Confidential manuscript submitted to JGR-Space Physics A Fast-Fermi acceleration at Mars bow shock 1 2 K. Meziane1,2 , C. X. Mazelle2 , D. L. Mitchell3 , A. M. Hamza1 , E. Penou2 , and B. M. Jakosky4 3 1 Physics 4 2 IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France. 3 Space Sciences Laboratory, University of California, Berkeley, USA. 5 4 Laboratory 6 • near the tangency point. 10 • Fast-Fermi process operating at the foot of the Martian shock structure rather than the ramp. 12 13 Flux spikes associated with sunward propagating energetic electrons observed upstream of the Martian bow shock when interplanetary field lines intersect the shock 9 11 for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, USA. Key Points: 7 8 Department, University of New Brunswick, Fredericton, Canada. • Similarities and strong contrasts with the terrestrial foreshock. This article has been accepted for publication and undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process which may lead to differences between this version and the Version of Record. Please cite this article as doi: 10.1029/2019JA026614 Corresponding author: K. Meziane, karim@unb.ca –1– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 14 Abstract 15 We report, for the first time, strong evidences that a fast-Fermi mechanism is taking place 16 at the Mars bow shock. The MAVEN spacecraft observations from the SWEA instrument 17 show electron flux spikes with energies up to ∼ 1.5 keV. These spikes are associated with 18 sunward propagating electrons and appear when the interplanetary field line threading the 19 spacecraft is connected near the Martian bow shock tangency point. The observed loss 20 cone distribution is a salient feature of these backstreaming electrons as the phase space 21 density peaks on a ring centered along the magnetic field direction. Moreover, the data 22 show no evidence of any effect due to a hypothetical cross-shock electric potential on 23 the observed angular distributions. Although similar distributions are seen at the terres- 24 trial bow shock, the quantitative analysis of the measurements strongly indicates that the 25 electrons are produced at the shock foot, and escape upstream before exploring the entire 26 shock structure. 27 1 Introduction 28 The Phobos–2 spacecraft reported for the first time the existence of energetic elec- 29 trons upstream of the Martian bow shock [Skalsky et al., 1993]. Using the HARP differen- 30 tial electrostatic analyzer [Kiraly et al., 1991], Skalsky et al. [1993] show that the electron 31 flux is enhanced only when the Field Of View (FOV) of the instrument and the magnetic 32 field directions are nearly parallel. The authors interpreted these observations as a signa- 33 ture of the shock reflection of solar wind electrons. The Phobos–2 detector restricted FOV 34 as well as a limited time measurement resolution provided an incomplete picture of the 35 foreshock electrons. 36 Using a state of art instrumentation onboard of the MAVEN orbiter, a recent study 37 from Meziane et al. [2017] revealed new insights of the Martian electron foreshock. An 38 electron population emanating from the entire bow shock surface of Mars with energies 39 reaching up to ∼ 2 keV and having a flux intensity that is independent of shock geometry 40 θ Bn , the angle that the shock normal makes with the upstream ambient magnetic field, 41 forms the main source of backstreaming electrons. This electron population exhibits a flux 42 decrease with distance from the shock. This unexpected feature has been interpreted as 43 the consequence of their impact with Martian exospheric hydrogen [Mazelle et al., 2018]. 44 The production mechanism at the shock remains to be elucidated, although the observed 45 pitch angle distributions seem to indicated that electron reflection may be dominant. These –2– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 46 findings somehow contrast with what is known in the terrestrial foreshock environment. A 47 second foreshock electron population appearing as spikes with energies up to ∼ 1.5 keV 48 are detected when the interplanetary field line threading the spacecraft is connected near 49 the Martian bow shock tangency point. These electron signatures are similar to analogous 50 well-established observations in the terrestrial electron foreshock [Anderson et al., 1979]. 51 The present work focusses on this latter population. 