turns N1 required to achieve a targeted value of the NEMI at a given frequency much smaller than the resonance frequency (in the present case 2000fT/√(Hz) at 10Hz): let us nevertheless notice that R1 is proportional to N1. More modeling details are given in 7 and 8 especially with respect to the effect of the flux-feedback which is not taken into account in the present qualitative discussion.

V. FEASIBILITY OF A WIDE BAND SEARCH COIL USING TWO WINDINGS ON A UNIQUE MAGNETIC CORE

The designed LF coil is not enough sensitive to detect natural waves at frequencies larger than a few tens of kHz. An obvious idea to extend the frequency range of measurements up to 1MHz is to implement a second winding with a higher resonance frequency fHF of the order of 300kHz. The transition frequency ftr between the two bands, defined by the intersection of the LF and HF NEMIs, is chosen equal to 10kHz. Let us first consider the frequency band [1Hz, 10kHz] covered by the LF coil; accordingly to Fig. 2 the LF-NEMI at 10kHz is equal to 100fT/√Hz, which is also the value of the LF-NEMI at f1~200Hz in the validity range of formula [START_REF] Prance | Ultra low noise induction magnetometer for variable temperature operation[END_REF].Then, in order to design a HF coil operating in the frequency band [10kHz, 1MHz], and having a HF-NEMI equal to the LF-NEMI at the transition frequency ftr =10kHz, we make use of an expression similar to (13) as ftr is much smaller than fHF. Considering the same magnetic core, and assuming the same noise level at the entry of the preamplifier, we can express the number of turns of the HF coil from the number of turns of the LF coil, multiplied by the ratio of the two frequencies:

50 1 1 1 2 N f f N N tr   (15)
When a HF coil with 2 N =280 turns is wound all alone on a magnetic core (Ferrite diabolo core: L=100mm, D=14mm, d=4mm), its transfer function is the expected one: the gain increases with frequency up to the resonance frequency fHF, slightly above 300kHz, and decreases beyond due to the capacitive behavior of the coil as shown by the curve labeled HF1 in Fig. 4. But when the same HF coil is wound over the LF coil, together on the same magnetic core, the transfer function represented by curve HF2 on Fig. 4 exhibits a pair of resonance and anti-resonance at ~6 and ~18kHz, above the resonance frequency fLF of the LF coil. The gain increases with frequency beyond the anti-resonance but remains roughly 20dB below the HF1 gain. Transfer functions of the HF winding: (i) all alone on a magnetic core (HF1), and (ii) together with the LF winding (HF2) on the same magnetic core.

In order to explain qualitatively this behavior let us consider the magnetic flux  through each coil;

I M I L B Sµ N app     (16) 1 12 2 2 2 2 I M I L B Sµ N app     (17)
where indices 1 and 2 relate respectively to the LF and HF windings, and symbols L and M denote the self and mutual inductances.

At frequencies lower than the HF resonance frequency fHF the current intensity 1 I flowing through the LF coil is not much influenced by the magnetic coupling with the HF coil and is approximately given by: ) /( 1

1 1 1 1 1    jC jL R Bj Sµ N I app     (18)
At frequencies lower than the LF resonance frequency fLF this current is small. At frequencies larger than fLF the main contribution to the impedance of the LF winding comes from the inductive part jL1ω and 1 I is further approximated by:

1 1 1 L B Sµ N I app     for 1 1 2 2 1 1 C L C L     (19)
Substituting approximation (19) into equation (17) gives:

1 1 12 2 2 2 2 L B Sµ N M I L B Sµ N app app     (20) 2 2 2 12 2 ) 1 ( I L B Sµ N app      (21)
where 12 is the mutual coupling coefficient between the two windings. When, the windings are implemented on a unique magnetic core, this coefficient 12 is close to 1 and the latter expression is almost independent of the external magnetic induction. Thus a HF coil wound directly over the LF coil, together on the same magnetic core, is inefficient to measure the external magnetic induction in the frequency range [fLF , fHF].

VI. PHYSICAL DESCRIPTION OF A MUTUAL REDUCER

It is therefore mandatory to reduce the mutual coupling between the LF and HF coils wound together on the same magnetic core in order to extend the frequency range of measurements. The original solution we propose consists in inserting a tubular magnetic shield between the two windings as shown by 5. This shield offers a new path to the selfinduction flux of the LF winding (red lines on 6), which results in a considerable decrease of the LF self-induction flux seen by the HF winding, hence the name "mutual reducer". The dual-band search coil magnetometer consists of two coils wound on the same magnetic core and separated by a tubular magnetic shield reducing the mutual coupling of the two coils.

