SPIS Multitimescale and Multiphysics Capabilities: Development and ...

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SPIS Multitimescale and Multiphysics Capabilities: Development and Application to GEO Charging and Flashover Modeling Jean-François Roussel, Guillaume Dufour, Jean-Charles Matéo-Vélez, Benoît Thiébault, Bjarne Andersson, David Rodgers, Alain Hilgers, and Denis Payan

Abstract—While it demonstrated its capability to simulate many common situations, Spacecraft Plasma Interaction Software (SPIS) open source code lacked the possibility to model more challenging situations. The major cases of interest were identified as related to either multitimescale or multiphysical situations. Two major improvements were brought to SPIS code to answer these needs. The first one was an implicit circuit solver with an automatic determination of time steps. The implemented Newtontype algorithm makes use of a predictor for the plasma current variations when surface potentials change. The second major development was a multiphysical model for electrons. The approach consisted in using equilibrium or dynamical electron models in two different zones and connecting these zones at their boundary through a Child–Langmuir (CL)-type condition. Fulfilling this condition dynamically determines the location of the boundary and the electron current to be injected from the dense thermal zone to the space-charge zone. These new features were then used to simulate validation and application cases. The first one consisted in modeling a charging situation in GEO, which had been modeled with NASA charging analyzer (NASCAP) codes and published. Concerning the multiphysical model of electrons, the loop controlling the CL condition was first tested on elementary cases, exhibiting a good qualitative and quantitative behavior. It was then applied to the modeling of a ground experiment performed in JONAS plasma tank at the Office National d’Etudes et Recherches Aérospatiales, i.e., the expansion of the flashover generated by an electrostatic discharge over a precharged solar array coupon, leading to its neutralization. Index Terms—Child–Langmuir (CL), flashover (FO), implicit circuit solver, multiphysics, numerical methods, numerical modeling, plasmas, spacecraft charging.

Manuscript received April 5, 2011; revised September 27, 2011; accepted November 5, 2011. Date of publication January 6, 2012; date of current version February 10, 2012. This work was supported by the European Space Research and Technology Centre under Contract 19884/06/NL/JD [Advanced Research in Telecommunication Systems (ARTES) Program, French funded]. J.-F. Roussel, G. Dufour, and J.-C. Matéo-Vélez are with the Office National d’Etudes et Recherches Aérospatiales (ONERA), 31000 Toulouse, France (e-mail: [email protected]; [email protected]; [email protected]). B. Thiébault is with Artenum Company, 75010 Paris, France (e-mail: [email protected]). D. Rodgers and A. Hilgers are with the European Space Research and Technology Centre, European Space Agency, 2200 AG Noordwijk, The Netherlands (e-mail: [email protected]; [email protected]). B. Andersson is with the Swedish Space Corporation, 171 04 Solna, Sweden (e-mail: [email protected]). D. Payan is with the Centre National d’Etudes Spatiales (CNES), 31401 Toulouse, France (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPS.2011.2177672

I. I NTRODUCTION

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INCE its development started in 2003, Spacecraft Plasma Interaction Software (SPIS) open source code [1] proved its capability to model most common situations. It was used to model spacecraft interactions with space plasmas [1]–[4] or ground plasmas [5], [6], probe behavior [5], [7], [8], or electricpropulsion-induced environment [8]–[10]. It mostly resulted from the initial development funded in the 2003-05 time frame under the European Space Agency (ESA) Basic Technology Research Programme contract leading to the version 3 of the code. However, more ambitious problems such as the modeling of electrostatic discharge triggering remained difficult to address [11]. As a consequence, a second major improvement of SPIS numerical solvers was recently funded under ESA Advanced Research in Telecommunication Systems sponsorship (with French optional funding). It addressed the modeling of much more complex situations, requiring more advanced models. It led to major solver enhancements, which are reported here. The upgraded code, numbered version 4, has been freely available on www.spis.org since mid 2009. An advanced application to the actual modeling of electrostatic discharge (ESD) onset, with rather convincing experimental validation, has been also recently reported in [12]. The two major improvements of the solvers aimed at developing multitimescale and multiphysics capabilities in SPIS. They are presented in the first section. The application of these models to practical situations is then reported in another section. The first one is charging of spacecraft in GEO, and the second one, which is much more challenging, is the expansion of a flashover (FO) on a solar panel. II. N EW M ODELING C APABILITIES A. Multitimescale It is not uncommon to meet situations involving simultaneously very different timescales. Charging in GEO, for example, involves both a quick absolute charging at millisecond scale and a slow relative charging at minute scale, as a result of small absolute capacitance (smaller than 1 nF) and large coating capacitance (a few to hundreds of microfarads). Triggering of ESDs is also thought to involve electron avalanche at subnanosecond scale and, again, coating relative charging at minute scale. In such situations, the slow process is usually a surface charging, which is modeled through an equivalent spacecraft