52 Despite the lack of a global magnetic field, the existence of an induced magneto- 53 sphere produced by the interaction of the solar wind plasma with the planetary atmosphere 54 and ionosphere implies the presence of the Martian bow shock, which has an impact on 55 major upstream phenomena such as foreshock formation. Precisely, ions and electrons 56 of solar origin, in addition to pickup ions, encounter the shock structure, which in turn 57 modifies their complex trajectories, respectively. Moreover, the difference in plasma scale 58 lengths as compared to the sizes of the Martian and Terrestrial obstacles suggests some 59 fundamental dissimilarities between the solar wind interactions with the Martian bow 60 shock and the Terrestrial foreshock, respectively. It is clear that the study of foreshock 61 particle distributions will potentially shed some light on our understanding of important 62 physical aspects of shock structure and its impact on downstream plasma thermalization, a 63 phenomenon poorly understood and in need of thorough investigation. In addition, particle 64 reflection at the Martian shock still prevails and needs to be investigated thoroughly since 65 the separation between quasi-parallel and quasi-perpendicular remains ill-defined [Moses 66 et al., 1988]. 67 In the present report, quantitative arguments are developed to explain that the lo- 68 cal acceleration of electrons at Mars results from a Fast Fermi process. According to 69 our knowledge, although this may appear to be ordinarily associated with particle shock- 70 related acceleration, this is the first time such a phenomenon is reported in a planetary 71 environment other than the terrestrial one. The observations are depicted in the next sec- 72 tion and a quantitative analysis is developed in Section 3. Using an instructive parallel 73 comparison with the terrestrial foreshock, a conclusion that summarizes the main results is 74 presented in the last section. 75 2 Observations 76 77 The present study is based on observations from the MAVEN spacecraft, which currently is in orbit around Mars. The main objective of MAVEN’s mission is to understand –3– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 78 the physical mechanisms leading to the outflow of volatile gas at Mars as a consequence 79 of the solar radiation and the solar wind’s interaction with the upper Martian atmosphere 80 [Jakosky et al., 2015]. The orbiter carries a state of art instrumentation able to fully ac- 81 complish the proposed science goals. In this study, we focus on data from the Solar Wind 82 Electron Analyzer (SWEA) and the magnetometer (MAG). SWEA consists of a symmet- 83 rical hemispheric shaped detector able to measure the energy and angular distributions of 84 3-4600 eV electrons throughout the Martian environment [Mitchell et al., 2016]. The in- 85 strument field of view spans 80% of all sky and a half distribution function is obtained 86 every 32 seconds while the integrated flux is collected every 4 seconds near the shock, 87 typically, the rate depending on altitude and Mars-Earth distance. The MAG sensors mea- 88 sure the vector magnetic field with a precision of ∼ 0.35 nT with a sampling rate of 32 89 Hz [Connerney et al., 2015a], and are designed to perform high precision reliable mea- 90 surements of the magnetic field in the Mars environment. The measurements’ accuracy 91 has been confirmed by the first results and compared with the electron pitch-angle dis- 92 tribution in the solar wind [Connerney et al., 2015b]. In terms of time resolution, MAG 93 provides, in the maximum high-telemetry mode, 32 vectors per second, sufficiently enough 94 to study the dominant ion scale plasma processes occurring at the bow shock of Mars. In 95 addition, solar wind ion plasma measurements are also used and these are from the Solar 96 Wind Ion Analyzer (SWIA) [Halekas et al., 2015]. 100 The time series of electron flux for ten selected energy ranges is shown on the top 101 panel of Figure 1 as recorded by MAVEN/SWEA on January 4, 2015 between 0230 UT 102 and 0320 UT. The following successive panels display the magnetic field magnitude, the 103 solar wind speed, the angle θ Bn that the IMF makes with the local shock normal and the 104 foreshock depth DI F, the distance parallel to the X−direction of the MAVEN position 105 from the IMF tangent line to the shock, respectively. In the case where the magnetic field 106 line is not connected to the shock, DI F is negative and the angle θ Bn is not calculated. 107 The remote determination of connection parameters, θ Bn and DI F, necessitates the use of 108 a model for the Martian bow shock surface; this shape has been investigated by several au- 109 thors based on shock crossings identified in satellite data. All these models revolve around 110 a fitting procedure that uses shock crossing locations to determine the best conic section. 111 In all these available models, the conics’ parameters are fixed and no adjustment to solar 112 wind conditions is considered. In an aberrated solar ecliptic system, the Martian shock 113 surface is usually represented in polar coordinates (r,θ) by –4– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics r= 114 L 1 + ǫ cosθ In Mars Solar Orbital (MSO) system, the three parameters of the conics, the semi- 115 116 latus rectum L, the eccentricity ǫ and the focus distance X0 from the center of the planet, 117 must be determined in order to fix the model. Based on Expression 1, one approach to 118 determine the triplet (L,ǫ,X0 ) is to consider the function F(L, ǫ, X0 ) given by the following 119 form 120 121 (1) F(L, ǫ, X0 ) = (X − X0 )2 + Y 2 + Z 2 − (L − ǫ(X − X0 ))2 (2) where (X,Y ,Z) are the MSO-coordinates of the spacecraft. The function F links 122 the position of the MAVEN spacecraft with respect to the shock, and at the time of the 123 crossing F(L, ǫ, X0 ) = 0. An approximate solution for (L,ǫ,x0 ) is obtained by minimiz- 124 ing F(L, ǫ, X0 ) at the time of the Martian bow shock crossing by MAVEN, which occurs 125 at 0318:25 UT. We found L = 2.53 RM (Mars’ Radius), ǫ = 1.03 and X0 = 0.70 RM . 