# Sunward Oxygen Ion Fluxes and the Magnetic Field Topology at Mars From Hybrid Simulations

E Dubinin, Ronan Modolo, François Leblanc, M Pätzold, N Romanelli

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► To cite this version:

E Dubinin, Ronan Modolo, François Leblanc, M Pätzold, N Romanelli. Sunward Oxygen Ion Fluxes and the Magnetic Field Topology at Mars From Hybrid Simulations. Geophysical Research Letters, 2024, 51 (18), pp.e2023GL106925. 10.1029/2023gl106925. insu-04705074

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# Geophysical Research Letters®

## RESEARCH LETTER

10.1029/2023GL106925

**Key Points:**

* Hybrid simulations show a drastic change of the field topology at altitudes less than ~1,000 km due to crustal field sources

* Although the magnetic field topology is modified, the sunward fluxes do not essentially affect the total ion loss

* Sunward fluxes of oxygen ions in the tail vary between ~5% and ~20% compared to the anti-sunward fluxes

**Correspondence to:**

E. Dubinin,
dubinin@mps.mpg.de

**Citation:**

Dubinin, E., Modolo, R., Leblanc, F., Pätzold, M., & Romanelli, N. (2024). Sunward oxygen ion fluxes and the magnetic field topology at Mars from hybrid simulations. *Geophysical Research Letters*, *51*, e2023GL106925. https://doi.org/10.1029/2023GL106925

Received 26 JAN 2024

Accepted 12 JUL 2024

**Author Contributions:**

**Conceptualization:** F. Leblanc, M. Pätzold

**Funding acquisition:** M. Pätzold

**Investigation:** F. Leblanc

**Methodology:** F. Leblanc

**Validation:** M. Pätzold

© 2024. The Author(s).
This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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## Sunward Oxygen Ion Fluxes and the Magnetic Field Topology at Mars From Hybrid Simulations

E. Dubinin¹ ID, R. Modolo² ID, F. Leblanc³ ID, M. Pätzold⁴, and N. Romanelli⁵,⁶ ID

¹Max-Planck-Institute for Solar System Research, Göttingen, Germany, ²LATMOS, Université de Versailles Saint Quentin, CNRS, Sorbonne Université, CNES, Guyancourt, France, ³LATMOS, Sorbonne Université, CNRS, Université de Versailles Saint Quentin, CNES, Paris, France, ⁴Abteilung Planetforschung, Rheinisches Institut Fuer Umweltforschung, Cologne, Germany, ⁵NASA Goddard Space Flight Center, Greenbelt, MD, USA, ⁶Department of Astronomy, University of Maryland, College Park, MD, USA

**Abstract** It is commonly believed that because of the direct solar wind interaction with the Martian atmosphere/ionosphere, the planet could have lost a significant part of its atmosphere. Closed field lines of the crustal magnetic field can weaken a transport of the ionospheric ions to the tail. Reconnection of the interplanetary magnetic field lines draping around Mars and the crustal magnetic field can also lead to a presense of sunward fluxes of planetary ions that might affect the total ion loss. The LatHyS (LATMOS Hybrid Simulation) three-dimensional multispecies hybrid model is used here to characterize sunward fluxes of $O^+$ ions and the magnetic field topology at Mars. It is shown that although reconnection between the interplanetary magnetic field (IMF) and the crustal magnetic fields strongly modifies the field topology, then sunward ion fluxes are rather small and do not significantly change the total ion loss.

**Plain Language Summary** Although Mars has no a global intrinsic magnetic field and solar wind interacts directly with the planetary atmosphere/ionosphere, the existence of strong but localized crustal magnetic field modifies the field topology around Mars. As a result, the Martian magnetosphere contains elements of the intrinsic and the induced magnetospheres. Reconnection between the interplanetary magnetic field and the crustal magnetic field can generate the plasma flows toward the planet and decrease the ionospheric losses, which is very important for the evolution of the Mars atmosphere/ionosphere. We have performed the numerical simulations of these potential effects and shown that the sunward ion fluxes are significantly less than the losses induced by the solar wind impact on the Martian ionosphere.

## 1. Introduction

Due to a direct interaction of solar wind with the Martian ionosphere and the existence of the localized regions with strong crustal magnetic fields (Acuña et al., 1999) the Martian magnetosphere contains elements of induced and intrinsic origin (see e.g., Brain et al., 2017; Dubinin, Luhmann and Slavin, 2020; Halekas et al., 2021). As a result, a hybrid magnetosphere is formed in which both induced and crustal magnetic fields can reconnect leading to a complex field geometry. It is assumed that magnetic reconnection between the draping IMF and the crustal magnetic field might operate commonly at Mars. Signatures of magnetic reconnection (ion jets and sunward flows) were investigated in the nightside magnetotail of Mars using the Mars Atmosphere and Volatile Evolution (MAVEN) data (Harada et al., 2017). Harada et al. (2017) observed ion flow enhancements in the directions consistent with the reconnection outflow directions expected from the Hall magnetic field polarity. Harada et al. (2020) have analyzed ion jets in the current sheets in the whole Martian magnetosphere and obtained statistical map showing that sunward and anti-sunward ion jets embedded within current sheets are commonly and widely observed in the dayside and nightside magnetosphere of Mars. The authors have concluded that the sunward ion fluxes observed at Mars are most probably caused by reconnection between the IMF and the crustal magnetic field.