Then the magnetic parts of the LF and HF coils have different apparent permeabilities, µapp1 and µapp2 respectively, which depend upon the shapes and cross-sectional areas of the magnetic core and mutual reducer. The various parameters of the sensor: auto and mutual inductions, and apparent permeabilities, are obtained via numerical computation. The flux through the HF winding can be written:

1 1 1 1 12 2 2 2 2 2 2 L B µ S N M I L B µ S N app app     (23)
where S1 is the cross-sectional area of the core, and S2 denotes the sum of the cross-sectional areas of the core and the reducer. 2  can be written:

2 2 2 2 * 2 2 I L B S N µ app    (24) 1 2 1 2 1 1 12 2 * 2 app app app µ S S N N L M µ µ   (25)
where * 2 app µ is the apparent permeability for the HF coil reduced by the mutual coupling to the LF coil. The coupling must be as low as possible in order to keep this reduced apparent permeability as large as possible. Fig. 6 shows that part of the LF auto-induction flux is captured by the mutual reducer, and thus the HF coil feels only the remaining part of this LF flux.

The measured transfer function for an HF winding combined with a mutual reducer is presented on 7 (curve labelled HF3). The HF3 curve is close to the transfer function HF1 of the HF coil wound all alone on the magnetic core. However a remaining mutual coupling with the LF winding is revealed by a resonance occurring at about 5 kHz followed by an antiresonance at about 6kHz. The resonance clearly originates from the coupling to the LF winding, while the antiresonance is supposed to result from the energy exchange between the capacitance of the LF winding and the mutualinductance. This assertion is motivated by the comparison of Fig. 4 and Fig. 7: the anti-resonance frequency decreases when the mutual coupling decreases. The abrupt variation of HF3 between 5 and 6kHz on Fig. 7 is due to the close proximity of the resonance and anti-resonance when the mutual reducer is added. The achieved HF transfer function makes possible the measurement of weak magnetic fields between 10kHz and 1MHz. Transfer function for of the HF coil wound all alone on the magnetic core (HF1), and transfer function of the HF coil wound together with the LF coil on the magnetic core, and combined with a mutual reducer (HF3).

VII. PERFORMANCES OF THE DUAL-BAND SEARCH-COIL MAGNETOMETER

Thalès Research and Technology has designed several ferrite materials that keep a high magnetic permeability in the stringent temperature range [-100°C, 200°C] that will be met during the BepiColombo mission. The Mn-Zn ferrite selected for the dual-band search-coil has a relative permeability higher than 1000 on the full temperature range 11. The apparent permeability of the core for the LF coil is reduced from 295 to 265 when the mutual reducer is inserted, meanwhile the apparent permeability of the HF winding increases from almost 0 to 24, a value slightly larger than the apparent permeability for the HF coil when it is wound all alone on the magnetic core. The 10% loss of apparent permeability that affects the LF coil performance is compensated for by an almost proportional increase of the number of turns N1. Each winding of the sensor is connected to its own low noise preamplifier. A first amplification stage involving a JFET is well suited for a high impedance sensor, and is used in order to minimize the contribution to the shot noise. The output noise can be written, similarly to (11):

  1 2 2 2 4kTR V G V PA v out   (25)
where GV represents the voltage gain of the preamplifier.

A flux feedback is used to flatten the transfer function of search coil around its resonance: the principle of this flux -feedback is detailed in 12. The transfer function of the LF coil with the flux-feedback has been presented in section II. The bloc diagram on 8 shows schematically how the output of each preamplifier is connected to a secondary coil in serial with a feedback resistor Rfb in order to create a feedback flux. Hence the electronic noise is fed into the sensor and produces the following noise (26) which is added to the measured magnetic induction: where NEMI0 is the NEMI defined by [START_REF] Tumanski | Induction coil sensors-a review[END_REF].

The current source used for the LF flux feedback entails a wide band noise which has to be low-pass filtered in order to get the lowest possible NEMI in the HF frequency range. The coil used for the feedback also allows to inject into the sensor the magnetic flux created by an external signal in order to calibrate the instrument in flight. The NEMI curves (in fT/√(Hz)) of the Bepicolombo dual-band search-coil, including the effect of the fluxfeedback, are represented on 9. The LF-NEMI is plotted from 1Hz to 50kHz, and the HF-NEMI from 10kHz to 1MHz. The DBSC-NEMI defined as the minimum of the LF and HF NEMIs is lower than NEMIs of other sensors in comparable frequency ranges reported in the literature 13. Measurement have been performed at the Magnetic Observatory at Chambon la Forêt (France), which is a very quiet place for magnetic measurements, free from man-made magnetic perturbations. The designed sensor has a NEMI of 2000fT/√Hz at 10Hz, lower than 50fT/√Hz from 500 Hz to 500kHz, with a minimal value equal to 7,5fT/√Hz at 100kHz. These performances are among the best known for this family of magnetic sensors. However let us mention that an abrupt variation of the transfer function appears above 500kHz. This behaviour is still unexplained but seems to be linked to a LF resonance seen by the HF winding. Further investigations will be led to understand the origin of this resonance.