126 These numerical values can be compared with statistical models from Vignes et al. [2000] 127 (L = 2.04 RM , ǫ = 1.03, X0 = 0.64 RM ), Trotignon et al. [1991] (L = 2.17 RM , ǫ = 0.95, 128 X0 = 0.50 RM ), Slavin et al. [1991] (L = 2.07 RM , ǫ = 1.01, X0 = 0.55 RM ) or 129 Schwingenschuh et al. [1990] (L = 2.72 RM , ǫ = 0.85, X0 = 0.0 RM ). During the time 130 interval of Figure 1, all previously cited models point to a situation where the MAVEN 131 spacecraft remains magnetically disconnected from the shock, which seems to be in agree- 132 ment with the electron data since the fluxes for all energies are sustained to a constant 133 level corresponding to solar wind electrons. However, none of these models captures the 134 0318:25 UT crossing. Moreover, the shock parameters derived from the minimization of 135 Expression 2 point at the fact that the IMF field lines threading the MAVEN spacecraft re- 136 main unconnected (DI F < 0) during the entire interval shown on Figure 1 except for two 137 short durations that we examine next. The model, however, reproduces MAVEN’s inbound 138 crossing as indicated by the vertical line in DI F (or θ Bn ) plot, remarkably. Furthermore, 139 Figure 1 shows short-lived/abrupt electron flux enhancements for E ≥ 37 eV which peak 140 at ∼ 0236:40 UT, ∼ 0237:45 UT and ∼ 0255:00 UT, respectively. It is important to note 141 that the model bow shock used here captures the magnetic connection when the electron 142 bursts are observed, indicating that the shock has not moved significantly. These electron 143 bursts, as indicated in the DI F panel plot, appear in the SWEA analyzer due to a rapid –5– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 144 back and forth change in the IMF direction, while the spacecraft remains clearly outside 145 the foreshock (DI F < 0) grazing the shock-IMF tangent line; the short MAVEN intrusions 146 in the foreshock are indicated by DI F > 0. Interestingly, it is worth noticing the associ- 147 ation of the electron spectrum with the connection parameters. For the 0237:45 UT burst, 148 the lower energy threshold corresponds to E ∼ 74 eV while it is lower for the 0255:00 UT 149 burst (E ∼ 37 eV), and at the same time MAVEN is located deeper in the foreshock for 150 the latter when compared to the former. 154 The association of backstreaming electrons with the Martian bow shock prompts a 155 scrutiny of the shock region. Figure 2 shows an enlargement of Figure 1 around the time 156 of interest, between 0315 UT and 0320 UT, in which the DI F and the θ Bn panels have 157 been replaced by time series representing the IMF MSO components. Before the shock 158 ramp crossing, indicated by the dashed vertical line, Figure 2 clearly shows, starting at 159 0317:57 UT, a magnetic structure that is strongly similar to a foot commonly seen in front 160 of quasi-perpendicular supercritical shocks. It is important to notice the electron flux en- 161 hancement, up to ∼ 1.5 keV, when MAVEN happens to be inside the foot region. As we 162 elaborate below, the existence of the magnetic foot at the shock front plays a determinant 163 role in understanding the observed electron distribution functions. 168 Pursuing further the observation, we now examine in detail the electron angular dis- 169 tribution. For this purpose, the Hammer-Aitoff equal area projection [Mailing, 2004] is 170 used to represent three-dimensional measurements of electron distributions as shown on 171 Figure 3. The projection is appropriate to display 4π steradians projections for a given 172 energy and has been used with terrestrial foreshock electron observations [Larson et al., 173 1996] and ions [Meziane et al., 2001]. Each slice is a representation in pitch-angle (radial 174 extent)-gyrophase (polar angle) dimensions for a fixed energy. In this representation, field- 175 aligned propagating particles show a space phase density peak centred on the ’+’ or ’⋄’ 176 symbol (indicating the direction of B or -B respectively). The blank polar sectors visible 177 in each distribution are velocity space regions that are not covered by SWEA while the as- 178 terisk symbol ’∗’ shows the solar wind direction. During the time interval of interest, the 179 magnetic field direction is planetward, the backstreaming particles are therefore primarily 180 streaming in -B direction indicated by the ’⋄’ symbol as shown on each Hammer-Aitoff 181 slice. Figure 3 shows eight snapshots for 12 selected energy ranges as indicated on the top 182 