Reconnection also strongly changes a field topology. The magnetic field topology traced by a study of the electron dynamics (Xu et al., 2019) consists of different classes of the field lines. Within the draping IMF, closed loops of the field lines connected to the crustal field sources, open field lines with one end in the solar wind and another end on the Mars surface, formed by the reconnection between the crustal field and the IMF — are present (Weber et al., 2017, 2019; Xu et al., 2017, 2020). As a result, the magnetic field topology within the tail varies with solar wind pressure (Weber et al., 2019) and the IMF direction (Weber et al., 2020; Xu et al., 2020).
Observations on Venus, where the crustal magnetic field is absent, also show the existence of the planet-ward ion fluxes in the Venusian tail. Zhang et al. (2010) have found that draping magnetic field lines are wrapped more tightly around Venus in the hemisphere in which the motional electric field ~ $-V_{sw} \times B_{IMF}$ is directed toward the planet (E⁻ hemisphere). Such a reversal of the cross-flow component ($B_y$) of the magnetic field produces the inward directed magnetic field stresses and might be responsible for the sunward ion motions (Dubinin et al., 2013).

Return or sunward flows are also often considered an important factor which can affect the total loss of atmospheric species at Mars and Venus. Kollmann et al. (2016) have observed that Venus-ward flowing ions might be important for a problem of atmospheric loss since the deposition rate into the atmosphere is on the same order of magnitude as the rate of escaping ions (see also Masunaga et al., 2019; Persson et al., 2020). Using the MAVEN data, Brain et al. (2015) have estimated that the return fluxes at Mars are about of 10% compared to the outward fluxes. Zhang et al. (2022) have analyzed the appearance of the sunward flows using the ASPERA-3 data on Mars Express. They have found that the occurrence rate and the total flux of Mars-ward flows are relatively low.

## 2. Simulations

In this paper we investigate the problem of sunward ion flows and the magnetic field topology at Mars using hybrid simulations. It is worth noting that modeling efforts using different numerical methods have been conducted to support the analysis of in situ measurements of the Martian space. Multispecies MHD (e.g., Ma et al., 2002, 2004; Ma et al., 2014; Y. Ma and Nagy, 2007), multifluid MHD (e.g., Dong et al., 2014, 2015; Harnett & Winglee, 2006; Ma et al., 2019; Najib et al., 2011; Riousset et al., 2013) and hybrid models (e.g., Modolo et al., 2005, 2006, 2012, 2016; Kallio et al., 2010; Brecht & Ledvina, 2010; Bößwetter et al., 2007; Wang, Fatemi, Nilsson, et al., 2023; Wang, Fatemi, Holmstrom, et al., 2023) successfully reproduced many observational features of the solar wind interaction with Mars. We used the three-dimensional multispecies parallelized hybrid simulation model called LatHyS. The parallelization is based on a domain decomposition to be able to track about 1.3 billions of particles on a 320 × 608 × 608 mesh during 18,000 time steps. Simulation Package is given in (Numerical Simulations, 2023). This modeling effort allows us to describe the Mars-solar wind interaction on a uniform Cartesian grid of 80 km resolution. The main features of the model: (a) a kinetic description for ions, including Hall term and Larmor radius effects; (b) a multispecies description (6 ion species); (c) two electron fluids (for solar wind and planetary electrons); (d) local ion production from three ionization processes (photonization, electron impact ionization, and charge exchange); (e) a realistic ionosphere described by a simplified set of chemical equations; (f) a drag force term included in the equations of ion motion which describe the ion-neutral collisions in the ionosphere; and (g) computed locally effective ionospheric conductivity. Details of the model can be found in (Modolo et al., 2016). The crustal magnetic field following the model by Cain et al. (2003) was added too (Romanelli et al., 2018). Simulation results used in this manuscript can be found in our LatHyS simulation database available at http://impex.latmos.ipsl.fr/LatHyS.htm. This catalog provides a full description of the simulation and their products as well a possibility to download the 3D data cubes. Paths to different runs with simulation parameters used in this paper are given below.

<table><thead><tr><td>RunID</td><td>Simulation parameters</td></tr></thead><tbody><tr><td>LatHyS Mars-23-01-13</td><td>nominal SW, SSL = 180°</td></tr><tr><td>LatHyS Mars-14-01-13</td><td>nominal SW, SSL = 90°</td></tr><tr><td>LatHyS Mars-18-01-13</td><td>nominal SW, SSL = 0°</td></tr><tr><td>LatHyS Mars-06-02-13</td><td>nominal SW, SSL = 270°</td></tr><tr><td>LatHyS Mars-18-01-16</td><td>nominal SW except B<sub>IMF</sub> = (0.0, 3.0, 0.0)nT, SSL = 180°</td></tr><tr><td>LatHyS Mars-28-02-16</td><td>nominal SW except V = 600 km/s, SSL = 180°</td></tr><tr><td>LatHyS Mars-08-01-16</td><td>nominal SW except n(H<sup>+</sup>) = 5.0 cm<sup>-3</sup>, SSL = 180°</td></tr><tr><td>LatHyS Mars-13-01-23</td><td>nominal SW except B<sub>IMF</sub> = (-1.6, -2.5, 0.0)nT, SSL = 180°</td></tr></tbody></table>
<figure><img src="image_4.png" /><figcaption>**Figure 1.** Maps of the $B_x$ components of the magnetic field projected from spheres at $r = 1.1$; 1.2; 1.3; 1.5 and $2R_M$ onto latitude-longitude planes (view from the tail) for different longitudes (SSL) of the strong crustal magnetic field. Solid and dashed lines at $r = 1.1$; 1.2 $R_M$ are contour lines of the magnetic field value of 60 and 40 nT, respectively.</figcaption></figure>

Where the solar wind number density for the nominal conditions was $n_{sw} = 2.7$ (protons) + 5% ($\text{He}^{++}$) = 2.84 cm$^{-3}$ and $V = 485$ km/s, $B_{IMF} = (-1.6, 2.5, 0.0)$ nT.

