Numerical modelling of the Luna-Glob lander electric charging on the lunar surface with SPIS-DUST

Accepted Manuscript Numerical modelling of the Luna-Glob lander electric charging on the lunar surface with SPIS-DUST I.A. Kuznetsov, S.L.G. Hess, A.V. Zakharov, F. Cipriani, E. Seran, S.I. Popel, E.A. Lisin, O.F. Petrov, G.G. Dolnikov, A.N. Lyash, S.I. Kopnin PII:

S0032-0633(17)30269-6

DOI:

10.1016/j.pss.2018.03.004

Reference:

PSS 4489

To appear in:

Planetary and Space Science

Received Date: 31 July 2017 Revised Date:

1 March 2018

Accepted Date: 1 March 2018

Please cite this article as: Kuznetsov, I.A., Hess, S.L.G., Zakharov, A.V., Cipriani, F., Seran, E., Popel, S.I., Lisin, E.A., Petrov, O.F., Dolnikov, G.G., Lyash, A.N., Kopnin, S.I., Numerical modelling of the Luna-Glob lander electric charging on the lunar surface with SPIS-DUST, Planetary and Space Science (2018), doi: 10.1016/j.pss.2018.03.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT NUMERICAL MODELLING OF THE LUNA-GLOB LANDER ELECTRIC CHARGING ON THE LUNAR SURFACE WITH SPIS-DUST I.A. Kuznetsov(1), S.L.G. Hess(2), A.V. Zakharov(1), F. Cipriani(3), E. Seran(4), S.I. Popel(1), E.A. Lisin(5), O.F. Petrov(5), G.G. Dolnikov(1), A.N. Lyash(1), S.I. Kopnin(1) (1)

Space Research Institute of the RAS, Moscow, Russia, email:[email protected] (2) French Aerosp. Lab., ONERA, Toulouse, France (3) ESTEC/TEC-EES, Noordwijk, The Netherlands (4) Laboratoire Atmospheres, Milieux, Observations Spatiales/UVSQ/UPMC, Paris, France (5) Joint Institute for High Temperatures of the RAS, Moscow, Russia

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Abstract

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15 One of the complicating factors of the future robotic and human lunar landing missions is the influence of the dust. The 16 upper insulating regolith layer is electrically charged by the solar ultraviolet radiation and the flow of solar wind 17 particles. Resulted electric charge and thus surface potential depend on the lunar local time, latitude and the electrical 18 properties of the regolith. 19 Understanding of mechanisms of the dust electric charging, dust levitation and electric charging of a lander on the lunar 20 surface is essential for interpretation of measurements of the instruments of the Luna-Glob lander payload, e.g. the Dust 21 Impact sensor and the Langmuir Probe. 22 One of the tools, which allows simulating the electric charging of the regolith and lander and also the transport and 23 deposition of the dust particles on the lander surface, is the recently developed Spacecraft Plasma Interaction Software 24 toolkit, called the SPIS-DUST. 25 This paper describes the SPIS-DUST numerical simulation of the interaction between the solar wind plasma, ultraviolet 26 radiation, regolith and a lander and presents as result qualitative and quantitative data of charging the surfaces, plasma 27 sheath and its influence on spacecraft sensors, dust dynamics. The model takes into account the geometry of the Luna28 Glob lander, the electric properties of materials used on the lander surface, as well as Luna-Glob landing place. Initial 29 conditions are chosen using current theoretical models of formation of dusty plasma exosphere and levitating charged 30 dust particles. 31 Simulation for the three cases (local lunar noon, evening and sunset) showed us the surrounding plasma sheath around 32 the spacecraft which gives a significant potential bias in the spacecraft vicinity. This bias influences on the spacecraft 33 sensors but with SPIS software we can estimate the potential of uninfluenced plasma with the data from the plasma 34 sensors (Langmuir probes). SPIS-DUST modification allows us to get the dust dynamics properties. For our three cases 35 we’ve obtained the dust densities around the spacecraft and near the surface of the Moon. As another practical result of 36 this work we can count a suggestion of improving of dusty plasma instrument for the next mission: it must be valuable 37 to relocate the plasma sensors to a distant boom at some distance from the spacecraft. 38 39 Index Terms— Moon, regolith, lander, plasma, dust electric charging, dust levitation 40 41 42 1. INTRODUCTION 56 grains are predicted to levitate from the lunar surface 57 and to stay suspended near the surface (Sickafoose et 43 The images and direct observations of the lunar horizon 58 al., 2002), while the ~1 µm grains may escape the lunar 44 glow made almost 50 years ago by the Surveyor-7 59 gravity in the case they reached the escape velocity 45 (Rennilson and Criswell, 1974) and Apollo-17 60 which is 2,38 km/s for the Moon’s equator (Heiken et 46 astronauts (Zook and McCoy, 1991), stay today in our 61 al., 1991). Such grains were observed up to an altitude 47 mind as one of the most mysterious observations related 62 of ~10 km and higher (Stubbs et al., 2006, Horanyi et 48 to Moon and are still under debate. Stubbs at al. (2006) 63 al., 2104a, 2014b). The novel work by Wang et al. 49 stated that surface electric charging in particularly near 64 (2016) proposes the so-called “Patched charge model” 50 the lunar terminator might result in the levitation of the 65 where the main trigger for the dust particles lifting off is 51 lunar dust grains with radii less than 10 µm. 66 explained as highly negative charged surfaces in micro52 Straightforward levitation mechanism explanation is 67 cavities in the regolith. Rennilson and Criswell (1974) 53 based on the idea that the electrically charged surface 68 found the 5 µm grains suspended at ~10 cm above the 54 and electrically charged dust grains repel each other. 69 surface. During the Apollo missions, ~0.1 µm dust 55 Under the action of electrostatic forces, the ~10 µm 70 particles were observed in the lunar exosphere at the

