Induced Magnetic Fields and Plasma Motions in the Inner Part of the Martian Magnetosphere

Analysis of Mars Atmosphere and Volatile Evolution (MAVEN)/Supra‐Thermal And Thermal Ion Composition observations in the Martian upper atmosphere, bounded at higher altitudes by the shocked solar wind, shows that the draping of interplanetary magnetic field penetrates down to low altitudes (∼200−250 km) and governs dynamics of the ionosphere. The upper ionospheric plasma is driven into motion flowing around Mars similar to the shocked solar wind in the adjacent magnetosheath. Such a fluid‐like motion is accompanied by ion acceleration caused by the bending of the magnetic field, leading to ion extraction and finally to ion pickup. Extraction of ions and their acceleration produces a recoil effect of the bulk ionosphere in the opposite direction. This provides a strong asymmetry in ion dynamics in two different hemispheres, accompanied by wrapping of the magnetic field lines around Mars and respective reconnection.


Introduction
The absence of a global magnetic field at Mars leads to nearly direct interaction of the solar wind with its atmosphere and ionosphere and to the formation of an induced magnetosphere where the interplanetary magnetic field (IMF) drapes around the ionospheric obstacle. In the case of a planet with an intrinsic magnetic field, the dayside plasma density is generally much lower than the density in the adjacent magnetosheath. By contrast, in the Martian case of an induced magnetosphere, the situation is different -the inner part of the induced magnetosphere of Mars or Venus is filled by much denser ionospheric plasma in which the dominant ion species are + 2 and O + (Dubinin et al., 2011;Halekas et al., 2017;Nagy et al., 2004). An important feature of the induced magnetosphere of Mars is that the draping IMF penetrates into the ionosphere because the solar wind dynamic pressure generally exceeds the thermal plasma pressure in the upper Martian ionosphere (see e.g., Sanchez-Cano et al., 2020). A similar effect is observed at Venus during the periods of high solar wind pressure and/or during periods of low solar activity when the Venusian ionosphere becomes weaker (Luhmann et al., 1980;Russell & Vaisberg, 1983).
At Mars, the existence of strong localized crustal magnetic fields (Acuña et al., 1999) significantly influences the interaction adding features typical for planets with a global intrinsic magnetic field. The topology of the magnetic field lines around these regions becomes very intricate, due to reconnection between the IMF and crustal fields (Hara et al., 2016;Harada et al., 2017Harada et al., , 2018Harada et al., , 2020J. Halekas & Brain, 2010;Xu et al., 2017Xu et al., , 2020. The net result might be the appearance of a twisted magneto tail Dubinin et al., 2017).
To separate features of the draping and crustal components of the Martian magnetosphere one can use different coordinate systems. The influence of the crustal field is rather complicated because of the intricate, localized • Draping of the interplanetary magnetic field around Mars penetrates deep to the ionosphere enveloping the planet and driving the ionosphere to the bulk motion • Draping and motion of the ionospheric plasma is characterized by asymmetry by the direction of the motional electric field in solar wind • Ion acceleration and extraction from the ionosphere is accompanied by a shift of the bulk ionosphere in the opposite direction topology of the crustal field lines coupled with Martian rotation. Nevertheless, one may expect a global effect of the crustal fields on the magnetic topology at Mars while considering a statistical field configuration by averaging over many Mars rotations and using the Mars Solar Orbital (MSO) coordinates in which the X-axis is directed from the center of Mars to Sun, the Z-axis is perpendicular to the planetary orbital plane and directed to the north, and Y completes the right-handed system Dubinin et al., 2017). The net field topology resembles topology of a hybrid magnetosphere with elements of the induced and intrinsic magnetospheres (Dubinin et al., 1980).