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Fig. 1. Spacecraft equivalent circuit used in SPIS. Supernodes are local grounds (e.g., a solar array ground). Capacitors and leakage resistors on top of these grounds represent coatings (on each mesh element).

circuit in SPIS (see Fig. 1). The solution thus consisted in developing a circuit solver supporting multiple timescales and automatic time step. A Newton-type implicit solver was designed and developed. Newton solvers require predictors to avoid the divergence of fast degrees of freedom when time steps are increased for efficient integration of slow degrees of freedom after the fast ones have converged. In this case, the predictors have to give an assessment on how the currents computed in a given situation through plasma dynamics modeling change if surface potentials slightly change. They are expressed under the form of d Ii /d Vj matrices for the current change in node i resulting from the change of potential on node j. If the influence of a potential change is local, the matrix is diagonal but it may be also nondiagonal (e.g., for potential barriers or other situation with large Debye length). Since the predictors can be only approximated, a validity range is supplied with each of them, beyond which this linear approximation is not considered valid. The time steps are automatically determined in order to keep the potential steps within these validity limits. As an illustration, the simple default predictor used for a Maxwellian plasma considers the effect of a potential change to be local and given by the diagonal matrix d Ii /d Vj = −qIi /kT and validity on the order of |kT /q|. This can be made consistent with orbital-motion-limited law by taking into account the extra (1 − qV /kT ) factor. More complex examples can be found in the freely available code or its documentation.1 Fig. 2 shows an example of application of these new capabilities to the simulation of charging in GEO (with a strong environment leading to absolute charging in sunlight even before relative charging happens). The same time evolution of ground and coating potentials are plotted at various timescales on the five charts. The time step automatically varies, allowing correctly modeling the fast initial charging at submillisecond scale and the slow relative charging at minute scale. B. Multiphysics It is not uncommon either to meet situations where different models should be used in different zones of the simulation box. Examples usually involve in the same simulation a dense 1 cf. http://www.spis.org, examples to be found as classes implementing the interface spis.Surf.SurfField.AbstractCurrentScaler.

Fig. 2. Multitimescale simulation of GEO charging (automatic time step): same time plots at 100-, 10-, 1-, 0.1-, and 0.01-s scales. Nodes 1 and 3 are the sunlit sides of two solar panels (covered with cover glass and epoxy, respectively), whereas the ground (node 0) is exposed to vacuum on the spacecraft body only.

Fig. 3. (Shaded) High-density quasi-neutral region and (white) low-density space-charge region in case of a plasma sink (environment) and a positively biased surface. Arrows are typical electron trajectories in the space-charge region.

Fig. 4. (Shaded) High-density quasi-neutral region and (white) low-density space-charge region in case of a plasma source and more positive surfaces around (inverse voltage gradient).

plasma somewhere and positive potentials elsewhere on the spacecraft. This situation may, for example, arise in the plasma collection by solar cell interconnects (see Fig. 3) or in the expansion of an ESD FO (see Fig. 4).

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Fig. 5.

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Overall algorithm for multiphysical modeling.