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128 developed three-dimensional version of SPIS-DUST 129 code (Anuar et al., 2013) includes the phenomena 130 related to the electric charging of regolith and dust 131 injection from the regolith surface and was recently 132 used to simulate the European Lunar Lander and the 133 lunar surface irregularities (Hess et al., 2015; Anuar et 134 al., 2013). 135 In this paper we use the SPIS-DUST code to simulate 136 the electric charging of the regolith and lander external 137 structures, to deduce the plasma and dust parameters 138 near the lunar surface and in the vicinity the lander 139 instruments. 140 The structure of this paper is the following. We start in 141 section 2 with the description of the “Luna-Glob” lander 142 and its Lunar Dust Monitoring instrument (PmL). The 143 brief description of the SPIS-DUST software is given in 144 section 3. In section 4 we present several results of the 145 SPIS-DUST simulation of the Luna-Glob lander 146 performed at different local times. The main findings 147 are summarized in section 5. 148 149 2. LUNA-GLOB LANDER AND ITS INSTRUMENTS

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71 altitude up to ~100 km (Zook and McCoy, 1991). The 72 Lunar Dust Experiment (LDEX) onboard the Lunar 73 Dust Atmosphere and Dust Environment (LADEE) 74 observed the dust grains at heights ranged from 30 to 75 110 km above the Lunar surface that moved with the 76 first escape velocity (Horanyi et al., 2014b). Horanyi et 77 al. (2014a) also found that concentration of the observed 78 dust particles is correlated to the impact of 79 micrometeorites. 80 Despite the numerous study performed during last 50 81 years, many issues related to the mechanisms of the dust 82 electric charging and levitation from the lunar surface, 83 its transport above few tens of km and its interaction 84 with exospheric plasma remain open. 85 Many parameters that are critical for proper modeling of 86 the regolith surface electric charging are not definitely 87 determined. Among them we can cite the quantum yield 88 and the work function, parameters of the secondary 89 electrons emission, electron-ion balance (Stubbs et al., 90 2007b, Popel et al., 2014, Colwell et al., 2007). Electric 91 charging mechanisms of the lunar regolith at the lunar 92 terminators and in a situation when the Moon is found 93 in Earth's magnetotail (Vaverka, et al., 2016) need to be 94 understood and modeled. 95 In recent years, the Particle-in-Cell (PiC) simulation 96 method has become an important and powerful tool to 97 model the plasma interaction with space objects 98 (including spacecrafts) and lets a possibility to consider 99 a complex geometry and different types of materials of 100 such bodies (see, for example, Han et al., 2016). Several 101 powerful codes were developed in last few years with 102 the aim to simulate the spacecraft electric charging in 103 different plasma conditions. Among them we can cite 104 the NASCAP-2K (Mandell et al., 2006), Coulomb-2 105 (Novikov et al., 2016), MUSCAT (Muranaka et al., 106 2008), SPIS (Sarrailh et al., 2016), EMSES (Miyake and 107 Usui, 2009), CPIC (Delzanno et al., 2013), PTetra tool 108 (Marchand, 2012), KARAT (Lisin et al., 2013), DPEM 109 (Kallio et al., 2016), iPic3D (Markidis et al., 2010, Deca 110 et al., 2013). Comparison of these software shows the 111 similar potential distribution for spacecrafts (Novikov et 112 al., 2016, Marchand et al., 2014). 113 The PiC methods also allow to introduce the dust 114 particles in the simulation medium and to follow their 115 dynamics in plasma. Poppe and Horanyi (2010) 116 performed one-dimensional modelling of exospheric 117 plasma near the lunar surface with the aim to simulate 118 the lunar dust particles levitation. In Lisin et al. (2013) 119 authors investigated the nature of lunar plasma 120 environment and previously observed dusty plasma 121 phenomena. Focused basically on plasma dynamics and 122 dust particles levitation phenomena, authors show the 123 possibility of lunar dust particles levitation by PiC 124 method. Since then several works had been performed 125 with dust particle levitation accent on the base of the 126 PiC methods: Wang et al., 2008, Lisin et al. 2015., 127 Kallio et al. 2016, Piquette and Horanyi 2017. A newly

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150 The Luna-Glob (also Luna-25) mission is the first 151 Russian lunar mission after a long interruption and this 152 mission is going to be followed by several other 153 missions with increasing complexity and finally with 154 delivering the lunar regolith to the Earth. These 155 missions are to be focused on lunar poles investigation 156 and three landers (Luna-25, -27 and -28) planned to be 157 land on the south pole (V.V. Efanov and V.P. 158 Dolgopolov, 2016). 159 The landing side of the Luna-Glob mission, which is to 160 be launched on 2019, is still the matter of discussion, 161 however, supposed landing sites are bound by 68°÷76° 162 S and 11°÷44° E, near the South Pole. Three landing 163 sites candidates are presented in Table 1 (Kazmerchuk 164 et al., 2016), another three candidates are given in 165 Table II (Djachkova et al., 2017). 166 167 TABLE I 168 POSSIBLE LUNA-GLOB LANDING SITES (KAZMERCHUK ET AL., 2016) Location Latitude Longitude South 1 76,8°S 26,5°E South 2 73,3°S 43,9°E South 3 72,9°S 41,3°E 169 170 TABLE II 171 POSSIBLE LUNA-GLOB LANDING SITES (DJACHKOVA ET AL., 2017) Location Latitude Longitude South 1 68,8°S 21,2°E South 2 68,6°S 11,6°E South 3 69,5°S 43,5°E 172 173 The scientific payload of Luna-Glob Spacecraft includes 174 distance (ADRON-LR, LIS-TV-RPM) and in situ 175 (LASMA-LR, TERMO-LR) regolith properties 176 investigation instruments, plasma investigation