of each slice. The solar wind strahl, a population of solar wind electrons (energies > 40 183 eV at 1 AU) that propagate in beams parallel to the magnetic field direction [Feldman –6– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 184 et al., 1975; Rosenbauer et al., 1977], is clearly identified in Figure 3 for Energie E > 74 185 eV. It coincides with the IMF direction as indicated by the ’+’ symbol; its intensity de- 186 creases with energy. Figure 3 also depicts a nearly-closed ring or annulus centred along 187 the -B direction and representing a peak in phase space density seen above E > 37 eV. In 188 addition, it seems that the pitch angle (the ring radius) appears slightly larger for the elec- 189 tron energy-channel E = 378 − 477 eV than for E = 188 − 237 eV and below, though for 190 the highest energy channel the ring is not well resolved. 193 In support of further analysis, the electron angular distribution recorded after the 194 burst during the inbound MAVEN motion, and precisely within the shock foot just before 195 MAVEN shock crossing is shown on Figure 4; a similar format as in Figure 3 is used. 196 Similar ring distributions are observed throughout the shock foot between 0317:52 UT 197 and 0318:72 UT and the ring structure disappears after the shock ramp. The ring can be 198 clearly identified on energy channels starting from 46 − 59 eV up to 780 − 960 eV (not 199 shown). 200 3 Quantitative analysis 205 From a quantitative standpoint, the continuous lines on Figure 5 show a more con- 206 ventional representation of the pich-angle distribution. For the electron burst observed at 207 0255:11 UT, the distribution is sampled in the plasma rest frame and is retrieved from the 208 3D angular distribution of Figure 3, and in which the integration over the gyrophase has 209 been performed. In addition, the dashed lines in Figure 5 represent the solar wind pitch 210 angle distribution measured at a not so distant instant (0253:59 UT) when MAVEN was 211 outside the foreshock. Figure 5 clearly depicts the solar wind electron isotropic core (and 212 part of the halo) (E = 14 − 18 eV) and the strahl (E ≥ 37 eV). Both solar wind com- 213 ponents are clearly identified whether MAVEN is inside or outside the Martian foreshock. 214 The electron spike is associated with a significant flux enhancement above the solar wind 215 threshold and corresponds to sunward moving electrons (pitch angle > 90o ). Clearly, the 216 electron phase-space density maximum is not aligned with the magnetic field direction. 217 While E ≥ 149 eV electrons exhibit a peak at ∼ 130o , at lower energy (E = 59 − 118 eV) 218 the phase space density values peak sensitively at higher pitch-angle values (∼ 150o ). Due 219 to a limited angular resolution of SWEA, the progressive decrease of the pitch angle from 220 higher to lower electron energies is fairly noticeable [Meziane et al., 2017]. –7– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 221 The observations presented in the above Section clearly point to similarities with 222 the terrestrial foreshock. It is known that sheets of sunward propagating energetic elec- 223 trons are always present on IMF field lines nearly tangent to the Earth bow shock [An- 224 derson et al., 1979]. The most energetic electrons emanate near the tangent line, whereas 225 less energetic ones emerge from regions located relatively deeper, downstream of the IMF 226 tangent line. Therefore, the bursty appearance is due to the IMF line tangent to the bow 227 shock sweeping the spacecraft. The occurrence of electron bursts at the Martian foreshock 228 result in the same fashion as they are seen when the foreshock connection depth DIF nears 229 zero. The analogy pinpoints to a similar physical mechanism, responsible for the electron 230 energization, operating at both planetary shocks. In this context, the seminal works by Wu 231 [1984] and Leroy and Mangeney [1984] are fundamentally relevant since they provide the 232 theoretical framework for the production mechanism of electron bursts seen at planetary 233 bow shocks. The theoretical models are based on an adiabatic reflection mechanism of a 234 subpopulation of solar wind electrons by planetary bow shocks. In agreement with these 235 models, a later work from Larson et al. [1996] provided strong observational evidence that 236 a mirror reflection of a population of solar wind electrons takes place at the Earth’s bow 237 shock. In this latter study, based on WIND-3DP experiment, Larson et al. [1996] report 238 that the distributions have a loss cone angle increasing with decreasing energy pinpointing 239 the presence of a significant cross-shock potential affecting lower-energy reflected elec- 240 trons. In the present study, no such effect is observed, and as explained below, the vari- 241 ation of the loss cone angle with energy stipulates in fact that the adiabatic reflection of 242 electrons occurs in a static electric potential-free space region. 