Figure 1 shows the $B_x$-component of the magnetic field (X-axis points toward the Sun) plotted in Latitude-Longitude coordinates in the Mars Solar Orbital reference frame at different radial distances from Mars. Longitude = 0° (360°) corresponds to the noon meridian. Longitudes = 90° and 270° are at the dawn and dusk, respectively. The midnight is at Longitude = 180°. The simulation data are presented for different phases of Mars rotation, for four subsolar longitudes (SSL) for which the southern strong crustal magnetic fields are located on the dayside (SSL = 180°), dawn (SSL = 90°), dusk (SSL = 270°), and nightside (SSL = 0°, 360°). Solid and dashed lines at $r = 1.1R_M$ and $r = 1.2R_M$ are contours of the field strength of 60 and 40 nT, respectively. Each simulation corresponds to a steady configuration of the solar wind - Mars interaction. For $r > 1.2R_M$, white areas correspond the regions upstream of the induced magnetospheric boundary (Vignes et al., 2000). Upstream parameters in the solar wind were: $n_{sw} = 2.7$ (protons) + 5% ($\text{He}^{++}$) = 2.84 cm$^{-3}$, $V = 485$ km/s, $B = 3$ nT. The magnetic field was in ecliptic plane ($B_x < 0, B_y > 0$) at Parker spiral angle (57°). Two magnetic field lobes with inclusions of crustal fields are clearly observed. It is observed that a shape of the current sheet separating two magnetic tail lobes formed by the draping IMF is strongly affected by the crustal field. With distance from Mars a contribution from the crustal sources gradually decreases while distortions of the lobes are seen even at $2R_M$.

Figure 2 shows in the same format as Figure 1 fluxes of oxygen ions $nV_x$. Positive values correspond to sunward fluxes. At $r = 1.1 R_M$ a lot of sunward fluxes are observed even in the northern hemisphere. At the nightside (90° < Longitude < 270°), sunward fluxes correlate with clumps of the crustal magnetic field (compare with Figure 1). For SSL = 180° (noon) a broad band of the sunward fluxes is at the southern polar latitudes. Note that this region was sampled by the MAVEN measurements. With increase of the radius r sunward fluxes decrease. At
<figure><img src="image_5.png" /><figcaption>**Figure 2.** Maps of the oxygen ion fluxes projected from spheres at *r* = 1.1; 1.2; 1.3; 1.5 and 2*R<sub>M</sub>* onto latitude-longitude planes (view from the tail) for different longitudes (SSL) of the strong crustal magnetic field. Red (blue) values correspond to *nV<sub>x</sub>* > 0 (sunward) and *nV<sub>x</sub>* < 0 (anti-sunward), respectively. Solid and dashed lines at *r* = 1.1; 1.2 *R<sub>M</sub>* are contour lines of the magnetic field value of 60 and 40 nT, respectively.</figcaption></figure>

*r* = 1.2 *R<sub>M</sub>* and 1.3 *R<sub>M</sub>* we see the localized clumps with the sunward fluxes which generally correlate with the *B<sub>x</sub>* signatures of crustal magnetic field. At larger distances we observe noticeable sunward fluxes only for SSL = 180°, that is, when the strong crustal sources are on the dayside. We also see a clear shift of anti-sunward ion fluxes to the southern hemisphere which coincides with *E<sup>-</sup>* hemisphere (*B<sub>y</sub>* in the solar wind is positive) in the MSE coordinates. Recall here that in MSE coordinates, *X<sub>MSE</sub>* axis is anti-parallel to the upstream solar wind flow, *Y<sub>MSE</sub>* axis is along the cross-flow magnetic field component of the IMF in the solar wind, and *Z<sub>MSE</sub>* axis is pointing in the direction of the solar wind motional electric field (−*V<sub>sw>* × *B<sub>IMF</sub>*). Then *E<sup>+</sup>* ( *E<sup>-</sup> ) hemisphere corresponds to *Z<sub>MSE</sub>* > 0 (<0), respectively. Such a shift of ion fluxes is also clearly observed by MAVEN (Dubinin et al., 2019, 2021, 2023; Inui et al., 2018). Table below compares the values of the total ion loss through the tail with the sunward fluxes for different SSL of crustal magnetic field. The anti-sunward and sunward fluxes have been computed on a shell with a radius of 2 *R<sub>M</sub>* and with a latitude-longitude resolution of 1° × 1°. Calculation of ion fluxes have been limited to the tail region inside the induced magnetoshare as defined by the average location of the induced magnetosphere (Vignes et al., 2000), in order to exclude a contribution from the plume. It is seen that in the most cases (SSL = 90°, 270°, 0°) the sunward oxygen ion fluxes are significantly less than the tailward ion loss. Maximum values of the sunward ion fluxes are observed when the area with strong crustal magnetic sources occurs in the noon. Thus, in contrast to Venus (Kollmann et al., 2016), the sunward ion fluxes at Mars do not strongly affect the ion loss. We also see that the values of the anti-sunward fluxes are not very sensitive to the longitude of the strong crustal magnetic sources that is in agreement with the MAVEN observations (Dubinin et al., 2020).