Electrons often follow thermal equilibrium in the dense region while their dynamics need to be modeled close to a positive electrode. Modeling their dynamics over the whole computation domain, e.g., through a particle-in-cell (PIC) model, is often impossible in practice because this would require meshing at Debye length scale over the whole domain. The chosen approach consisted in using the existing electron models (Boltzmann distribution or PIC model) in different zones (depending on the ion density and potentials nearby) and connecting these zones at their boundary through suitable boundary conditions. The physics ruling the boundary was considered to be the injection of the maximum electron current (from the dense zone into the space-charge zone) that can be tolerated by space charge. A current that is too large leads to a potential barrier and blocks (or reduces) the current, whereas a current that is too small results in an extractive field and to a larger current. In the zero-temperature approximation, the limit in between is reached when the normal electric field on the boundary is zero, which is the Child–Langmuir condition (CL). The resulting algorithm is depicted in Fig. 5. The lower level loop 1 iterates on the plasma dynamics, mostly on the PIC electrons in the space-charge zone. The next nested CL loop 2 iteratively adjusts the local 3-D CL current in order to fulfill the null electric field CL condition. The boundary is defined as the location where the thermal current that the plasma can supply is equal to our local estimation of the 3-D CL current. This adjustment thus simultaneously determines the location of the boundary and the electron current to be injected from the dense thermal zone into the space-charge zone. The third external loop relies on an electron balance equation that is needed in case of a plasma bubble (see Fig. 4, as opposed to Fig. 3 with a plasma sink). Although quasi-neutral, a small imbalance between electron and ion space charges exists and may easily lead to large potential shifts in the plasma bubble. The determination of this potential should thus result from an

electron balance equation. Several versions of this electron balance loop were implemented and tested but no implementation proved really satisfactory until now, and we shall thus postpone its discussion after further work. Next figures show the results of basic test cases. The first test case involves a plasma source on the left-hand side (Maxwellian 30-eV O+ ions, with total current of 40 µA), and a positively biased electrode on the right-hand side (+300 V). In this hybrid model, the total electron density is obtained from two different models in the dense and the space-charge zones, all displayed in Fig. 6. The electron Boltzmann distribution has 5-eV temperature and 109 #/m3 reference density (density at zero reference potential). The resulting hybrid electron density is larger in the dense plasma region close to the plasma source, and another local maximum is also seen close to the positive electrode to which they converge. The potential in the domain is shown as equipotential lines in these plots and in the color scale in Fig. 7. The equipotential lines are approximately orthogonal to the zone boundary, showing that the CL condition, i.e., zero normal electric field, is approximately fulfilled. The ion dynamics is much simpler since the single PIC distribution simply does not see the (electron) zone boundary and is only influenced by the potential map. Fig. 8 shows that they are simply repelled by the positive potential close to the right-hand-side electrode. Next figures show similar plots of the same model where the plasma source flux was increased by a factor of 100 to test the stability range of the model (see Fig. 9) . Smaller Debye length leads to a smaller sheath around the positive electrode (see Fig. 10). For a more quantitative test, a 1-D CL-like situation was eventually modeled. Fig. 11 exhibits the potential map and zone boundary. A dense plasma is forced above the boundary due to a fixed ion density, and it behaves as a source for the

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Fig. 8. Ion density (PIC model all over the simulation box) with the Boltzmann–PIC boundary for electrons visible as a line.

Fig. 6. Hybrid electron model: (middle panel) Boltzmann distribution in the dense region, (bottom panel) PIC in the low-density space-charge region, and (top panel) total hybrid distribution. The plotted cutting plane is the symmetry plane of the computation box. The line crossing the isolevels (approximately vertical) is the boundary between the Boltzmann and PIC zones. The emission zone and the biased electrode are indicated in white.

Fig. 7. Plasma potential. The color scale was restricted to the [0–60 V] interval, but the potential reaches +300 V on the right-hand-side electrode (red saturation).