Since the orientation of the IMF varies with time, the relevant coordinate system for the description of the draping magnetosphere is the Mars Solar Electric System (MSE) which has the X MSE axis antiparallel to the upstream solar wind flow (the solar wind aberration was not taken into account), the Y MSE axis along the cross-flow magnetic field component of the IMF in the solar wind, and the Z MSE axis pointing in the direction of the solar wind motional electric field (−V sw × B IMF ), where V sw and B IMF are the vectors of the velocity and the magnetic field in the solar wind, respectively (Dubinin et al., 1996;Moore et al., 1990;Russell et al., 1995;Yeroshenko et al., 1990). When we rotate the spacecraft trajectories into MSE coordinates and apply temporal averaging the effects of the crustal magnetic field on an asymmetry are significantly reduced. Figure 1 compares the values of the magnetic field in the MSE-reference frame in the +Z MSE and −Z MSE hemispheres (panels (a) and (d)) with the corresponding values in the +Z MSO and −Z MSO hemispheres of the MSO-frame (panels (b), (c), (e) and (f)). The magnetic field values in the MSO coordinates were plotted for B ysw ≥ 0 and two cases of the Mars position. A reference point (CF) on the Mars surface with the aerographic coordinates Lat = −40° and Long = 180° characterized by the strong crustal sources of the magnetic field was near the noon (0°−30°) and midnight meridians (150°−180°), respectively. Comparing the data for +Z MSE and +Z MSO hemispheres we observe only a weak contribution of the crustal sources at low altitudes (≤200 km) at small and large solar zenith angles. Effects of the crustal fields clearly seen in the −Z MSO hemisphere (panels (e) and (f)) are strongly attenuated while plotting the data for the −Z MSE hemisphere that justifies our approach. Another biases might be related with the seasonal variations which can drive the important changes in the ionosphere dynamics. Their potential contribution is beyond the current study and must be tested in a future analysis.
In this investigation we focus on characterizing the main phenomenological features of the induced Martian inner magnetosphere, including the topology of the magnetic field as well as the induced ionospheric dynamics, and therefore we use MSE-coordinates. This is important because ultimately, this regime of interaction of the solar wind with the Martian upper atmosphere has important implications for the ionospheres global dynamics. It is a follow-up study of our previous work Dubinin et al., 2019) with a particular focus on low altitude distributions of draped IMF and ionospheric plasma flows. The previous studies of Dong et al. (2015), Fang et al. (2010), Luhmann (1990) have suggested that the ion escape is driven through the induced electric field E sw = −V sw × B IMF , resulting in an asymmetric outflow with the ion plume. However, the mechanisms of ion extraction from the ionosphere have not been fully investigated. The observations by Dubinin et al. (2019) showed that the ion escape at the nightside is driven through the ion trail filled by a dense ionospheric plasma and shifted to the hemisphere opposite to the hemisphere with the ion plume. Here we also investigate processes which lead to the formation of the ion trail.

Instrumentation
The Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft arrived at Mars in September 2014 to study the processes in the upper atmosphere/ionosphere and its interaction with the solar wind (Jakosky et al., 2015). MAVEN was inserted into an elliptical orbit with periapsis and apoapsis of 150 and 6,200 km, respectively, and with a period of 4.5 hr. In this paper, we discuss observations made by the Supra-Thermal And Thermal Ion Composition (STATIC) instrument from November 2014 to May 2018. The STATIC instrument mounted on the actuated payload platform is used to study the dynamics of planetary ions. It measures energy spectra of ion fluxes in the range of 0.1 eV-30 keV and the ion composition . The measurements allow a retrieval of the velocity distribution functions and their moments (density, velocity, temperature) for different ion species. The STATIC instrument samples all received time-of-flight events onboard with a resolution of 64 energy bins, 64 mass bins, 16x16 field of view bins, and 4s time resolution. Because the resulting matrix is far too big to be downloaded as a whole, only down-sampled 'products' are transmitted which represent sums over one or more dimensions of the original 5-dimensional matrix . Not all products are transmitted at the same time. We take a subset of these products (c0,cf,d1,ce,d0,cd,cc,ca -depending on availability) to reconstruct a