243 Furthermore, the mirror loss cone-angle αc provides an unambiguous component for 244 testing the theoretical models since it is precisely determined. For a quasi-parallel geom- 245 etry, a simple approximate expression for αc independent of the shock speed VS can be 246 obtained [Larson et al., 1996]. However, for nearly perpendicular shocks, the approxima- 247 tion does not hold. Following Decker [1983], and making a readjustment to account for 248 the cross-shock potential energy eΦ we can show (see Appendix) that the critical pitch 249 angle αc for an electron energy E is given by: 250 " # r 1 eΦ 2 2 η + (N − 1)(N − η ) − Nη ( ) µc = cos αc = N ES (3) –8– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 251 with N = BM /B1 and η2 = ES /E, where B1 and BM are the magnetic field mag- 252 nitude upstream and at the mirror point, respectively. To derive Expression (3), a planer 253 shock is assumed. As the Larmor radius of a typical solar wind electron is several order 254 of magnitude smaller than the curvature of the Mars’ bow shock, the assumption is not 255 violated. 256 In Expression (3), all reflected electrons that escape upstream have an energy E 257 larger than the critical energy ES = me VS2 /2, i.e. η ≤ 1. For fixed values of ES and 258 eΦ, one can determine µc using Expression (3) for different ranges of electron energy 259 E and compression ratio N. For supercritical shocks, N may exceed by about 25% the 260 MHD asymptotic value of N = 4. The theoretical prediction of µc requires knowledge of 261 the parameters eΦ and ES . The cross-shock electric potential Φ is inherent to supercrit- 262 ical shocks as it arises mainly from a combination of electron pressure gradients and the 263 Hall current [Scudder et al., 1986]. At the Earth’sbow shock, the cross-shock potential en- 264 ergy in the deHoffmann-Teller frame may reach a significant fraction of the incident flow 265 energy (up to ∼ 30%) [Schwartz et al., 1988]. Measurements suggest a tendency of the 266 electric potential jump to decrease in magnitude with increasing Mach number. In terms 267 of magnitude, the Mach number is slightly higher at Mars [Halekas et al., 2017]. It is 268 therefore expected that the cross-shock potential at Mars to be less in comparison to that 269 of Earth, but remains significant still. As a result, the incoming ions are repelled by the 270 macroscopic electric field while the electron reflection is mitigated since electrons should 271 overcome the cross-shock potential to escape upstream. 274 Figure 6 depicts the effects of the cross-shock potential on electrons encountering 275 the shock boundary. For illustration purposes, the particle energy and the shock potential 276 energy are normalized to ES and a shock compression ratio N = 3 is arbitrarily chosen. 277 On the figure, the black continuous curve corresponds to eΦ = 0 while the red, cyan, blue 278 and green curves correspond to the cases eΦ = 0.5ES, ES, 1.5ES, 2ES , respectively. By 279 analogy with the observations, 180o − αc is plotted instead of αc which given is by Ex- 280 pression 3. While at high energy, the effect of the cross-shock potential on the loss cone 281 tends to remain small, at low energy the variation of the loss-cone (with energy) is re- 282 versed when the cross-shock potential is present. In comparison with the case eΦ = 0, the 283 effect on the loss-cone is more important as the potential jump across the shock increases. 284 In other terms, in the presence of a significant cross-shock potential, the loss-cone angle at 285 high electron energy appears smaller when compared to the case of low energy electrons. –9– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 286 On the contrary, a reflection from a potential-free shock is considered, higher energy es- 287 caping electrons requires pitch angles that are larger than those of low-energy electrons 288 (since the parallel velocity is relevant). 291 The determination of ES requires more caution. The inspection of the electron dis- 292 tribution shown in Figure 5 also reveals sunward moving electron fluxes over the solar 293 wind flux level only for energies larger than ∼ 37 eV, which is consistent with the lack of 294 electron bursts below this energy (Figure 1). The absence of E ≤ 37 eV flux enhance- 295 ment may be due to two distinct factors. The burst occurrence at 0255:11 UT results from 296 a small IMF rotation. In the situation where the shock θ Bn remains larger than a threshold 297 value, E ≤ 37 eV electrons cannot escape upstream; in this particular case, ES ∼ 37 eV. 298 Another possibility is related to particle velocity filtering. Due to solar wind convection, 299 thin-sheet particle layers are not located in the same region of space, and therefore all 300 energies are not seen simultaneously. As a consequence, dispersed bursts in time should 301 occur. The electron burst presents no evidence for any dispersion; however, it is likely that 302 the time measurement resolution remains insufficient to catch a possible dispersion. For 303 this particular situation, ES < 37 eV. Finally, the numerical value of ES could be esti- 304 mated from the connection parameters derived from the bow shock model. We found that 305 the 0255:11 UT electron burst occurs for θ Bn ∼ 84.5o and θV n ∼ 129o the angle the di- 306 rection of the plasma flow makes with the local shock normal. With a solar wind speed 307 VSW ∼ 495 km/s, we found ES ∼ 31 eV in good agreement with the observed electron 308 spectrum. 