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233 potentials difference in simple solar wind-SC interaction 234 case was 2%; with addition of photoelectrons, 235 secondary electrons and with additional orbital speed 236 and solar wind magnetic field floating potentials differ 237 became 23 %), Theillaumas et al. (2014) performed 238 simulations in SPIS and NASCAP software which in 239 different simulation conditions gave the differences 240 from 3 % (for “sunlight configuration”) up to 20 % 241 (“out of eclipse” conditions); authors concluded that 242 ‘the results agree qualitatively and quantitatively’. Up to 243 23 % of differences between the models with various 244 approach doesn’t mean that we have 23 % of error in 245 one software simulation results. And taking into account 246 relatively big variations in solar wind and relatively big 247 variations of other conditions which depend on landing 248 site, angles, surface properties, etc. we can suggest that 249 qualitative agreement is very important for us when 20 250 % of quantitative disagreement is good enough to use in 251 our case for investigation the principal possibility of 252 plasma potential measurements controlling. Davis et al. 253 (2013) performed a comparison of Nascap-2k, SPIS and 254 MUSCAT software for the low Earth orbit (LEO) wake 255 current collection estimation, which shows the good 256 agreement in Debye screening of the surface potential 257 by the plasma, the distribution of the current, collected 258 to the surface and other parameters. 259 However, the dust modification of SPIS (SPIS-DUST) 260 considers lunar dust fluxes, properties of dust particles 261 (such as density, speeds, obscuration, charges, high 262 altitude dust distribution) and properties of the lunar 263 surface, and this modification had been developed 264 exactly for the simulation of physics of the dust 265 charging and transport above the lunar surface (Hess et 266 al., 2015). To estimate the influence of the lander on the 267 near-surface electric fields and, oppositely, to estimate 268 the influence from lunar exosphere on the lander with 269 the different conditions we decided to use SPIS-Dust 270 numerical simulation code. 271 For the plasma currents computation, SPIS uses the 272 Boltzmann distribution. For the Electric field 273 computation, the Poisson equation is used. The 274 computations perform with the nonlinear stabilized 275 Newton and Finite element methods. SPIS is provided 276 with its own User interface SPIS-UI (Thiebault et al., 277 2015). 278 In the SPIS-DUST special lunar surface material with 279 predefined dust distribution have been added (Hess et 280 al., 2015; Hess et al., 2016). 281 In this set of simulations, we will try to estimate the 282 potential bias in the spacecraft vicinity for a various 283 local time in the case of the South Pole landing site. 284 Also, we expect the levitated dust particle distribution 285 results. 286 In the following sections, we describe the simulation 287 approach for the each of three stages and for the whole 288 simulation.

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177 instruments (ARIES-L, LINA-EKSAN) and dusty 178 plasma monitoring instrument (P.V. Kazmerchuk et al., 179 2016). 180 Lunar Dust Monitoring instrument (PmL) is a part of 181 the scientific payload of Luna-Glob and Luna-Resource 182 (2021) landers of Russian space program (Kuznetsov et 183 al., 2016). 184 The PmL package consists of the Impact Sensor (IS) 185 and two Electrostatic Probes (EP). The IS is designed to 186 measure the electric and mechanical properties of 187 micrometeorites and the dust particles levitated from the 188 lunar surface. The EP is developed to measure the 189 parameters of the ambient plasma. 190 The IS comprises (Fig. 1) an entrance grid and a layer of 191 24 lead zirconate titanate piezoelectric detectors (PZT). 192 The distance between the grid and PZTs is ~10 mm. 193 The entrance grid measures a signal that proportional to 194 the electric charge of the dust particle that passes 195 through the grid, while the PZT detectors develop a 196 signal proportional to the momentum of the dust impact. 197 The time shift between the grid and PZT signals 198 provides an estimation of the particle speed. 199 The sensitivity of the Impact Sensor is estimated to be 200 ~10-12 N·s and 8·10-16 C (i.e. 5·103 e). 201 The EP is a Langmuir probe shown in Fig. 2. The EP 202 consists of a truncated conical electrode polarized by a 203 voltage swept from –88 V to +88 V and a circular 204 electrode accommodated on the EP top part which is 205 floating. Current measured by the truncated Langmuir 206 probe allows deducing the local plasma parameters, 207 while the potential measured by the circular electrode 208 gives an estimation of the plasma potential at the EP 209 height. 210 The IS and lower EP sensor are fixed (Fig. 3) at the 211 lander at height of ~0,7 m above the lunar surface, while 212 the upper EP sensor is accommodated at height of 213 1.4 m. EP sensors will be pointed toward the north-west. 214 IS will be pointed to north-east. 215 The measurements of the PmL instruments 216 accommodated directly on the lander will be likely 217 perturbed by the lander electric charging. Thus, these 218 perturbations should be estimated and considered in the 219 interpretation of the plasma and dust measurements. 220 221 3. SOFTWARE AND SIMULATION APPROACH