matrix M with the dimension of 32 energy bins, 4 mass bins, 16x4 field of view bins and 4s time resolution by linear interpolation from this subset. In each interpolation step we normalize the respective dimension to guarantee that the sums over all dimensions of M stays the same as for the original products. By this procedure we get a time series with commensurate sampling in energy, field of view, and time for the 4 major ion groups ( + , ++ , + , + 2 ) . From this time series we calculate density, velocity, and temperature for these groups with even time sampling. Since the measurements of the low-energy ions in the dense ionosphere and in the planetary wake are affected by the spacecraft (s/c) potential we made corrections using the values of the s/c potential presented by the STATIC team. Calculations of the corrected moments from three-dimensional distribution functions were based on Liouvilles theorem (see, for example, Lavraud & Larson, 2016). Here we focus only on the observations of the flux of the oxygen ions (O + and + 2 together) which dominate in the topside ionosphere and in the tail. The STATIC observations were complemented by the measurements of the magnetic  . We derive the IMF orientation by taking the median value of the magnetic field vector components from 30 min around the time where the maximum proton velocity measured by the solar wind monitor SWIA  was observed. We do not exclude orbits with a high variation of the field vector. We processed all orbits in order to study the global features without any assumptions about stationarity of the IMF orientation. During the orbits when MAVEN was not in the solar wind we use the magnetic field measurements in the magneto sheath. Note that for these cases the clock angle errors due to the IMF deformations may appear (Dong et al., 2019).

Observations
We constrained our analysis to the region inside the nominal boundary of the induced magnetosphere of Mars  and altitudes below 1,000 km in the regions where the boundary is above this altitude. Figure 2 shows projections of the magnetic field onto XY planes at different Z MSE distances in the E + (Z MSE > 0) (upper row) and E − (Z MSE < 0) (lower row) hemispheres based on the median components of the magnetic field. Blue curves present the Mars position and position of the nominal magnetospheric boundary at the corresponding XY planes. The size of each spatial bin is 300 km. We observe that in both the E + and E − dayside hemispheres draping of the IMF propagates down to low altitudes. At the nightside of the of E + hemisphere the field lines slightly converge to the wake. With increase of Z MSE this convergence disappears and the field lines begin to diverge in accordance with a classical draping topology. The picture is different in E − hemisphere. Wrapping of the field lines increases with distance from the central XY plane and at Z MSE ∼ −1R M we observe an almost closing of the field lines (see the panel at Z MSE = −0.9 − 1.1R M in which we use a bin size 100 km for a better spatial resolution).     (b)) shows projections of the bulk velocity of oxygen ions onto the XY MSE plane in the E + and E − hemispheres (bin size is 300 km). Here we present the components of the bulk plasma velocity = ( + 2 + 2 + + + )∕( + 2 + + ) . Although deviations exist, the ions generally exhibit a dayside to nightside flow. Figure 5c shows projections of the bulk speed onto the XY plane at Z MSE = 0.9-1.1R M , in which we observe a reversal of the velocity of the oxygen ions with the appearance of the sunward flow that indicates reconnection of the magnetic field in this area. This region is highlighted by the red vectors that also use a bin size of 100 km.     To make this plot more compact some long vectors are green colored with the tagged values of the ion speed. They probably correspond to oxygen ions originated from the hot oxygen corona and accelerated outside the magnetosphere.   Figure 8 shows the median V Z velocity component in E + and E − hemispheres as a function of altitude and solar zenith angle. As in Figure 3 each bin shows the median of the quantity across a half-ring around the planet. To see where acceleration of oxygen ions starts the color bar is oversaturated. Velocities in red and black dashed bins are higher (lower) than +/−2 km/s, respectively. At the dayside of the E + hemisphere (SZA ∼ 90 ) ions are moving in +Z MSE direction as one may expect for plasma fluid flowing around Mars. The velocity generally increases with altitude. It is observed that beginning of a regular ion acceleration in E + hemisphere occurs at ∼300 km. On the nightside (SZA 90 ) plasma flows in the opposite direction supplying the nightside ionosphere.