Fig. 9. Hybrid electron model with increased density: (middle panel) Boltzmann distribution in the dense region, (bottom panel) PIC in the lower density space-charge region, and (top panel) total hybrid distribution. The line crossing the isolevels (on the right-hand side) is the boundary between the Boltzmann and PIC zones. The emission zone and the biased electrode are indicated in white.

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TABLE I E NVIRONMENT PARAMETERS OF THE GEO S IMULATION C ASE

Fig. 10. Plasma potential. The color scale was rescaled on the [0–60 V] interval, but the potential reaches + 300 V on the right-hand-side electrode (red saturation). The 3-D surface is the boundary between the electron zones.

Fig. 12. NASCAP-2k potentials at 1000 s from [16].

Fig. 11. One-dimensional CL-like case potential map. The surface boundary between the Boltzmann and PIC zones is represented in red.

electrons. They are then attracted to the positive electrode at the bottom and cross the space-charge region below the boundary (completely void of ions). In the CL ideal case [13]–[15], the (maximum) current density crossing the space-charge zone is analytical
3 4ε0 2e V 2 . jCL = 9 m d2 The 100-V potential drop V and 10-cm distance d lead to jCL = 0.23 A/m2 , whereas the SPIS model yielded 0.35 A/m2 . The difference was thought to be mostly due to the nonzero temperature in the SPIS model, whereas the ideal case of CL theory has zero temperature. III. S IMULATION C ASES A. Charging in GEO The first application case to be addressed was spacecraft charging in GEO conditions in sunlight. The new capabilities needed for the solvers were not only the implicit circuit solver already described to handle the different timescales but also a particle backtracking method to improve the collected current statistics. Regular forward tracking usually leads to poor PIC statistic for the particles collected on the spacecraft since only a small fraction of the particles injected in the big computation box are collected by the spacecraft. This feature, based on Liouville’s theorem, is not described here.

Fig. 13. SPIS potentials at 1000 s.

For validation purposes, it was chosen to model a case already modeled with NASCAP-2k, which was published in [16]. Spacecraft geometry and materials were identical. The same environment, as described in Table I, was used. The sun orientation was also similar [from the (0.92, 0.39, and −0.02) direction, the x-axis being orthogonal to the arrays and the y-axis parallel to their axis]. Fig. 12, extracted from [16], shows a NASCAP-2k potential map after 1000 s of charging in the orbit. The same potential map resulting from SPIS computation is displayed in Fig. 13. Although the color scales are different, it can be checked that potentials are globally rather close. Yet, some differences can be seen. The optical solar reflector (OSR), the red strip on the left side of the spacecraft chassis in NASCAP mode, does not appear to have such a negative potential with SPIS. The gradient along the arrays is also smaller with SPIS. The difference in OSR potential might be due to a difference in secondary electron emission (SEE) since another SPIS computation performed without SEE yielded potentials closer to NASCAP’s. In theory, these models should be, however, quite close. The true secondary yield is extrapolated from its peak value with similar theories, i.e., a linearly varying linear energy transfer (LET) throughout the material for NASCAP and

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Fig. 14. Comparison of spacecraft ground potential evolution modeled with SPIS and with NASCAP-2k, the old NASCAP/GEO, and the simplified SEE Handbook from [16].

Fig. 15. Evolution of various potentials in SPIS simulation.

constant LET for SPIS, but this should not change a lot since secondary emission is a surface phenomenon. The time evolution values of NASCAP and SPIS potentials were also compared. Fig. 14 shows the evolution of spacecraft ground potential in SPIS and NASCAP code series simulations. The overall shape of SPIS potential evolution is very similar to the one of NASCAP-2k and is quantitatively in between the NASCAP-2k and NASCAP/GEO values. Fig. 15 also displays the time evolution of potentials on various dielectric surfaces in SPIS simulation. Equivalent data were not available for NASCAP. An accurate comparison can yet be done for dielectrics in Table II gathering SPIS and NASCAP code series results on this test case. NASCAP results are presented as intervals while both the average potential and the interval (in parentheses) are supplied for SPIS. SPIS results are always close to NASCAP’s, and within the range of results of the three NASCAP codes, they are often closer to NASCAP-2k, similar to the time evolution of the ground potential plotted above. B. FO Expansion The second application case was much more challenging. It consisted in modeling the expansion of the FO on a 1.33 m × 0.6 m solar array performed in ONERA plasma tank JONAS