309 Maintaining a value of ∼ 37 eV for the predicted critical energy ES , the mirror angle 310 180o − acos(µc ) contours for a range of N and energy E are shown on Figure 7; the 180o - 311 offset is enforced because sunward moving electrons have pitch angles > 90o . In Figure 7, 312 eΦ = 0 eV, and this choice is discussed below. One should emphasize that the analytical 313 results of Figure 7 remain qualitatively unchanged for other possible values of ES < 37 314 eV (not shown). Quantitatively, at the same time, the contour values slightly increase but 315 remain insignificant in comparison with the angular resolution of the measurements. 316 It is reasonable to assume, under nominal solar wind conditions, that one is deal- 317 ing with a supercritical quasi-perpendicular shock, as it is the case for the Martian bow 318 shock crossing above (we estimated MM S ∼ 3.7), and the typical shock magnetic com- 319 pression ratio N is larger than ∼ 2. For the present case event N ∼ 3.2 and it reaches –10– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 320 N ∼ 4 if the overshoot is taken into account. It clearly appears from Figure 7 that typ- 321 ical shock magnetic compression ratios predict critical pitch angles significantly smaller 322 than the observed ones. Precisely for E = 760 − 960 eV range, the observed critical pitch 323 angle is accounted by a compression ratio N ∼ 1.3. The agreement for the lower ener- 324 gies with a similar compression ratio cannot be dismissed. Moreover, a reflection from 325 the shock ramp, where presumably a cross-shock potential must be significant, would re- 326 sult, as explained above and shown on Figure 6, noticeable signatures in the electron pich- 327 angle distributions. Based on Equation 3, we found an upper threshold for eΦ ∼ 0.1ES 328 (or eΦ ∼ 3.7 eV). Such a value is of the same order as the expected spacecraft potential 329 (not taken into account here since negligible for the energies considered). These results 330 strongly suggest that the electrons do not explore the entire shock ramp and consequently 331 the shock overshot. As described in detail in Section 2, from the instant where the spike 332 is seen to the shock crossing, the time evolution of the connection depth DI F shown on 333 Figure 1 indicates that MAVEN spacecraft remains in a grazing position with respect to 334 the IMF tangent line. Before reaching the shock ramp, the spacecraft encounters a foot 335 for which the maximum magnetic compression ratio BM /B1 is 1.5 − 1.6. The increase of 336 the magnetic field magnitude inside the foot region is sufficient to prompt a reflection of 337 incoming electrons and the observed pitch-angles are in good agreement with what is ex- 338 pected from a magnetic mirror reflection. Although the source region of the electron spike 339 observed upstream cannot be determined precisely, the similarities of the associated an- 340 gular distribution with the mirror reflected electrons at the foot are striking. This strongly 341 suggests that the source region of the electron spike is very similar to the shock structure 342 seen subsequently. At this point, a conclusive empirical determination can only be reached 343 through higher time resolution electron measurements and a comprehensive understanding 344 of the encounter of the solar wind electrons with the the Martian bow shock demands a 345 theoretical development that goes beyond the simple process emulated in Expression 3. 346 4 Conclusion 347 In the present study, we report bursts of sunward propagating energetic electrons up- 348 stream of the Martian bow shock. These events are seen along IMF field lines that are 349 nearly tangent to the Martian shock surface. The quantitative analysis of the electron pitch 350 angle distribution demonstrates that the electron spikes are produced, like at the terrestrial 351 bow shock, by a fast-Fermi acceleration process. The present observations show for the –11– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 352 first time that such a coherent process occurs at the Martian quasi-perpendicular shock. 353 Nevertheless, an essential difference regarding the source region exists between Earth and 354 Mars. While solar wind electrons explore the entire shock layer, including the overshoot, 355 before getting reflected upstream of the Earth’s bow shock, they can bounce back at the 356 shock foot in the Martian case. and not necessarily at the ramp or the overshoot. This 357 distinction needs to be investigated as the Martian shock structure remains to be fully un- 358 derstood. 