In the E − hemisphere ion velocities are smaller. At the dayside (SZA 90 ) the oxygen ions are moving in the -Z MSE direction following the flow of the shocked solar wind in the adjacent magnetosheath. At the night side the ionospheric plasma flows upwards (V z > 0) also filling the nightside ionosphere.
Extraction of ions from the ionosphere with their following acceleration at the dayside might be related with draping features of the magnetic field lines. Figure 9a shows the B YZ projections of the magnetic field measured at the dayside onto the YZ MSE plane looking at the planet from the solar wind perspective. In both E + and E − hemispheres, we observe draping features with a different sign of the field bending indicating that the central parts of the field lines are moving slower than their rear parts. That implies the initiation of the magnetic tail formation already at the dayside. A geometry of the field bending occurs different in both hemispheres. In the E + hemisphere, the B Z component becomes significant only in the central part, near the noon-midnight plane, while in the E − hemisphere the region with a large B Z is much broader although the tension forces are also stronger near the noon meridian enhancing the plasma drag force in the ionosphere in the +/−Z MSE directions. Figure 9b depicts the V YZ projections of the oxygen bulk speed. In the E + hemisphere, the ions gain more velocity, producing ion beams with energies that increase with altitude Dubinin, Ludin, et al., 2006). This enhancement of V z in the E + -hemisphere is clearly shown in Figure 9c which depicts the projections of the ion speeds measured by STATIC at 0 < X < 1R M onto the whole YZ MSE plane sampled by MAVEN. The observed fan of extracted and accelerated oxygen ions corresponds to a pickup ion population originated already at high altitudes of the upper ionosphere.
A strong asymmetry in the motion of oxygen ions is also shown in Figures 9d and 9e which depict the V z and V y components of the velocities measured at 0 < X < 1R M . White dotted circle in these panels represent the nominal position of the magnetosphere boundary in the terminator plane. The region inside this circle corresponds to the ionospheric area discussed in the paper. Here plasma moves parallel to the motion of the solar wind in the magnetosheath symmetrically flowing around Mars. Such motion across the draping magnetic field induce the electric fields −V × B, but with much smaller values than in the adjacent magnetosheath. Ions freshly generated by photoionization will either be quickly assimilated into this flow or -if they are close to the boundary and gain a sufficient speed -can escape and be picked up by the much higher motional electric field in the sheath. Outside of the dotted circle the motion of the oxygen ions is governed by the direction of motional electric field in the magnetosheath. In E + hemisphere, V z > 0, V y > 0 for Y > 0 and V y < 0 for Y < 0, while in E − hemisphere, V z > 0, V y < 0 for Y > 0 and V y > 0 for Y < 0 (Figures 9d and 9e). The ion motion in both hemispheres is depicted by   (Figure 10b). In the trail plasma is denser and moves tailward with slower speed because the magnetic tension forces begin to act in the sunward direction (B y -component of the magnetic field changes sign (Figure 10c).
To examine the role of the magnetic tension forces in the ion acceleration at the dayside we plot the absolute value of the V z component of the bulk speed as a function of B x at different altitudes in the E + and E − hemispheres ( Figure 11, upper row). A change of sign of the B x component corresponds to crossing of the emerging tail current sheet. We observe two different regions with noticeable ion acceleration. One region is near the current sheet where the tension forces are stronger, and another one at large |B x | that matches the region adjacent to the induced magnetosphere boundary with pileup of the IMF. We also observe that ion acceleration by tension forces is more efficient in the E + hemisphere. Similar features are seen while plotting the horizontal component of the ion velocity ( Figure 11, lower row).