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(CNES R&T). Among its 19 strings of 60-cm length, five were independently monitored with individual current probes (strings 9 to 13 out of the 19 strings). Fig. 16 shows the signals monitored at the occurrence of a typical ESD, i.e., the one that was modeled. The blow off (BO) quickly stops, and the FO expansion can be seen as a current peak successively reaching each string. The smaller current measured on each string as early as ESD triggering is thought to be due to a few electrons moving quickly ahead of the plasma front. The total amount of these electrons is of course limited by their space charge. This situation was a very challenging application case for the multiphysical model previously developed. First, the expanding character of the plasma bubble made the multizone modeling somewhat more complex. Second and above all, the sweeping of the precharged array made things more complex in two respects. It first made the currents collected on the cover glasses highly variable. The intersection of the zone boundary with the array surface also constitutes singularity that is moving (cf. Fig. 17), i.e., quite difficult to model, which shall be discussed again later. The simulation was started at the end of the BO when the absolute potential of the array ground has come back close to zero (the tank wall reference potential). At that time, before FO occurs, the relative charging of the cover glasses is unchanged. Since it was set to approximately 1 kV by biasing the cells to −1 kV and neutralizing the cover glasses (through plasma in this case), the cover glass potential is then about +1 kV, as sketched in Fig. 17. This indeed assumes that the BO is very short so that the FO can be considered to start after the BO, whereas in reality, it already starts during the BO. Fig. 16 yet shows that the BO and FO overlap is small enough to make this approximation rather reasonable. The simulation was thus limited to the FO expansion. Modeling the evolution of the array ground potential during the BO was indeed not possible since its close coupling to the plasma bubble through the cathode spot made the implementation of the electron balance loop in Fig. 5 necessary. Due to the lack of this electron balance loop, Boltzmann distribution reference potential (or, equivalently, its reference density) had to be also arbitrarily fixed and so was the ion emitted current since no energy balance was implemented in this first attempt to model FO. The values of these somewhat arbitrary parameters used for the case reported below were 10-eV electrons with 1016 m−3 reference density (density at zero potential), ions emitted with energy of 100 eV, and a total current of 0.15 A. They should be considered as the conditions at a macroscopic distance from the cathode spot. Fig. 18 shows the ion density at a given time during the plasma expansion. The ESD location is on the right of the coupon, i.e., at the location of highest density. The boundary between the dense and low-density electron zones is plotted on the right-hand-side panel. It is clearly controlled by ion density and Debye length. Fig. 19 shows the electron density at the same time. While it is close to the ion density in the quasi-neutral dense region, it significantly differs from the ion density in the low-density region. In particular, electrons spread all over the tank, although

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TABLE II P OTENTIALS R EACHED ON S PACECRAFT S UBPARTS (t = 1000 s)—C OMPARISON OF NASCAP C ODE S ERIES R ESULTS AND SPIS R ESULTS

Fig. 16. FO and BO experimental signals. This ESD happens on string 15, and the FO propagates to nearby strings (i.e., among the individually monitored ones, to string 13 first), and then to most of the coupon surface on this example ESD.