Table of the total ion fluxes for nominal solar wind conditions for Mars and IMF *B<sub>y</sub>* > 0.
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Maps of the different types of the magnetic field lines projected from spheres at $r = 1.1$; 1.2; 1.3; 1.5 and $2R_M$ onto latitude-longitude planes (view from the tail) for different longitudes (SSL) of the strong crustal magnetic field. Blue and light, green and olivine green, red and magenta correspond to draping field lines, open field lines with one end on the Martian surface, and closed field lines, with $B_x > 0$ and $B_x < 0$, respectively. The lower row shows for which type of the magnetic field topology we observe the sunward and antisunward ion fluxes for SSL = 180°. The values of the anti-sunward and sunward ion fluxes are also shown.</figcaption></figure>

<table><thead><tr><td>SSL of main crustal field</td><td>Total anti-sunward flux, ions/s</td><td>Total sunward flux, ions/s</td></tr></thead><tbody><tr><td>180° (noon)</td><td>1.2 × 10<sup>24</sup></td><td>1.0 × 10<sup>23</sup></td></tr><tr><td>90° (dawn)</td><td>1 × 10<sup>24</sup></td><td>0.1 × 10<sup>23</sup></td></tr><tr><td>270° (dusk)</td><td>1 × 10<sup>24</sup></td><td>0.2 × 10<sup>23</sup></td></tr><tr><td>0° (midnight)</td><td>1 × 10<sup>24</sup></td><td>0.2 × 10<sup>23</sup></td></tr></tbody></table>

Figure 3 presents maps of different types of the magnetic field lines for the same simulation runs as in Figures 1 and 2. Magnetic field line tracing performed by numerical solving the differential equations $dl \times \vec{B} = 0$ with a first order numerical scheme ($dx/Bx = dy/By = dz/Bz$) for the field lines provides steady-state snapshots of the Mars field topology. We used a constant spatial integration step of 0.3 $\Delta x$ and a three-linear interpolation of the magnetic field components determined from the simulation mesh. The field topology consists of draped field lines, open field lines connected by one end to the Mars surface, and closed field lines. Blue and light blue present the draped field lines (Open-Open, OO) with $B_x > 0$ and $B_x < 0$, respectively. Green and olive green areas correspond to the region filled by the open magnetic field lines (Open-Closed, OC) with $B_x > 0$ and $B_x < 0$. Red and magenta color show the regions with closed field lines (Closed-Closed, CC) with $B_x > 0$ and $B_x < 0$, respectively. Black curves depict crossings of the spherical surfaces ($r = 1.1$; 1.2; 1.3; 1.5 and $2R_M$) with the elliptical surface of the magnetospherical cavity (Vignes et al., 2000). Close to Mars ($r = 1.1 R_M$) we see that closed field lines (CC) occupy a large area in both hemispheres. At $r = 1.2 R_M$ and $r = 1.3 R_M$ a lot of space is
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Maps of the B<sub>x</sub>-component of the magnetic field, sunward and anti-sunward fluxes of oxygen ions, the total anti-sunward and sunward fluxes observed on the different type of the field lines at *r* = 1.5 *R<sub>M</sub>* and SSL = 180° (noon) and different solar wind and the IMF conditions.</figcaption></figure>

filled by the open field lines (OC) which appear either due to reconnection of the draping IMF with crustal magnetic fields or due to a deep penetration of the draped field lines inside the atmosphere and further inside the planet. It is difficult to distinguish both types of the open field lines. The draping field lines mainly occupy the dayside of the northern hemisphere. In the southern hemisphere, open field topology dominates. Area with closed field lines decreases with distance to tail and at *r* = 2*R<sub>M</sub>* only a small clump of them is observed for SSL = 180° when the strong crustal field is at the dayside. The bottom row of Figure 3 shows for which type of the magnetic field topology we observe the sunward and anti-sunward fluxes, limited to the tail region (*X* < 0). The left axis (blue) indicates the anti-sunward ion flux as a function of its magnetic connectivity. For instance, at 2 *R<sub>M</sub>* the most important contribution (~8.6 × 10<sup>23</sup> ions/s) is associated to OC field lines while ion flux connected to draped field lines (OO) is only about 2.2 × 10<sup>23</sup> ions/s, and tailward fluxes linked to CC field lines is the less important contribution with 1.2 × 10<sup>23</sup>. For sunward ion fluxes, right axis (red), the major contribution are associated to connected to the planet (~0.5 × 10<sup>23</sup> ions/s for CC field lines and ~0.4 × 10<sup>23</sup> ions/s for OC). It is also seen that the anti-sunward flux is relatively constant between 1.3 and 2 *R<sub>M</sub>*; emphasizing the absence of significant production of oxygen ions above 1,000 km and the stationary solution of the simulations. The main contribution for tailward escape is associated to OC field lines. The anti-sunward fluxes on CC field lines are significantly smaller. Sunward fluxes are mostly related to the magnetic field lines connected to the planet, their relative contribution with respect to the anti-sunward fluxes varies between a factor of one at *r* = 1.1 *R<sub>M</sub>* to 1/13 at 2*R<sub>M</sub>*.