A difference in the magnetic field bending in the two hemispheres is well seen in Figure 12 which shows the B yz projections of the unit vectors of the magnetic field at Z MSE = 0.5-0.7R M and Z MSE = −0.5-−0.7R M plotted as a function of the variables altitude and SZA. At the dayside, at small SZA of the E + hemisphere bending of the field lines is strong at all altitudes. With increase of SZA the bending becomes at first weaker while at SZA > ∼70° and at the nightside the B z component changes sign and prevails. At the dayside of the E − hemisphere both components are comparable at all altitudes implying a broader expansion of the bending features that might lead to a bulk plasma motion in the −Z MSE direction. At the nightside the horizontal B y component dominates but the picture becomes much less regular with a frequent reversal of the sign of the B y component.

Discussion
The Martian magnetosphere contains elements of induced and intrinsic origin (see e.g., Chai et al., 2019;Di-Braccio et al., 2018;Dubinin et al., 2017;Ramstad et al., 2020;Weber et al., 2019;Xu et al., 2017Xu et al., , 2018Xu et al., , 2020. To display these components one must use specific coordinate systems. Because of a strong asymmetry of the magnetosphere controlled by the direction of the motional electric field, the MSE coordinate system adequately describes aspects of the induced magnetosphere but loses features caused by the presence of the local crustal magnetizations. To study effects of the induced origin we used here the MAVEN data obtained for the period from November 2014 to May 2018 and utilized the MSE coordinate system. One should keep in mind that the  presented distributions of the magnetic field and plasma motions are not snapshots of the different cross-sections of the Martian magnetosphere, but rather characterize only the main properties of the induced magnetosphere but removes/suppresses features caused by the crustal magnetic sources while rotating the spacecraft orbits to the MSE-coordinate system and averaging over many orbits. The solar winds interactions with magnetized and nonmagnetized planets share many similarities in their features upstream of the bow shock, in processes at the bow shock itself, and in the magnetosheath (J. S. Halekas et al., 2017;Mazelle et al., 2004). However, the structures of the inner magnetosphere is very different. Although solar wind is mostly terminated at a certain distance from Mars by the induced magnetic field barrier formed by the draping of the IMF lines, the draping IMF penetrates deep into the ionosphere because the solar wind dynamic pressure generally exceeds the thermal plasma pressure in the upper Martian ionosphere. We show that draping features propagate down to low altitudes (∼200−250 km) sampled by MAVEN and envelop the planet.
When looking at the draping of the IMF, which penetrates into the ionosphere, in planes parallel to the central XYplane, which contains the IMF, we observe that draping differs between the E + and E − hemispheres. A wrapping of the field lines becomes stronger and stronger when approaching the E − 'polar region' in the MSE-coordinates and then reconnection signatures with reversal of ion flows appear. Note that the values of the sunward ion speeds are significantly less than the Alfven speed implying only a partial ion coupling (see also Harada et al., 2020). The hybrid simulations of the solar wind/Mars interaction (Dubinin et al., 2019) confirm the permanent existence of a such area. Observations by Harada et al. (2017) of the trapped electrons with two-sided loss cones near the terminator, in the area not connected to the strong crustal sources, also support the reconnection scenario in this region. Mechanisms responsible for such a permanent reconnection in this area still remain unknown. This phenomenon is probably related to the formation of the plasma bulge in this region due to convergence of the ion fluxes in the E − hemisphere and a reduced ion outflow due to a wrapped field geometry (see Figure 10). In hybrid simulations (Dubinin et al., 2019) performed for fixed upstream conditions with B ysw > 0 and without the crustal fields, such bulge appears in the region near X ∼ 0 and Z MSE ∼ −1 R M and then spreads to the tail. The observations show a broader region with the increased plasma density and a general shift of the ionosphere in the −Z MSE directionion trail. It is assumed that such a shift is a result of the recoil effect due to ion extraction in the +Z MSE direction although the recoil forces are not well identified. Dubinin et al. (2019) suggested that these forces are caused by the arising additional magnetic field draping along the Z-axis (see also Chai et al., 2019;Ramstad et al., 2020).
Asymmetrical wrapping of the magnetic field lines was also observed in the near Venus tail (Zhang et al., 2010) implying that this feature might be typical for the induced magnetospheres.