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222 As we described in Introduction, some special 223 spacecraft charging investigation software are known. 224 Validation tests show high result repeatability for SPIS 225 with the other PiC software in the case of spacecraft 226 surface charging. According to (Novikov et al., 2016), 227 the results of on-orbit simulation in these software are 228 similar for surface potentials and mostly similar for 229 plasma population distributions. Marchand et al. (2014) 230 performed a comprehensive tests with 5 different 231 softwares (EMSES, iPic3D, LASP, PTetra, SPIS) and 232 obtained a good agreement between them (for floating

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299 3.1 Simulation Approach and Global 300 Parameters

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Figure 2. Electrostatic Probe

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Figure 1. Impact Sensor

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301 In these simulations we used a simplified model of the 302 Luna-Glob lander with legs, solar arrays (Fig. 4a), 303 placed on the surface inside a simulation box with 304 dimensions 10x10x60 m (Fig. 4b). 305 The simulation volume has meshed with a 0.5 m grid 306 near the surface and the spacecraft, where the Debye 307 length is about 1 m due to photoelectrons, and up to 5 m 308 grid at the 60 m altitude boundary where the Debye 309 length in the solar wind is about 10 m. 310 The simplified model gives us first approach to the 311 plasma and surface properties after the steady state 312 establishes. Although it is important for further deeply 313 understanding of the plasma conditions and therefore 314 the instrument measurements, other experience tells us 315 that simulation with the complex model of SC with its 316 instruments (including their detailed models, dielectric 317 surfaces, etc.) doesn’t globally change results of the 318 simulation (S. Guillemant, 2014). So then we made a 319 decision to make the first attempt for global SC-Lunar 320 exosphere interaction in these simulations, to figuring 321 out the next situation of interest for further simulations 322 in which the more detailed models of instruments are to 323 appear. 324 As soon as we are interested in lunar south region 325 conditions for the lander (Tables I and II), the first thing 326 to understand is relative sun position from the SC point 327 of view. Taking landing site candidate 1 from Table II 328 (68,8 °S; 21,2 °E), we can count the lunar sun angle at 329 this site. Using the Lunar Sun Angle Calculator (LSAC, 330 https://the-moon.wikispaces.com/Sun+angle), we’ve 331 obtained that Sun angle for afternoon case is 21,8° from 332 the horizon. 333 We chose three situations for the relative sun position 334 (see Fig. 5 where θ is solar elevation angle, so we’d 335 took 22°, 11°, and 1°, see below, and α is solar azimuth 336 from the North which we calculated with LSAC): 337 • right after landing (with hibernation SC 338 temperatures and potentials, local noon – sun at 339 22 degrees above the horizon – α=0°, θ=22°); 340 • local evening (SC works stable, sun at 11 341 degrees above the horizon – α=45°, θ=11°); 342 • local sunset (SC is cooling down, the sun is 1 343 degree above – α=90°, θ=1°). 344 345 From electrical point of view, we divided the SC and 346 lunar surface on three basic equipotential types: the 347 basic spacecraft surface (the instruments, covered by the 348 thermostabilizing shield with the gold layer and Al 349 Oxide for the landing platform parts); two solar panels 350 made of the cerium doped silicon glass; and the lunar

295 296 Figure 3. PmL accommodation at the Luna-Glob 297 lander. The EPs are indicated with green circles, while 298 the IS with the red circle.

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387 et al., 2016). Considering fluctuations in slow solar 388 wind (Feldman et al., 2005) and various parameters 389 given in literature (D.J. Rodgers and A. Hilgers, 2000, 390 M. Bessell, 2001, Kivelson, M., and C. Russell, 1995; 391 Hundhousen A.J., 1995; Feldman et al., 2005), we can 392 assume that this recommendation represents in between 393 meanings of solar wind measurements and it fits with 394 our goals. Photoelectron temperature was estimated by 395 B. Feuerbacher and B. Fitton (1972). 396 In these simulations, the dust source is the lunar surface 397 and we chose the automatic using force balance. In this 398 case, the lunar dusty surface emits dust according to a 399 force balance between all forces acting on the dusts. The 400 dust emission from the surface is controlled by a surface 401 TABLE III 402 INITIAL PLASMA CONDITIONS

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Figure 4. a) Luna-Glob lander general view, b) Luna-Glob simulation model

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354 355 Figure 5. The direction on the Sun and solar wind 356 relatively to Spacecraft in SPIS simulation. 357 358 surface. We assumed that the solar panels connected to 359 the SC body with the resistance not worse than 360 10 kOhms, also we assumed that the spacecraft body 361 with its 4 legs connected to the lunar surface material 362 with 1 kOhm resistivity. 363 There are two pre-sets for lunar regolith properties in 364 SPIS: “Conductive lunar dust material” and “Lunar dust 365 material”. In SPIS User Manual (Sarrailh et al. 2016) as 366 well as in other sources (e.g., Heiken et al., 1991) stated 367 that lunar dust conductivity has a strong dependence of 368 the temperature, and for the dayside, we should choose 369 a conductive material. However, these conclusions were 370 made from the near-equatorial samples and 371 recommendations for SPIS simulation are made for the 372 equatorial case. In our polar case, we meet much lower 373 temperatures (288 K maximum as follows from 374 Williams et al., 2016) in oppose to equatorial (up to 375 400 K). So then, we chose the non-conductive material, 376 however for simulations after the landing one should 377 use the specified knowledge about lunar soil 378 conductivity in the polar case. 379 The density of lunar soil of 1500 kg/m3 had been chosen 380 instead of default 1000 kg/m3 (Kring, 2006). The mass 381 density of separate dust particles is taken as 3000 kg/m3. 382 The default dust size distribution is taken from (Sarrailh 383 et al., 2016), referred as 71501,1 Mare. 384 In Table 3 we show the plasma conditions for our 385 simulation which come from slow solar wind conditions 386 as they recommended in SPIS documentation (Sarrailh