Fig. 17. Principle of the expansion of the plasma bubble on top of the photovoltaic solar array (PVSA).

with a limited density due to space charge. They are the ones responsible for the current collection seen on all strings immediately after the ESD starts, much ahead of the plasma bubble arrival. Fig. 20 finally displays the potential at the same time. In volume, the potential becomes more negative throughout the dense region from the cathode spot to the zone boundary, as a consequence of quasi-neutrality and electron barometric law. Then, it gets more positive in the space-charge zone from the boundary to the tank walls (at zero reference potential). On top of the coupon, the surface potential is neutralized where it was reached by the plasma. Fig. 21 displays the electron current collected on various strings or groups of strings. At the start of the simulation, all strings are immediately reached by the fast electrons traveling

Fig. 18. Ion density at 15-µs time (on the cutting plane) and boundary between the two electron zones (see the red surface on the lower chart). The wire frame surfaces are the PVSA coupon at the bottom and the tank shell.

Fig. 19. Electron density at 15-µs time. Wire frame isodensity surfaces are for 1010 , 1012 , and 1014 m−3 . Coupon and tank are not represented.

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Fig. 20. Potential at 15-µs time both in volume (cutting plane) and on the coupon surfaces (and on the tank).

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not described here due to lack of space, a specific electric field model was implemented in these boundary tetrahedra, with a flat potential inside the dense zone, and the potential gradient restricted to the space-charge region. However, the same was not done on the surface for the collection on surface nodes or elements, which thus exhibit steps when swept by the plasma front. We think that improving this by developing a more accurate collection model around this singularity should greatly improve the modeling of the plasma expansion on top of surfaces to be neutralized. A self-consistent model of cathode spot might also improve the overall model. Basing the ion production on the power available at the cathode spot (rather than having a fixed ion production), this power itself based on an electron balance equation for the plasma bubble might improve the behavior of the expansion on the panel surfaces. The time increasing ion production might improve both the too slow initial expansion and the too limited expansion in the long term. Both the needed extra models (i.e., electron balance loop and cathode spot models) had a first version developed but still need to be completed. IV. C ONCLUSION

Fig. 21. Collected currents on the coupon strings (to be compared with the opposite of the experimental signals in Fig. 16).

ahead of the plasma front. Then, at the arrival of the plasma front, current drastically increases. This successively happens for strings 13 (the closest to the ESD site), 12, 11, etc. When these currents are compared to the experimental measurements in Fig. 16, the order of magnitude of the initial currents (tens of milliamperes) is found correct, whereas the following larger currents in the presence of the plasma very significantly exceed the experimental ones. This is mostly due to an exceedingly rapid expansion and neutralization in the simulation. On the other hand, the plasma expansion was always found (even trying to vary the arbitrary parameters aforementioned) to be limited to the first few strings close to the ESD site, never reaching the other end of the panel. After a while, the progression of the ions to the left part of the panel is always stopped by the positive potentials prevailing there, without the collection of electrons ahead of the plasma being large enough to neutralize the array fast enough there. Clearly, the important place is the singular point (or line) in Fig. 17, i.e., the boundary between where lone electrons and plasma electrons are at work. Looking in detail at how this simulation works, its weak point is due to the fact that electron collected current exhibits a sharp step there, whereas the numerical scheme assumes smooth variations. In the volume, this step, or singularity, has been specifically modeled in the tetrahedral split by the zone boundary. Although

Major improvements of SPIS solvers have been implemented and tested. They mostly aimed at improving the multitime and multiphysics capabilities of the code. The major new solvers were implicit circuit solvers with automatic time step and a hybrid electron model, with Boltzmann electrons in the dense zone, PIC electron in the space-charge zone, and a dynamical self-consistent determination of the boundary between both zones. As a first application case, the charging of a spacecraft in a typical GEO environment was modeled. It was compared to previously published NASCAP modeling results. The agreement was found satisfactory both as potential maps and time evolution of both is concerned. The second application case, which is much more challenging, was the modeling of an FO while it sweeps a precharged solar array. It involved the dynamical modeling of dense and low-density electrons. The hybrid electron model, including a dynamical evolution of the boundary, behaved well in the volume. The modeling of the electron collection on the panel surfaces and the resulting cover glass neutralization was qualitatively satisfactory but still failed to quantitatively reproduce the experimental measurements. The collected currents had the correct order of magnitude for the space-charge-limited electrons ahead of the plasma front but were too large at the arrival of the plasma. The expansion of the plasma on the charged surface was found initially fast but then stopped too early, never neutralizing the full panel, whereas this sometimes happens in experiments. Since the major part of ambitious solvers was implemented, it should be now easier in the future to find the opportunities to correct their weaknesses, which have been largely understood due to the reported test or application cases. This is already in progress concerning GEO charging modeling with an extensive testing campaign of the code starting soon.