We also see a slipping of the ionospheric plasma around Mars from the dayside to the nightside with a gradual ion acceleration. Near the terminator the bulk velocity = ( + 2 + 2 + + + )∕( + 2 + + ) achieves ∼3 − 4 km/s. At the nightside the velocity reaches ∼10 km/s. This motion might be driven either by the thermal pressure gradient (Ergun et al., 2016) or/and by the magnetic tension forces. According to Collinson et al. (2019) and Xu et al. (2018) the potential drop of the ambipolar electric field near the terminator is ≤1.5 V that corresponds to ∼3 and ∼4.4 km/s for + 2 and O + ions, respectively, that could explain the observed ion speeds. Further, at the nightside, contribution of j × B forces probably dominates.
Projections of the magnetic field onto the XZ-planes reveal another interesting feature of the field topology -the appearance of a large B z component. At the dayside the central parts of the field lines, immersed in a denser ionosphere, are moving slower than their rear parts. As a result, a bending of the field lines with different sign in E + and E − hemispheres arises. Such bending gives start to formation of the current sheet of the magnetotail (see also J. S. Halekas et al., 2006). Bending of the field lines propagates to low altitudes (∼200 km) and its geometry occurs different in both hemispheres. In the E + hemisphere the bending is more localized around the noon-midnight plane while in the E − hemisphere bending spreads to a much broader area. With distance from the noon-midnight plane (|Y| > 0.7R M ) the field topology becomes more and more asymmetrical between the E + and E − hemispheres with a turn of the magnetic field lines into the −Z MSE direction. Such a twist gives rise to a peculiar draping along the Z-axis Dubinin et al., 2019;Ramstad et al., 2020).
The asymmetry is also evident in plasma flows. Although the ionospheric plasma flow in both hemispheres is parallel to the shocked solar wind in the magnetosheath (a comet-like fashion of the flow, Lundin et al., 2008) the velocities in the E + hemisphere are higher implying the important role of the direction of the motional electric field in the solar wind. Acceleration of ions starts at rather low altitudes (∼250 − 300 km) and continues with gain in ion energy at higher altitudes. These ions give origin to ion beams and ion plume observed at higher altitudes in the E + hemisphere (Dong et al., 2015;Dubinin, Ludin, et al., 2006). We observe that the magnetic field tensions related to the strong bending of the field lines in the E + hemisphere can accelerate ions from ∼300 km and lift them to altitudes at which the motional electric field further accelerates them to much higher speeds. With increase of altitude the asymmetry of oxygen ion motions between E + and E − hemispheres becomes more and more significant and in the adjacent magnetosheath is determined by the direction of the motional electric field driven by the shocked solar wind -in the E + (E − ) hemisphere, ions are moving outward (inward) to the planet, respectively.
In conclusion, Figure 13 shows a sketch illustrating the main features of the asymmetry in the magnetic field topology and plasma flow within the induced magnetosphere of Mars. Panels (a) and (b) depict views from Sun and from the dusk side, respectively. We show that the IMF penetrates very deep to the ionosphere draping around the planet. Plasma in the upper ionosphere (h ≥ ∼250 − 300 km) is not at rest, but is driven into motion from the dayside to the nightside and further to the tail, streaming parallel to the shocked solar wind in the adjacent magnetosheath but with much smaller velocities. The motion is driven by the gradients of the thermal and the magnetic pressure, and by the magnetic field tensions. As a result, such a motion is not axially symmetrical. An asymmetry between E + and E − hemispheres controlled by the direction of the motional electric field in the solar wind also exists implying penetration of the attenuated motional electric field into the ionosphere. Extraction of ions and their significant acceleration in the E + ionosphere is accompanied by a recoil effect of the bulk ionosphere in the opposite direction that produces a strong wrapping of the magnetic field lines around Mars and their subsequent reconnection.

Data Availability Statement
Mars Atmosphere and Volatile Evolution data are publicly available through the Planetary Data System (https:// pds-ppi.igpp.ucla.edu/mission/MAVEN).