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403 404 interactor which set up in Global parameters stage 405 (Sarrailh et al., 2016). This interactor computes the 406 current collection from electrons and ions volume 407 distribution in PiC-simulation, in a Monte Carlo way 408 and in an Orbited Limited Motion (OML) law (Hess et 409 al., 2016) way for the other distributions. The total 410 charge of the dust is updated at each time step following 411 the current balance: 412 ௗொ೏ 413 ൌ‫ܬ‬ (1) ୢ୲ 414 415 We also include the photoemission process in the 416 simulations. From case to case the photoemission 417 changes relative to the Sun position. The current 418 density at the normal sunlight incidence angle is 4,5 419 µA/m2 at 1 AU for the lunar dust. On the surface, the 420 flux is moderated by the sun incidence angle. For dust 421 in the gaseous phase, the photocurrent is maximal when 422 irradiated and null when in the shade of a crater for 423 instance. On the lunar surface, the energy distribution 424 function of the photoelectron is Maxwellian by default, 425 with a temperature of 2 eV (Sarrailh et al., 2016). 426 Other dusty plasma conditions we used are default in 427 SPIS (Sarrailh et al., 2016) as soon as they are a subject 428 to discussion, especially in lunar polar regions. 429 430

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501 4.1.1 Local noon case

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452 For the evening case, we have some changes in initial 453 parameters. Due to the PmL thermal simulation, the 454 temperature for the instrument and shielded surfaces is 455 323 K. From the (Williams et al., 2016) we know that 456 the surface temperature at 70° latitude is close to 240 K. 457 So then, the unshielded SC body and legs have a 458 gradient temperature from 323 K down to 240 K. 459 According to (Stubbs et al., 2007), the surface potential 460 on the lunar dayside is close to 0 V, however the 461 northside solar panel already should work and have a 462 potential of about 27 V. For this case, we also changed 463 angle of the Sun which is seen from the SC point of 464 view (and the solar wind and irradiation components) to 465 elevation angle θ=11° above the surface and azimuth 466 angle α=45° to the north as shown on Fig. 5. 467 3.4 Sunset

500 4.1 Plasma Potentials

502 For the noon case (Fig. 6) we have the strong 503 correspondence of the variation of the potentials on the 504 same levels but at the different distances from SC 505 (results from the plasma potential sensors in SPIS 506 simulation) throughout the simulation time. We can see 507 the difference up to 7 V between the onboard sensors 508 and the distance sensors. The central cut of 3-d volume 509 potential map at the steady-state (after approximately 15 510 s) of “Noon” simulation is shown in Fig. 9. It matched 511 with the sensor data. Also, the cut provides that the SC 512 sheath has a strong negative potential (-30 V) from the 513 shadow side of the SC.

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450 3.3 Evening – sun at 11 degrees above the 451 horizon

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432 Simulating the local noon conditions, we assumed that 433 the spacecraft landed recently and still hadn’t begun it’s 434 in situ operations. However, the time from the landing 435 procedure was enough to let the dust particles lofted 436 from the surface to return. 437 We used the initial temperatures for lander’s body in 438 this case of 233 K – the temperature which guaranteed 439 by radioisotope thermoelectric generator (RTG). 440 According to the Diviner Lunar Radiometer Experiment 441 (DLRE) data on the Lunar Reconnaissance Orbiter 442 (LRO) mission (Williams et al., 2016), the lunar surface 443 temperature is close to the 288 K for the noon 444 conditions. 445 According to (Manka, 1973), the surface potential on 446 the lunar dayside is close to 0 V with a little positive 447 bias (for the initial conditions we choose it 0 V). For the 448 initial conditions, we chose the same potential for each 449 SC surface.

483 from them at the same levels (1 m and 2 m 484 respectively), as shown in Figures 6-8. As expected, we 485 can see the plasma potential bias near the SC. 486 The simulation timeline here is the representation of 487 time that takes from the software to reach the electrical 488 equilibrium of the SC, surrounded plasma, lunar 489 surface, and solar wind. As soon as equilibrium reached, 490 simulations interrupt and then we can deal with the 491 results. However, even it is not a final result for preset 492 conditions, it is still interesting to observe the dynamics 493 of the potentials in the matter of understanding the 494 variations in potentials at the EP locations and in the 495 exosphere during the changes in this SC-plasma system. 496 In some way, we can consider these changes as an 497 accelerated lunar plasma dynamics with influence on 498 SC, which gave us the comprehension of its influence 499 on Langmuir probes during the changes.