Figure 4 shows how a picture of the field topology and the sunward fluxes changes with variations in the solar wind. Here we compare the results of the simulations for SSL = 180° at *R* = 1.5 *R*<sub>M</sub>. Column (a) corresponds to the nominal conditions used for Figures 1–3. Column (b) shows the data when the solar wind density increased, *n*<sub>H+sw</sub> = 5 cm<sup>-3</sup>. In column (c) the results are given for the higher solar wind speed (V = 600 km/s). At last, column (d) corresponds to a change of the angle between the solar wind vector and the IMF (90°). It is seen that with increasing solar wind dynamic pressure caused either by the density or velocity enhancement, the sunward ion fluxes at *r* = 1.5 *R*<sub>M</sub> are strongly reduced. Area with closed field lines at the nightside shrinks and almost vanishes. It is in a general agreement with the changes of the magnetic topology during the strong ICME event
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Maps of the oxygen ion fluxes ($nV_x$) (upper row), the field topology (middle row) and the total anti-sunward and sunward fluxes observed on the different type of the field lines (bottom row) are presented for SSL = 180° (noon) and for the different signs of the $B_y$ component in the solar wind.</figcaption></figure>

deduced from analysis of the electron fluxes measured by Mars Global Surveyor (Xu et al., 2019). During the strong increase in the dynamic pressure the field topology changes from closed field lines during quiet periods to open field lines during disturbed periods, suggesting more reconnection occurring between the crustal magnetic fields and the IMF. A similar conclusion was made by Weber et al. (2019) analyzing the MAVEN data. When the IMF changes to the cross-flow orientation (90°) the sunward fluxes and the area with the closed field topology are increasing. Note that the area with closed field lines at the night side does not coincide with the regions adjacent to the current sheet. Total tailward fluxes through the tail vary as $1.4 \times 10^{24}$ (nominal conditions), $1.2 \times 10^{24}$ ($n_{H^+_{sw}} = 5$ cm$^{-3}$), $1. \times 10^{24}$ ($V_{sw} = 600$ km/s), $0.9 \times 10^{24}$ (angle 90°). A decrease is mainly caused by a contraction of the tail. Correspondingly, the sunward fluxes are $1.8 \times 10^{23}$, $0.7 \times 10^{23}$, $0.7 \times 10^{23}$ and $1.8 \times 10^{23}$, respectively.

Figure 5 shows how the field topology and a map of ion fluxes varies with a change of sign of the cross-flow component ($B_y$) of the magnetic field in the solar wind. Maps of the oxygen ion fluxes (upper row), the field topology (middle row) and the type of the field line on which we observe the sunward fluxes (bottom row) are presented for SSL = 180° (noon) of the crustal field and $n_{sw} = 2.7$ (protons) + 5% ($He^{++}$) = 2.84 cm$^{-3}$, $V_{sw} = 485$ km/s, $B = 3$ nT and the Parker spiral field orientation. It is observed that the most of anti-sunward fluxes shift to the hemisphere in which the motional electric field in the solar wind points toward the ecliptic plane (E$^-$ hemisphere) that is in a good agreement with the MAVEN observations (e.g., Dubinin et al., 2017, 2021, 2023) and simulations (Dubinin et al., 2019; Modolo et al., 2016). Such a shift is a typical feature of the induced Martian magnetosphere and controlled by sign of the cross-flow component of the IMF. The sunward fluxes also occur sensitive to sign of the $B_y$ component in the solar wind and are observed mainly in the E$^-$ hemisphere that is also consistent with the MAVEN data (Dubinin et al., 2023). Such fluxes might be driven by
the reversal of the local $B_y$ component of the magnetic field at the night side due to enhanced wrapping of the draping field lines and change of sign of the field tension forces. The reconnection of the wrapped field lines in the tail will increase the occurrence rate of the sunward ion fluxes. It is worth noting that the sunward fluxes on the closed field lines are detected more often when the $B_y$ component in solar wind is negative. The area filled by the closed field lines shifts to the south or north with change of sign of the $B_y$. Such a behavior might be explained by asymmetrical plasma motion in the tail with their predominance in the $E^-$ hemisphere. Then the reconnected flux tubes will be carried by plasma either southward ($B_y > 0$) or northward ($B_y < 0$). The anti-sunward flux decreases by a factor 2 for $B_y < 0$ while the sunward flux is the same although the area filled by these fluxes increases. For $B_y > 0$ the total tailward and sunward fluxes are $1.4 \times 10^{24} \text{ s}^{-1}$ and $1.8 \times 10^{23} \text{ s}^{-1}$, respectively. For $B_y < 0$ these fluxes are $0.8 \times 10^{24} \text{ s}^{-1}$ and $1.8 \times 10^{23} \text{ s}^{-1}$, respectively.

### 3. Conclusions

Using three-dimensional multispecies hybrid model of the solar wind interaction with the Martian atmosphere/ionosphere and local crustal magnetic fields we investigated a potential effect of the sunward oxygen ion fluxes on total ion loss. The highest values of the sunward fluxes are observed when the area with the strongest crustal magnetic field occurs at the dayside. However, even in a such case, the sunward ion fluxes in the tail are almost absent at ~2 $R_M$ for the nominal solar wind and the IMF conditions. It is in a general agreement with the MAVEN observations of the sunward fluxes related with the reconnection events (Harada et al., 2020). Regions with closed field topology do not stretch to tail to large distances and at ~2 $R_M$ we almost do not see their signatures. In contrast, open field lines with one end at the Mars surface fill a significant part of the whole magnetosphere at the nightside. With enhancement of the solar wind dynamic pressure caused either by the density or velocity increase, a region at the nightside filled by the closed field lines and the return fluxes shrinks and is replaced by the open field lines. A similar trend is observed from the MAVEN data (Weber et al., 2019; Xu et al., 2019). In contrast, when the IMF vector is perpendicular to the solar wind velocity, the sunward fluxes in the area with closed field topology and the ion fluxes there increase. Regions with the sunward ion fluxes are generally correlate with the regions where the crustal fields produce perturbation clumps on a classical draping pattern with two lobes, suggesting a close relationship between such fluxes and reconnection. The maps of the sunward ion fluxes and the field topology are sensitive to sign of the cross-flow component of the IMF. Areas with the sunward fluxes and the closed field topology are shifted to the $E^-$ hemisphere in accordance with the plasma flows in the tail. For moderate changes in these simulations of the solar wind and the IMF the sunward fluxes in the tail at $r = 1.5 R_M$ vary between ~5% and ~20% compared to the outward fluxes, that is in a reasonable agreement with the MAVEN observations (Brain et al., 2015). Sunward fluxes are mainly observed on the CC or OC magnetic field lines.