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ACKNOWLEDGMENT The authors would like to thank the NASCAP team, particularly V. Davis, for supplying NASCAP results for comparison. R EFERENCES [1] J.-F. Roussel, F. Rogier, G. Dufour, J.-C. Matéo-Vélez, J. Forest, A. Hilgers, D. Rodgers, L. Girard, and D. Payan, “SPIS open source code: Methods, capabilities, achievements and prospects,” IEEE Trans. Plasma Sci., vol. 36, no. 5, pp. 2360–2368, Oct. 2008. [2] A. Hilgers, B. Thiébault, D. L. Estublier, E. Gengembre, J. A. Gonzalez del Amo, M. Capacci, J.-F. Roussel, M. Tajmar, and J. Forest, “A simple model of the effect of solar array orientation on SMART-1 floating potential,” IEEE Trans. Plasma Sci., vol. 34, no. 5, pp. 2159–2165, Oct. 2006. [3] J.-J. Berthelier, J. Yang, J. Forest, and M. Quassim, “DEMETER potential measurements: Observations from the ion analyzer, model calculation using SPIS and implications for plasma and field measurements,” in Proc. 10th Spacecraft Charging Technol. Conf., Biarritz, France, Jun. 18–21, 2007. [4] A. Eriksson, E. Engwall, R. Prakash, L. Daldorff, R. Torbert, I. Dandouras, and K. Torkar, “Making use of spacecraft–plasma interactions: Determining tenuous plasma winds from wake observations and numerical simulations,” in Proc. 10th Spacecraft Charging Technol. Conf., Biarritz, France, Jun. 18–21, 2007. [5] J.-C. Matéo-Vélez, J.-F. Roussel, D. Sarrail, F. Boulay, V. Inguimbert, and D. Payan, “Ground plasma tank modelling and comparison to measurements,” IEEE Trans. Plasma Sci., vol. 36, no. 5, pp. 2369–2377, Oct. 2008. [6] J.-C. Matéo-Vélez, J.-F. Roussel, V. Inguimbert, M. Cho, K. Saito, and D. Payan, “SPIS and MUSCAT software comparison on LEO-like environment,” in Proc. 11th Spacecraft Charging Technol. Conf., Albuquerque, NM, Sep. 20–24, 2010. [7] A. Hilgers, S. Clucas, B. Thiébault, J.-F. Roussel, J.-C. Matéo-Vélez, J. Forest, and D. Rodgers, “Modelling of plasma probe interactions with a PIC code using an unstructured mesh,” IEEE Trans. Plasma Sci., vol. 36, no. 5, pp. 2319–2323, Oct. 2008. [8] J.-C. Matéo-Vélez, J.-F. Roussel, T. Tondu, F. Boulay, D. Sarrail, and E. Chesta, “Neutralization for micro-propulsion—Experiments and SPIS simulation,” in Proc. 44th AIAA/ASME Joint Propulsion Conf., Hartford, CT, Jul. 21–23, 2008. [9] J.-F. Roussel, T. Tondu, J.-C. Matéo-Vélez, E. Chesta, S. d’Escrivan, and L. Perraud, “Modeling of FEEP electric propulsion plume effects on MICROSCOPE spacecraft,” IEEE Trans. Plasma Sci., vol. 36, no. 5, pp. 2378–2386, Oct. 2008. [10] D. Rodgers, S. Clucas, and D. Nicolini, “SPIS simulations in optimization of FEEP design and contamination analysis,” in Proc. 11th Spacecraft Charging Technol. Conf., Albuquerque, NM, Sep. 20–24, 2010. [11] L. Girard, D. Payan, J.-F. Roussel, and F. Séverin, “Simulation of an electrostatic discharge initiation with software SPIS,” in Proc. 10th Spacecraft Charging Technol. Conf., Biarritz, France, Jun. 18–21, 2007. [12] P. Sarrailh, J.-C. Matéo-Vélez, J.-F. Roussel, B. Dirassen, J. Forest, B. Thiébault, D. Rodgers, and A. Hilgers, “Comparison of numerical and experimental investigations on the ESD onset in the inverted potential gradient situation in GEO,” in Proc. 11th Spacecraft Charging Technol. Conf., Albuquerque, NM, Sep. 20–24, 2010. [13] C. D. Child, “Discharge from Hot Cao,” Phys. Rev. (series I), vol. 32, no. 5, pp. 492–511, May 1911. [14] I. Langmuir, “The effect of space charge on residual gases on thermionic currents in high vacuum,” Phys. Rev., vol. 2, no. 6, pp. 450–486, Dec. 1913. [15] I. Langmuir, “The effect of space charge and initial velocities on the potential distribution and thermionic current between parallel plane electrodes,” Phys. Rev., vol. 21, no. 4, pp. 419–435, Apr. 1923. [16] V. A. Davis, M. J. Mandell, B. M. Gardner, I. G. Mikellides, L. F. Neergaard, D. L. Cooke, and J. Minor, “Validation of NASCAP-2K spacecraft–environment interactions calculations,” in Proc. 8th Spacecraft Charging Technol. Conf., Huntsville, AL, Oct. 20–24, 2003.