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468 The sunset case deals with lower temperatures and very 469 low sun angle. Surface temperature descended to 130 K 470 for latitudes close to 70° S (Williams et al., 2016), when 471 the SC temperatures in heated thermal shielded zone 472 maintain 323 K. 473 We assumed that the surface potential became slightly 474 negative (-10 V according to Stubbs et al., 2007) and the 475 north solar array potential descended to 5 V. In this case 476 sun located at the westside, θ=1° above the horizon 477 (Fig. 5). 4. RESULTS 478 479 For the simulations, we added virtual instruments for 480 plasma dynamics investigation: 4 plasma potential 481 sensors on the edges of SC (two of them are situated at 482 the places close to the real EP locations) and 3 meters

514 4.1.2 Evening case 515 The similar situation we obtained for the “Evening” 516 conditions. In this case, the bias is much stronger (up to 517 50 V) than in the “Noon” case (Fig. 7, Fig. 10). 518 Obviously, the reason is both the solar array charging by 519 higher value due to the decreasing of sun angle to solar 520 array’s normal (better irradiation) and opposite worst 521 irradiation of the lunar surface which at the evening 522 starts to lose its potential. This process leads to the 523 situation when undisturbed exosphere above the lunar 524 surface reduces its potential, but the plasma in the 525 spacecraft vicinity acquires much higher potential than 526 in “Noon” case. 527 4.1.3 Sunset case 528 For the “Sunset” case the potentials of near-surface 529 lunar plasma decrease to -21 V. As we can see on Fig. 530 8, we still have significant biases (up to 23 V 531 difference) around the spacecraft; near the solar panel 532 surface (the EP sensors location) plasma potential is 533 13 V, that is higher than at the same levels in

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537 Plasma potential sheath in these simulations is 538 predictable, however, without the numerical simulation, 539 it is hard to estimate the exact numbers. The reason for 540 the sheath (and potential bias) is reciprocal influence 541 between lunar exosphere, lunar surface, and SC. So, the 542 lunar plasma conditions, solar irradiation (especially, 543 ultraviolet irradiation), the solar wind finally lead to the 544 equilibrium system, which includes SC, plasma and the 545 lunar surface. In these conditions depending mostly on 546 solar irradiation (including its direction) spacecrafts 547 start charge accumulation (for the detailed mechanisms 548 see, e.g., T. Mikaelian, 2009; D.J. Rodgers and A. 549 Hilgers, 2000). Then, considering spacecraft’s surface 550 conductivity properties, plasma and solar wind 551 properties we can start the numerical simulation for the 552 exact charges of surfaces and plasma sheath conditions 553 obtaining. In our case, for Luna-Glob we can estimate 554 the positive charging of the conductive (and grounded) 555 SC surfaces mainly due to photoelectron emission 556 processes, the stronger positive charge of the sunlit 557 dielectric surface (north solar panel in our case) and 558 negative charge of dielectric surface in shadow (south 559 solar panel) due to solar wind and plasma electrons 560 collection (Figure 12 provides the surface charges for 561 the “Noon” simulation which represents the result of 562 this charging mechanism). Thus, surface charges are the 563 reason of the relatively positive (e.g. around the sunlit 564 solar panel) or negative (e.g. around the shadowed solar 565 panel) sheath around the spacecraft (so, we can see it on 566 Fig. 6-11). Another factor of sheath changing is the 567 rotation of the Moon. Changing the relative sun position 568 (and therefore the direction of solar wind and 569 irradiation) leads to the spacecraft surfaces recharging 570 and then to the changing in plasma sheath. 571 The simulation results both confirms our awareness of 572 the sheath around the SC (very similar sheath obtained 573 in several other simulations, e.g. Deca et al., 2013, Hess 574 et al., 2015) and provides the possibilities for the 575 estimation of real plasma potential with the shifted 576 measurements from EP on the Moon (we cannot 577 compare our result with real lunar lander measurements 578 due the absence of the latter, however, we can expect 579 the significant influence relying on low earth orbit 580 measurements (Hastings, 1995)). The same conclusion 581 we can estimate for the other plasma probes on the 582 lander. Although in this work we simulate just 583 simplified SC body, it seems advisable to use such 584 software for all plasma (and related to) instruments for 585 careful understanding their measurements. 586 In the matter of the whole SC operating, charges do not 587 seem such critical that they can be a reason for 588 electrostatic discharges. However, we can give a strong

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536 4.1.4 Discussion

589 recommendation for the SC supply systems and 590 scientific payload developers to check the possible 591 influence on their sensors and devices (especially in the 592 case of them which don’t cover by the thermostabilizing 593 shield). 594 Dust contamination seems not so critical in these 595 simulations, but we can during the lunar day the dust 596 layer can appear on the surfaces. It barely can reduce 597 solar panel efficiency in some significant way, but 598 scientific payload developers (especially LASMA laser 599 spectrometry instrument) should take into account the 600 dust layer which can appear on some working surfaces. 601 Coming back to dusty plasma investigation 602 instrumentation, relying on the results we can suggest 603 the following actions: 604 1) Relocation of the EP sensors at some distance 605 from the SC to avoid the influence from the 606 plasma sheath around the SC. Probably the 607 good solution would be to open a boom with a 608 distance from about the 1 m from the SC body. 609 2) Include EP sensors at the opposite side of the 610 SC to compare the measurements of the 611 “negative” solar panel with the “positive” one. 612 3) Putting the IS at the lower level with probably 613 increasing the sensitive surface and field of 614 view.

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534 undisturbed exosphere for the lower EP sensor and 535 2,5 V for the upper EP sensor (Fig. 11).