359 5 Appendix: Rest frame pitch angle of a particle after its encounter with a shock 360 In presence of an electric potential Φ′ in region where a gradient of a magnetic field 361 exists, the pitch angle α ′ of an electron cannot be less than αc′ , where after [Fitzenreiter 362 et al., 1990; Leroy and Mangeney, 1984] 2 sin 363 364 αc′   B1 eΦ′ = 1+ ′ BM E (A1) In the context of a shock wave, E ′, αc′ and eΦ′ are respectively the particle kinetic 365 energy, the critical pitch angle and the electric potential energy expressed in deHoffmann- 366 Teller reference frame; B1 and BM are the magnetic field magnitude upstream and at the 367 mirror point. Setting N = and µc′ = cos αc′ yields: µc′ 368 369 BM B1 = r 1−   eΦ′/E ′ 1 1− N N −1 (A2) Clearly from above, the presence of a cross-shock potential implies a larger cone- 370 angle comparatively to the case eΦ′ = 0. Now, one needs to write the last equation in the 371 plasma rest frame. If E and µc are the particle energy and the cosine of the critical pitch 372 angle given in the plasma rest frame, the transformation from deHoffmann-Teller frame 373 provides [Decker, 1983]: E′ = 1 − 2ηµc + η2 E 374 and µc′ = p µc − η 1 − 2ηµc + η2 375 where η2 = 376 flected particles with η ≤ 1 can escape upstream. Since the reference frame transformation 377 is only parallel to the magnetic field direction, a Galilean transformation leaves the electric 378 field unchanged: Φ = Φ′. The critical pitch-angle µc is now derived after eliminating E ′, 379 Φ′ and µc′ from Expression A2. We obtain: ES E (A3) with ES the kinetic energy associated with the shock speed VS ; only re- –12– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics 380 " # r 1 eΦ µc = cos αc = η + (N − 1)(N − η2 ) − Nη2 ( ) N ES 381 which is Expression 3. Above Equation shows that a minimum value for µc exists at 382 (A4) particle energy E such that: η2 = 383 N(N − 1) 1 2 N − 1 − N(eΦ/ES ) (A5) 384 Acknowledgments 385 MAVEN data are publicly available through the Planetary Data System. This work is sup- 386 ported by the French space agency CNES for the observations obtained with the SWEA 387 instrument. Work at UNB is supported by the Canadian Natural Science and Engineering 388 Council. MAVEN data are publicly available through the Planetary Data System (https://pds- 389 ppi.igpp.ucla.edu/). 390 References 391 Anderson, K. A., R. P. Lin, F. Martel, C. S. Lin, G. K. Parks, and H. Rème (1979). Thin 392 sheets of energetic electrons upstream from the Earth’s bow shock. Geophys. Res. Lett., 393 6, 401–404. 394 Connerney, J. E. P., J. Espley, P. Lawton, S. Murphy, J. Odom, R. Oliversen, and D. Shep- 395 pard (2015a). The MAVEN magnetic field investigation. Space Sci. Rev. 195, 257–291, 396 doi:10.1007/s11214-015-0169-4. 397 Connerney, J. 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All rights reserved. Confidential manuscript submitted to JGR-Space Physics MAVEN - SWEA - 2015 January 04 10 10 14-18 eV 10 9 37-46 eV 59-74 eV 10 8 93-118 eV 149-188 eV 10 7 2 Flux #.(cm .str.s.keV) -1 237-299 eV 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 BMAG [nT] 1212-1530 eV 20 10 V SW [km/s] 0 500 Bn [deg] 250 90 60 30 DIF [R M ] 0 0 -2 02:30 02:45 03:00 03:15 TIME [UT] Top to bottom panels respectively show the electron flux for ten selected energy ranges, the mag- 97 Figure 1. 98 netic field magnitude, the solar wind speed, the shock θ Bn and the foreshock depth DI F for 2015 January 04 99 between 0230 and 0320 UT. MAVEN shock crossing is indicated by a thin vertical line at ∼ 0318 : 25 UT –17– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics MAVEN - SWEA - 2015 January 04 10 10 14-18 eV 10 9 37-46 eV 59-74 eV Flux #.(cm2.str.s.keV)-1 10 8 93-118 eV 149-188 eV 10 7 237-299 eV 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 500 250 BMAG [nT] VSW [km/s] 1212-1530 eV 20 10 20 0 [nT] By 10 Bz 0 Bx -10 3:16 3:18 3:20 TIME [UT] Top to bottom panels respectively show the electron flux for ten selected energy ranges, the solar 151 Figure 2. 152 wind speed, the magnetic field magnitude and the MSO components of the magnetic field for 2015 January 04 153 between 0315 and 0320 UT. The vertical dashed-line indicates the shock crossing. –18– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics Snapshots of electron angular distribution for selected energy ranges taken at 0255:11 UT. The 164 Figure 3. 165 Hammer-Aitoff equal area projection is used. The ’+’ (’⋄’) symbol represents the direction of B (-B) direc- 166 tion. The color scale corresponds to distribution function values, and are normalized for each Hammer-Aitoff 167 slice. –19– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics Snapshots of electron angular distribution for selected energy ranges taken between 0317: 43 UT 191 Figure 4. 