### Data Availability Statement

Simulation results used in this manuscript can be found in our LatHyS simulation database available at Numerical Simulations (2023) and Matthews (1994).

### Acknowledgments

Authors ED, MP, ST wish to acknowledge support from DFG by Grant PA 525/25-1. Authors also acknowledge the support of the IPSL data center ESPRI for providing us access to their computing resources. RM and FL are indebted to the French Space Agency CNES for its support. Authors also acknowledge the publication funding by LATMOS-CNRS.

### References

Acuña, M., Connerney, J., Lin, R., Mitchell, D., Carlson, C., McFadden, J., et al. (1999). Global distribution of crustal magnetization discovered by the Mars Global Surveyor MAG/ER experiment. *Science*, **284**(5415), 790–793. https://doi.org/10.1126/science.284.5415.790

Boößwetter, A., Lammer, H., Kulikov, Y., Motschmann, U., & Simon, S. (2010). Non-thermal water loss of the early Mars: 3D multi-ion hybrid simulations. *Planetary and Space Science*, **58**(14–15), 2031–2043. https://doi.org/10.1016/j.pss.a.2010.10.003

Brain, D., Barabash, S., Bougher, S., Duru, F., Jakosky, B., & Modolo, R. (2017). Solar wind interaction and atmospheric escape. In R. Haberle, R. Clancy, F. Forget, M. Smith, & R. Zurek (Eds.), *The atmosphere and climate of Mars* (pp. 464–496). Publisher: Cambridge University Press. https://doi.org/10.1017/9781139060172.015

Brain, D. A., McFadden, J. P., Halekas, J. S., Connerney, J. E. P., Bougher, S. W., Curry, S., et al. (2015). The spatial distribution of planetary ion fluxes near Mars observed by MAVEN. *Geophysical Research Letters*, **42**(21), 9142–9148. https://doi.org/10.1002/2015GL065293

Brecht, S. H., & Ledvina, S. A. (2010). The loss of water from Mars: Numerical results and challenges. *Icarus*, **206**(1), 164–173. https://doi.org/10.1016/j.icarus.2009.04.028

Cain, J. C., Ferguson, B. B., & Mozzoni, D. (2003). An n=90 Internal potential function of the Martian crustal magnetic field. *Journal of Geophysical Research*, **108**(E2), 5008. https://doi.org/10.1029/2000JE001487

Dong, C., Bougher, S. W., Ma, Y., Toth, G., Nagy, A. F., & Najib, D. (2014). Solar wind interaction with Mars upper atmosphere: Results from the one-way coupling between the multifluid MHD model and the MTGCM model. *Geophysical Research Letters*, **41**(8), 2708–2715. https://doi.org/10.1002/2014GL059515

Dong, C., Ma, Y., Bougher, S. W., Toth, G., Nagy, A. F., Halekas, J. S., et al. (2015). Multifluid MHD study of the solar wind interaction with Mars’ upper atmosphere during the 2015 March 8th ICME event. *Geophysical Research Letters*, **42**(21), 9103–9112. https://doi.org/10.1002/2015GL065944
Dubinin, E., Fraenz, M., Pätzold, M., McFadden, J., Halekas, J. S., DiBraccio, G. A., et al. (2017). The effect of solar wind variations on the escape of oxygen ions from Mars through different channels: MAVEN observations. *Journal of Geophysical Research: Space Physics*, 122(11). https://doi.org/10.1002/2017JA024741

Dubinin, E., Fraenz, M., Pätzold, M., Tellmann, S., Modolo, R., DiBraccio, G., et al. (2023). Magnetic fields and plasma motions in a hybrid Martian magnetosphere. *Journal of Geophysical Research: Space Physics*, 128(1), e2022JA030575. https://doi.org/10.1029/2022JA030575

Dubinin, E., Fraenz, M., Pätzold, M., Woch, J., Mcfadden, J., Fan, K., et al. (2020b). Impact of Martian crustal magnetic field on the ion escape. *Journal of Geophysical Research: Space Physics*, 125(10), e2020JA028010. https://doi.org/10.1029/2020JA028010

Dubinin, E., Fraenz, M., Woch, J., Zhang, T. L., Wei, J., Fedorov, A., et al. (2012). Bursty escape fluxes in plasma sheets of Mars and Venus. *Geophysical Research Letters*, 39(1). https://doi.org/10.1029/2011gl049883

Dubinin, E., Fraenz, M., Zhang, T. L., Woch, J., Wei, Y., Fedorov, A., et al. (2013). Plasma in the near Venus tail: Venus express observations. *Journal of Geophysical Research: Space Physics*, 118(12), 7624–7634. https://doi.org/10.1002/2013ja019164

Dubinin, E., Luhmann, J., & Slavin, J. (2020a). Solar wind and terrestrial planets. In *Oxford research encyclopedia of planetary science*. Oxford University Press. https://doi.org/10.1093/acrefore/9780190647926.013.184