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615 4.2 Dust Densities

616 Results of the simulations of the dust number density 617 near the lander for the “Noon” conditions presented at 618 the Fig. 13. We can see that in mentioned conditions 619 there is a significant amount of dust particles near the 620 spacecraft: ~103 m-3 near the IS location (red circle on 621 Fig. 3 and blue “X” sign on Figures 13-15). 622 Relatively left (southern) side of the SC on the Fig. 13 is 623 in the shadow and there we have the much higher 624 density for dust particles when the right side and the 625 space under the SC are open to the sunlit and we can see 626 less number of particles in there. The reason is the 627 electrostatic field (we can assume it from results for 628 surface and plasma potentials on Fig. 12 and Fig. 7 629 respectively) in which electrostatic force emits the 630 negatively charged dust particles in the shadow of SC to 631 the positively charged plasma. 632 For the “Evening” conditions (Fig. 14) we have also 633 ~103 m-3 near the IS. These tendencies keep for the 634 “Sunset” conditions too. We can see (Fig. 15) increasing 635 of near-surface dust densities near the IS unit (~104 m-3). 636 If we’d take the average dust densification at 0,1 m 637 level above the lunar surface, it would be 638 7,9·10-2 ± 6·10-2 m-3 (Fig.16). 639 These results correspond to the theoretical model (Popel 640 et al., 2013), where values of dust density vary from 641 4.5·103 m-3 to 7.5·1010 m-3 near the lunar surface (from 0 642 to 10 cm) depending on latitude (from 77° to 87°). 643

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686 687 Figure 7. Plasma potentials for the “Evening” 688 simulation: lower (1 m above the surface) and higher (2 689 m) potentials in the SC vicinity (green and red lines 690 respectively), which correspond with EP sensors 691 positions; the potentials on the 3 m distance from the SC 692 body on the same levels respectively (blue and yellow) 693 which represent the plasma potentials in undisturbed 694 exosphere. 695

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644 645 Figure 6. Plasma potentials for the “Noon” simulation: 646 lower (1 m above the surface) and higher (2 m) 647 potentials in the SC vicinity (yellow and blue lines 648 respectively), which correspond with EP sensors 649 positions; the potentials on the 3 m distance from the SC 650 body on the same levels respectively (green and purple) 651 which represent the plasma potentials in undisturbed 652 exosphere. 653 654 Popel et al. (2013) also estimate dust density at the level 655 of IS about 2·103 m-3 for 77° latitude which highly 656 corresponds with our results. 657 Even so, we can see that in SPIS model we have fewer 658 particles than in (Popel et al., 2013) what possibly 659 occurs due to the initial conditions of the simulation: 660 lower latitude then took Popel et al., (2013) and variety 661 of on-surface dust distribution model: dust distribution 662 in SPIS model, where we set the parameter that 663 responsible for dust size distribution to have a good 664 representation of the dusts between 100 nm and 10 nm 665 but worse representation of particles bigger than 1 µm 666 as recommended in (Sarrailh et al., 2016). However, it 667 is a matter for further exploration and simulation. 668 669 5. CONCLUSION AND DISCUSSION

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670 In the case of the Luna-Glob mission, usage of the SPIS 671 code helps to estimate the influence of the lander on the 672 results measurements of parameters of plasma and 673 levitated dust particles near the lunar surface in SC 674 vicinity. The results of this code can be used for the 675 deeper understanding and interpretation of the dust 676 measurements made onboard the Lunar Lander. 677 On this stage, these simulation provides us the 678 understanding of lunar exosphere influence on 679 Spacecraft and its Langmuir probes and Impact Sensor. 680 As a result, we have potential bias values on the 681 Langmuir probes for several local time cases, and, as 682 expected, that potentials much higher than the potential 683 of undisturbed exosphere. Also, we got the dust 684 densities in the simulation box and near the Impact 685 sensor

696 697 Figure 8. Plasma potentials for the “Sunset” 698 simulation: lower (1 m above the surface) and higher (2 699 m) potentials in the SC vicinity (green and red lines 700 respectively), which correspond with EP sensors 701 positions; the potentials on the 3 m distance from the SC 702 body on the same levels respectively (blue and yellow) 703 which represent the plasma potentials in undisturbed 704 exosphere. 705 706 location. The average dust densities near the Moon 707 surface are in agreement with theoretical models by 708 Popel et al. (2013). 709 In the simulation results, we have a significant amount 710 of dust at the level of IS for all three cases, which gives 711 us the confidence of some future practical result of PmL 712 instrument onboard the Luna-Glob lander. 713

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Figure 12. Lunar and SC surface potentials after the “Noon” conditions simulation.

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Figure 9. Plasma potentials at the steady-state in the “Noon” conditions. Sun is on the right. Virtual plasma potential sensors in SPIS simulation marked by “X” signs. Two of them matches with locations of the EP sensors on SC. Colours relate to Fig. 7. We can see the strong positive bias in the SC vicinity in relation to undisturbed exosphere plasma. However, we have the strongly negative bias in the south (shadow) solar panel vicinity.