192 and 0318:07 UT. A similar format as in Figure 3 is used. –20– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics MAVEN-SWEA 2015 January 04 - 0255:11 UT 10 1 14-18 eV 18-23 eV 29-37 eV 10 0 Distribution Function (cm-3 .keV -1 ) 46-59 eV 10 -1 74-94 eV 118-149 eV 10 -2 188-237 eV 299-378 eV 10 -3 477-602 eV 10 -4 602-760 eV 760-960 eV 10 -5 10 -6 0 20 40 60 80 100 120 140 160 180 Pitch-Angle (o ) The continuous lines show the phase space density variation versus pitch angle for selected en- 201 Figure 5. 202 ergy channels observed by MAVEN-SWEA analyzer on 2015 Jan. 04, 0255:11 UT. The thin dashed lines 203 correspond to the solar wind distribution taken 0253:59 UT for which MAVEN is not magnetically connected. 204 The vertical line indicate a pitch angle of 130o The energy ranges are indicated on the right of the figure. –21– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics Mirror loss cone-angle αc versus electron energy for a magnetic ratio N 272 Figure 6. 273 based on eΦ values as indicated by the color of each curve = 3 for various cases –22– ©2018 American Geophysical Union. All rights reserved. Confidential manuscript submitted to JGR-Space Physics Loss-Cone Angle Vs. Energy 160 4 3.5 ES = 37 eV 5 15 150 2.5 155 150 160 N = B /B 2 1 3 145 50 145 1 2 145 140 140 135 1.5 135 130 1 1055 11465 0 145 0 130 125 120 1 0 5 11313205 0 12 200 400 600 800 125 120 1000 1200 1400 1600 1800 2000 Energy E (eV) Left panel shows The contours provide the mirror reflection loss cone-angle αc in degrees for a 289 Figure 7. 290 particle with energy E and shock ratio N ranges while the critical energy ES = 37 eV and eΦ = 0 eV. –23– ©2018 American Geophysical Union. All rights reserved. Figure1. ©2018 American Geophysical Union. All rights reserved. 10 10 MAVEN - SWEA - 2015 January 04 14-18 eV 10 9 37-46 eV 59-74 eV 10 8 93-118 eV 149-188 eV -1 237-299 eV 2 Flux #.(cm .str.s.keV) 10 7 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 BMAG [nT] 1212-1530 eV 20 10 V SW [km/s] 0 500 Bn [deg] 250 90 60 30 DIF [R M ] 0 0 -2 02:30 02:45 03:00 TIME [UT] 03:15 ©2018 American Geophysical Union. All rights reserved. Figure2. ©2018 American Geophysical Union. All rights reserved. MAVEN - SWEA - 2015 January 04 10 10 14-18 eV 10 9 37-46 eV 59-74 eV Flux #.(cm2.str.s.keV)-1 10 8 93-118 eV 149-188 eV 10 7 237-299 eV 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 500 250 BMAG [nT] VSW [km/s] 1212-1530 eV 20 10 20 0 [nT] By 10 Bz 0 Bx -10 3:16 3:18 TIME [UT] ©2018 American Geophysical Union. All rights reserved. 3:20 Figure3. ©2018 American Geophysical Union. All rights reserved. ©2018 American Geophysical Union. All rights reserv Figure4. ©2018 American Geophysical Union. All rights reserved. ©2018 American Geophysical Union. All rights reserved. Figure5. ©2018 American Geophysical Union. All rights reserved. MAVEN-SWEA 2015 January 04 - 0255:11 UT 10 1 14-18 eV 18-23 eV 29-37 eV 10 0 Distribution Function (cm-3 .keV -1 ) 46-59 eV 10 -1 74-94 eV 118-149 eV 10 -2 188-237 eV 299-378 eV 10 -3 477-602 eV 10 -4 602-760 eV 760-960 eV 10 -5 10 -6 0 20 40 60 80 100 120 140 160 o Pitch-Angle ( ) ©2018 American Geophysical Union. All rights reserved. 180 Figure6. ©2018 American Geophysical Union. All rights reserved. ©2018 American Geophysical Union. All rights reserved. Figure7. ©2018 American Geophysical Union. All rights reserved. Loss-Cone Angle Vs. Energy 160 4 3.5 ES = 37 eV 5 15 150 160 2.5 155 150 145 0 145 15 2 145 140 140 135 1.5 135 130 130 125 120 1 1055 11465 0 145 0 N = B 2 /B 1 3 1 0 5 11313205 0 12 200 400 600 800 125 120 1000 1200 1400 1600 1800 2000 Energy E (eV) ©2018 American Geophysical Union. All rights reserved. 10 10 MAVEN - SWEA - 2015 January 04 14-18 eV 10 9 37-46 eV 59-74 eV 10 8 93-118 eV 149-188 eV -1 237-299 eV 2 Flux #.(cm .str.s.keV) 10 7 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 BMAG [nT] 1212-1530 eV 20 10 V SW [km/s] 0 500 Bn [deg] 250 90 60 30 DIF [R M ] 0 0 -2 02:30 02:45 03:00 TIME [UT] 03:15 ©2018 American Geophysical Union. All rights reserved. MAVEN - SWEA - 2015 January 04 10 10 14-18 eV 10 9 37-46 eV 59-74 eV Flux #.(cm2.str.s.keV)-1 10 8 93-118 eV 149-188 eV 10 7 237-299 eV 378-477 eV 10 6 602-760 eV 10 5 960-1212 eV 10 4 500 250 BMAG [nT] VSW [km/s] 1212-1530 eV 20 10 20 0 [nT] By 10 Bz 0 Bx -10 3:16 3:18 TIME [UT] ©2018 American Geophysical Union. All rights reserved. 3:20 ©2018 American Geophysical Union. All rights reserv 2019JA026614-f04-z-.png ©2018 American Geophysical Union. All rights reserved. MAVEN-SWEA 2015 January 04 - 0255:11 UT 10 1 14-18 eV 18-23 eV 29-37 eV 10 0 Distribution Function (cm-3 .keV -1 ) 46-59 eV 10 -1 74-94 eV 118-149 eV 10 -2 188-237 eV 299-378 eV 10 -3 477-602 eV 10 -4 602-760 eV 760-960 eV 10 -5 10 -6 0 20 40 60 80 100 120 140 160 o Pitch-Angle ( ) ©2018 American Geophysical Union. All rights reserved. 180 2019JA026614-f06-z-.png ©2018 American Geophysical Union. All rights reserved. Loss-Cone Angle Vs. Energy 160 4 3.5 ES = 37 eV 5 15 150 160 2.5 155 150 145 0 145 15 2 145 140 140 135 1.5 135 130 130 125 120 1 1055 11465 0 145 0 N = B 2 /B 1 3 1 0 5 11313205 0 12 200 400 600 800 125 120 1000 1200 1400 1600 1800 2000 Energy E (eV) ©2018 American Geophysical Union. All rights reserved.