Dubinin, E., Modolo, R., Fraenz, M., Pätzold, M., Woch, J., Chai, L., et al. (2019). The induced magnetosphere of Mars: Asymmetrical topology of the magnetic field lines. *Geophysical Research Letters*, 46(22), 12722–12730. https://doi.org/10.1029/2019GL084387

Halekas, J., Luhmann, J. G., Dubinin, E., & Ma, Y. (2021). Induced magnetospheres: Mars. In R. Maggiolo, N. Andre, H. Hasegawa, D. Welling, Y. Zhang, et al. (Eds.), *In book magnetospheres in solar system, geophysics monograph series*. https://doi.org/10.1002/9781119815624

Harada, Y., Halekas, J. S., McFadden, J. P., Espley, J., DiBraccio, G. A., Mitchell, D. L., et al. (2017). Survey of magnetic reconnection signatures in the Martian magnetotail with MAVEN. *Journal of Geophysical Research: Space Physics*, 122(5), 5114–5131. https://doi.org/10.1002/2017ja023952

Harada, Y., Halekas, J. S., Xu, S., DiBraccio, G. A., Ruhunusiri, S., Hara, T., et al. (2020). Ion jets within current sheets in the Martian magnetosphere. *Journal of Geophysical Research: Space Physics*, 125(12), e2020JA028576. https://doi.org/10.1029/2020ja028576

Harnett, E. M., & Winglee, R. M. (2006). Three-dimensional multifluid simulations of ionospheric loss at Mars from nominal solar wind conditions to magnetic cloud events. *Journal of Geophysical Research*, 111(A9), A09213. https://doi.org/10.1029/2006JA011724

Inui, S., Seki, K., Namekawa, T., Sakai, S., Brain, D. A., Hara, T., et al. (2018). Cold dense ion outflow observed in the Martian-induced magnetotail by MAVEN. *Geophysical Research Letters*, 45(11), 5283–5289. https://doi.org/10.1029/2018GL077584

Kallio, E., Liu, K., Jarvisen, R., Pohjola, V., & Janhunen, P. (2010). Oxygen ion escape at Mars in a hybrid model: High energy and low energy ions. *Icarus*, 206(1), 152–163. https://doi.org/10.1016/j.icarus.2009.05.015

Kollmann, P., Brandt, P. C., Collinson, G., Rong, Z. J., Futaana, Y., & Zhang, T. L. (2016). Properties of planetward ion flows in Venus’ magnetotail. *Icarus*, 274, 73–82. https://doi.org/10.1016/j.icarus.2016.02.053

Ma, Y., Fang, X., Russell, C. T., Nagy, A. F., Toth, G., Luhmann, J. G., et al. (2014). Effects of crustal field rotation on the solar wind plasma interaction with Mars. *Geophysical Research Letters*, 41(19), 6563–6569. https://doi.org/10.1002/2014GL060785

Ma, Y., Nagy, A. F., Hansen, K. C., Dezeeuw, D. L., Gombosi, T. I., & Powell, K. G. (2002). Three-dimensional multispecies MHD studies of the solar wind interaction with Mars in the presence of crustal fields. *Journal of Geophysical Research*, 107(A10), 1282. https://doi.org/10.1029/2002JA009293

Ma, Y., Nagy, A. F., Sokolov, I. V., & Hansen, K. C. (2004). Three-dimensional, multispecies, high spatial resolution MHD studies of the solar wind interaction with Mars. *Journal of Geophysical Research*, 109(A7), A07211. https://doi.org/10.1029/2003JA010367

Ma, Y. J., Dong, C. F., Toth, G., van der Holst, B., Nagy, A. F., Russell, C. T., et al. (2019). Importance of ambipolar electric field in driving ion loss from Mars: Results from a multifluid MHD model with the electron pressure equation included. *Journal of Geophysical Research: Space Physics*, 124(11), 9040–9057. https://doi.org/10.1029/2019JA027091

Ma, Y.-J., & Nagy, A. F. (2007). Ion escape fluxes from Mars. *Geophysical Research Letters*, 34(8), L08201. https://doi.org/10.1029/2006GL029208

Masunaga, K., Futaana, Y., Persson, M., Barabash, S., Zhang, T. L., Rong, Z. J., & Fedorov, A. (2019). Effects of the solar wind and the solar EUV flux on O+ escape rates from Venus. *Icarus*, 321, 379–387. https://doi.org/10.1016/j.icarus.2018.11.017

Matthews, A. P. (1994). Current advance method and cyclic leapfrog for 2D multispecies hybrid plasma simulations. *Journal of Computational Physics*, 112(1), 102–116. [CAMCL]. https://doi.org/10.1006/jcph.1994.1084

Modolo, R., Chanteur, G. M., & Dubinin, E. (2012). Dynamic Martian magnetosphere: Transient twist induced by a rotation of the IMF. *Geophysical Research Letters*, 39(1), L01106. https://doi.org/10.1029/2011GL049895

Modolo, R., Chanteur, G. M., Dubinin, E., & Matthews, A. P. (2005). Influence of the solar EUV flux on the Martian plasma environment. *Annals of Geophysics*, 23(2), 433–444. https://doi.org/10.5194/angeo-23-433-2005

Modolo, R., Chanteur, G. M., Dubinin, E., & Matthews, A. P. (2006). Simulated solar wind plasma interaction with the Martian exosphere: Influence of the solar EUV flux on the bow shock and the magnetic pile-up boundary. *Annals of Geophysics*, 24(12), 3403–3410. https://doi.org/10.5194/angeo-24-3403-2006