747 748 Figure 13. Common logarithm of the dust density in 749 particles per cubic meter at the local lunar noon. The 750 sun is on the right, 22° above the horizon. IS from the 751 PmL instrument location marked by “X” sign. 752

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753 754 Figure 14. Common logarithm of the dust density in 755 particle per cubic meter at the local lunar evening. The 756 sun is on the right, 11° above the horizon. IS from the 757 PmL instrument location marked by “X” sign. 758

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725 726 Figure 10. Plasma potentials at the steady state of 727 simulation in “Evening” conditions. Sun is on the right. 728 Virtual plasma potential sensors in SPIS simulation 729 marked by “X” signs. Two of them matches with 730 locations of the EP sensors on SC. Colours relate to 731 Fig. 8. We can see the stronger positive bias in SC 732 vicinity in relation to undisturbed exosphere plasma. 733 734

735 736 Figure 11. Plasma potentials at the steady state of 737 simulation in “Sunset” conditions. Sun is behind the SC, 738 1° above the horizon. Virtual plasma potential sensors 739 in SPIS simulation marked by “X” signs. Two of them 740 (red, green) matches with locations of the EP sensors on 741 SC. Colours relate to Fig. 10. 742

759 760 Figure 15. Common logarithm of the dust density in 761 particle per cubic meter at the local lunar sunset. The 762 sun is behind the SC, 1° above the horizon. IS from the 763 PmL instrument location marked by “X” sign. 764

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811 Nascap-2k, SPIS, and MUSCAT Computer Codes, Transactions on 812 Plasma Science, vol. 41, No 12, pp. 3303-3309, 2013 813 Deca J., G. Lapenta, R. Marchand, and S. Markidis, Spacecraft 814 charging analysis with the implicit particle-in-cell code iPic3D, Phys. 815 Plasmas 20, 102902 (2013); doi: 10.1063/1.4826951 816 Delzanno G.L., Camporeale E., Moulton J.D., Borovsky J.E., 817 MacDonald E.A., and Thomsen M.F., CPIC: A Curvilinear Particle818 in-Cell Code for Plasma–Material Interaction Studies, IEEE 819 TRANSACTIONS ON PLASMA SCIENCE, VOL. 41, NO. 12, 820 DECEMBER 2013

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Figure 16. Dust density at 0,1 m level at the “Local Noon” simulation results (blue) and it’s average 7.9·10-2 m-3 (black line) with error of ± 6·10-2 m-3 (dashed line).

824 Efanov V.V., Dolgopolov V.P., The Moon. From studies to 825 exploration (on 50th anniversary of «LUNA-9» and «LUNA-10» 826 satellites) [in Russian], Vestnik NPO imeni S.A. Lavochkina, 2016, 4 827 (34), pp. 3-8 828 Feldman, U., E. Landi, and N. A. Schwadron (2005), On the sources 829 of fast and slow solar wind, J. Geophys. Res., 110, A07109, 830 doi:10.1029/2004JA010918.

FURTHER WORK

831 Feuerbacher B. and B. Fitton, Journal of Applied Physics 43, 1563 832 (1972); doi: 10.1063/1.1661362 833 Guillemant S., Study and Simulations of Spacecraft/Plasma Interaction 834 Phenomena and their Effects on Low Energy Plasma Measurements. 835 Earth and Planetary Astrophysics [astro-ph.EP]. Universit´e Paul 836 Sabatier - Toulouse III, 2014. English.

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772 Sure, these results confirmed it would be strongly 773 preferred to mount IS and EPs of the PmL instrument on 774 the boom (at least about a meter long). Unfortunately, it 775 was not able to include the boom in the Luna-Glob 776 lander due to technical reasons. However, the next 777 Russian lunar lander Luna-Resource will include a 778 modified dust instrument, similar to PmL with the 779 ability to mount Langmuir probes on the boom at some 780 distance from the SC. It leads us to a huge further work 781 of boom and its sensor modelling in SPIS software. 782 The next big part of this estimation concerns the night 783 side of the Moon. It’s still important to use the PiC 784 methods to control the data from the spacecraft plasma 785 sensors. However, the night operations of the SC are 786 still under discussion. 787 The other very interesting and important field is to 788 perform a simulation of various interesting and specific 789 lunar conditions such as crater shadows and boulder’s 790 shadows. The goal is to estimate the dust dynamics on 791 the border between the sun irradiated surface and the 792 shadow, to estimate the possible dust ejecta. 793 794 7. ACKNOWLEDGEMENTS

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821 Djachkova M.V., M.L. Litvak, I.G. Mitrofanov, A.B. Sanin, Selection 822 of Luna-25 Landing Sites in the South Polar Region of the Moon, 823 2017, Astronomicheskii Vestnik, 2017, Vol. 51, No. 3, pp. 204–215.

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795 The research was carried out using funds of the Russian 796 science foundation (project №17-12-01458). 797 798 8. REFERENCES 799 Anuar, A. K., F. Honary, M. Hapgood, and J.-F. Roussel (2013), 800 Three-dimensional simulation of dust charging and dusty plasma using 801 SPIS, J. Geophys. Res. Space Physics, 6723–6735, 802 doi:10.1002/jgra.50599. 803 Bessell M., Encyclopedia of Astronomy and Astrophysics, Nature 804 Publishing Group and Institute of Physics Publishing, UK, 2001. 805 Colwell J.E., Batiste S., Horanyi M., Robertsson S., Sture S. (2007). 806 Lunar surface: Dust dynamics and regolith mechanics.Rev. of 807 Geophys.45, p.1-26. 808 Davis V.A., M.J. Mandell, D.C. Cooke, A. Wheelock, J.-C. Mateo 809 Velez, J.-F. Roussel, D. Payan, M. Cho, K. Koga, Comparison of 810 Low Earth Orbit Wake Current Collection Simulations Using

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This work presents Particle-in-Cell simulation for lunar polar lander and its interactions with plasma. Three possible conditions depending on sun angle simulated The plasma potential simulated and potential bias near the spacecraft estimated. Dust concentration estimated.

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