VIII. CONCLUSION

The Dual Band Search-Coil (DBSC) is a good alternative to the use of two distinct sensors in applications where mass and volume are limited as for example for onboard instrumentation. When two different sensors are used they should be separated by a distance at least of the same order as their size, which means that the mechanical structure needed to hold the sensors would have a larger mass. The implementation of the mutual reducer described in this article allows to build a DBSC able to measure magnetic field fluctuations from 0.1Hz up to 1MHz. The DBSC designed for BepiColombo/MMO is 10cm long, 17mm in diameter, weighs 60g, and has an upper cut-off frequency of 640 kHz imposed by the high frequency receiver used [START_REF] Kasaba | The Plasma Wave Investigation (PWI) onboard the BepiColombo/MMO: First measurement of electric fields, electromagnetic waves, and radio waves around Mercury[END_REF]. The DBSC is associated with two classical search coils, designed at Kanazawa University, to form a tri-axial AC magnetometer which is part of the Plasma Wave Instrument of the MMO spacecraft [START_REF] Kasaba | The Plasma Wave Investigation (PWI) onboard the BepiColombo/MMO: First measurement of electric fields, electromagnetic waves, and radio waves around Mercury[END_REF]. The DBSC is aligned with the spin axis of the spacecraft, while the two identical classical search coils are lying in the spin plane.

Fig. 1

 1 Fig. 1 Schematic view of the search coil sensor showing the low frequency coil wound around the optimized magnetic core consisting of a cylinder with added flaring extremities.

2

 2

Fig. 2

 2 Fig. 2 Transfer function and NEMI curve of the low frequency search coil between 1Hz and 100kHz, with their respective scales on the left and right sides of the plots.

Fig. 4

 4 Fig. 4Transfer functions of the HF winding: (i) all alone on a magnetic core (HF1), and (ii) together with the LF winding (HF2) on the same magnetic core.

Fig. 5

 5 Fig.5The dual-band search coil magnetometer consists of two coils wound on the same magnetic core and separated by a tubular magnetic shield reducing the mutual coupling of the two coils.

Fig. 6 Field

 6 Fig. 6Field lines of the magnetic induction modified by the mutual reducer which captures a fraction of the return auto-induction flux created by the LF coil and guides it inside the HF coil.

Fig. 7

 7 Fig. 7Transfer function for of the HF coil wound all alone on the magnetic core (HF1), and transfer function of the HF coil wound together with the LF coil on the magnetic core, and combined with a mutual reducer (HF3).

M

  is the mutual inductance between the main coil and the feedback coil. The resulting NEMI with the feedback is thus given by:

Fig. 8

 8 Fig. 8 Bloc diagram of the dual band search coil magnetometer.

Fig. 9 NEMI

 9 Fig. 9 NEMI curve of the Bepicolombo dual-band search coil magnetometer.

ACKNOWLEDGMENT S

The LPP team is indebted to Prof. H. Matsumoto, Kyoto University, for having fostered the franco-japanese collaboration which lead to the selection of this instrument onboard BepiColombo/MMO spacecraft, as part of the Plasma Wave Instrument. The LPP team addresses special thanks to Prof. S. Yagitani, Kanazawa University, for a friendly and instructive collaboration during the design and test of the tri-axial search coil magnetometer. This research has been funded by CNES and CNRS/INSU.

C. Coillot Working in space physics since 1975 he has studied instabilities and solitary waves in plasmas. Involved in numerical simulation of space plasmas he has done particle in cell, MHD and hybrid simulations. Co-I of the CLUSTER/STAFF experiment he has designed theoretical methods of data analysis for multi-spacecraft missions. Since 1998 he has started activities in planetary physics both as Co-I on BepiColombo/MMO and as computer physicist designing three-dimensional hybrid simulation models for the global plasma environment of small planets. Senior scientist at CNRS since 1997 he is author or co-author of about 50 publications in refereed journals. He has been lecturing computational methods at Versailles University and supervised 3 PhD thesis in space plasma physics and applied mathematics.