Modolo, R., Hess, S., Mancini, M., Leblanc, F., Chaufray, J., Brain, D., et al. (2016). Mars-solar wind interaction: LatHyS, an improved parallel 3-D multispecies hybrid model. *Journal of Geophysical Research: Space Physics*, 121(7), 6378–6399. https://doi.org/10.1002/2015JA022324

Najib, D., Nagy, A. F., Tóth, G., & Ma, Y. (2011). Three-dimensional, multifluid, high spatial resolution MHD model studies of the solar wind interaction with Mars. *Journal of Geophysical Research*, 116(A5), A05204. https://doi.org/10.1029/2010JA016272

Numerical Simulations. (2023). The core of the present hybrid model is based on the Current Advance Method and Cyclic Leapfrog (CAMCL) algorithm designed by Matthews (1994) [Dataset]. http://impex.latmos.ipsl.fr/LatHyS.htm

Persson, M., Futaana, Y., Ramstad, R., Masunaga, K., Nilsson, H., Hamrin, M., et al. (2020). The Venusian atmospheric oxygen ion escape: Extrapolation to the early solar system. *Journal of Geophysical Research: Planets*, 125(3), e2019JE006336. https://doi.org/10.1029/2019je006336

Riousset, J. A., Paty, C. S., Lillis, R. J., Fillingim, M. O., England, S. L., Withers, P. G., & Hale, J. P. M. (2013). Three-dimensional multifluid modeling of atmospheric electrodynamics in Mars’ dynamo region. *Journal of Geophysical Research: Space Physics*, 118(6), 3647–3659. https://doi.org/10.1002/jgra.50328

Romanelli, N., Modolo, R., Leblanc, F., Chaufray, J.-Y., Hess, S., Brain, D., et al. (2018). Effects of the crustal magnetic fields and changes in the IMF orientation on the magnetosphere of Mars: MAVEN observations and LatHyS results. *Journal of Geophysical Research: Space Physics*, 123(7), 5315–5333. https://doi.org/10.1029/2017JA025155

Vignes, D., Mazelle, C., Reme, H., Acuña, M. H., Connerney, J. E. P., Lin, R. P., et al. (2000). The solar wind interaction with Mars: Locations and shapes of the bow shock and the magnetic pile-up boundary from the observations of the MAG/ER Experiment onboard Mars Global Surveyor. *Geophysical Research Letters*, 27(1), 49–52. https://doi.org/10.1029/1999GL010703
Wang, X.-D., Fatemi, S., Holmstrom, M., Nilsson, H., Futaana, Y., & Barabash, S. (2023). S. Martian global current systems and related solar wind energy transfer: Hybrid simulation under nominal conditions. *MNRAS*, *527*(4), 12232–12242. https://doi.org/10.1093/mnras/stad3486

Wang, X.-D., Fatemi, S., Nilsson, H., Futaana, Y., Holmstrom, M., & Barabash, S. (2023). Solar wind interaction with Mars: Electric field morphology and source terms. *MNRAS*, *521*(3), 3597–3607. https://doi.org/10.1093/mnras/stad247

Weber, T., Brain, D., Mitchell, D., Xu, S., Connerney, J., & Halekas, J. (2017). Characterization of low-altitude nightside Martian magnetic topology using electron pitch angle distributions. *Journal of Geophysical Research: Space Physics*, *122*(10), 9777–9789. https://doi.org/10.1002/2017JA024491

Weber, T., Brain, D., Mitchell, D., Xu, S., Espley, J., Halekas, J., et al. (2019). Influence of solar wind pressure on Martian crustal magnetic field topology. *Geophysical Research Letters*, *46*(5), 2347–2354. https://doi.org/10.1029/2019GL081913

Weber, T., Brain, D., Xu, S., Mitchell, D., Espley, J., Halekas, J., et al. (2020). The influence of interplanetary magnetic field direction on Martian crustal magnetic field topology. *Geophysical Research Letters*, *47*(19), e2020GL087757. https://doi.org/10.1029/2020GL087757

Xu, S., Mitchell, D., Liemohn, M., Fang, X., Ma, Y., Luhmann, J., et al. (2017). Martian low-altitude magnetic topology deduced from MAVEN/ SWEA observations. *Journal of Geophysical Research: Space Physics*, *122*(2), 1831–1852. https://doi.org/10.1002/2016JA023467

Xu, S., Mitchell, D. L., Weber, T., Brain, D. A., Luhmann, J. G., Dong, C., et al. (2020). Characterizing Mars's magnetotail topology with respect to the upstream interplanetary magnetic fields. *Journal of Geophysical Research: Space Physics*, *125*(3), e2019JA027755. https://doi.org/10.1029/2019JA027755

Xu, S., Weber, T., Mitchell, D. L., Brain, D. A., Mazelle, C., DiBraccio, G. A., & Espley, J. (2019). A technique to infer magnetic topology at Mars and its application to the terminator region. *Journal of Geophysical Research: Space Physics*, *124*(3), 1823–1842. https://doi.org/10.1029/2018JA026366

Zhang, C., Futaana, Y., Nilsson, H., Rong, Z., Persson, M., Klinger, L., et al. (2022). Mars-ward ion flows in the Martian magnetotail: Mars Express observations. *Geophysical Research Letters*, *49*(21), e2022GL100691. https://doi.org/10.1029/2022GL100691

Zhang, T. L., Baumjohann, W., Du, J., Nakamura, R., Jarvinen, R., Kallio, E., et al. (2010). Hemispheric asymmetry of the magnetic field wrapping pattern in the Venusian magnetic tail. *Geophysical Research Letters*, *37*(14), L14202. https://doi.org/10.1029/2010GL044020