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Jean-François Roussel received the Diploma degree from École Polytechnique, Palaiseau, France, in 1990 and the Ph.D. degree in particle physics from the Université Pierre et Marie Curie-Paris VI, Paris, France, in 1995. Since then, he has been a Research Scientist with the Space Environment Department (DESP), Office National d’Etudes et Recherches Aérospatiales (ONERA)—the French Aerospace Laboratory, Toulouse, France. He was the Leader of the SPIS development project. He has been the Head of DESP, ONERA, since 2009. His research activities dealt with spacecraft–plasma interactions and spacecraft molecular contamination.

Guillaume Dufour, photograph and biography not available at the time of publication.

Jean-Charles Matéo-Vélez received the Master’s degree in engineering in fluid mechanics from the École Nationale Supérieure d’Électronique, d’Électrotechnique, d’Informatique, d’Hydraulique, et des Télécommunications, Toulouse, France, the Master’s degree in research in fluid dynamics from the University of Toulouse, Toulouse, in 2003, and the Ph.D. degree in fluid dynamics from SUPAERO, Institut Supérieur de l’Aéronautique et de l’Espace, Toulouse, in 2006. Since 2007, he has been a Research Scientist with the Space Environment Department (DESP), Office National d’Etudes et Recherches Aérospatiales (ONERA)—the French Aerospace Laboratory, Toulouse. His research interests include spacecraft charging, ground tests of electrostatic discharges, and numerical modeling of spacecraft–plasma interaction. Dr. Matéo-Vélez has served as a Referee for the IEEE T RANSACTIONS ON P LASMA S CIENCE . He is a member of the Spacecraft Plasma Interaction Network in Europe.

Benoît Thiébault, photograph and biography not available at the time of publication.

Bjarne Andersson, photograph and biography not available at the time of publication.

David Rodgers, photograph and biography not available at the time of publication.

Alain Hilgers received the Ph.D. degree in astrophysics from the Université Paris Diderot-Paris VII, Paris, France, in 1992. Since 1993, he has been with the European Space Research and Technology Centre (ESTEC) of the European Space Agency, Noordwijk, the Netherlands, in the area of space environment and effects. Dr. Hilgers is also the Chairman of the Spacecraft Plasma Interaction Network in Europe in the frame of which the SPIS software was initiated and developed.

Denis Payan, photograph and biography not available at the time of publication.