Influence of Crustal Magnetic Fields on Horizontal Plasma Transport and Ion Escape on Mars

Owing to its unevenly distributed crustal fields, Mars acts as a unique obstacle to the solar wind. In the presence of the crustal fields, the transport of the planetary ions on the dayside ionosphere exhibits north–south asymmetry. Additionally, the heavy-ion loss in the magnetotail is affected by the crustal fields. In this paper, a three-dimensional multispecies magnetohydrodynamic model is employed to simulate Mars–solar wind interactions. Numerical results indicate that the meridional transport is dominant in most areas on the dayside ionosphere. In the presence of the crustal fields, the meridional transport on the southern hemisphere (southward transport) is reduced by more than 70% above the strong crustal sources, and the zonal velocity shows local changes inside strong and weak crustal field regions. These effects result in an increase or decrease in the number density of the heavy ions reaching the terminator, thereby influencing the thickness of the ionosphere. Decreased southward velocity leads to a reduction in the heavy-ion loss on the southern magnetotail. The radial outward flux is reduced by more than 30% for O2 + and CO2 + and by 10% for O+. This study shows that in addition to the zonal transport, the meridional transport is important for the day-to-night transport on the dayside of Mars. Collectively, the horizontal plasma transport, controlled by crustal fields, is associated with the altered ionosphere structure and reduced heavy-ion loss in the magnetotail.


Introduction
The interaction between Mars and the solar wind is important for the formation and evolution of the magnetosheath, magnetic pileup region (MPR), magnetotail, and other large-scale configurations (Nagy et al. 2004).Without a global intrinsic magnetic field, the solar wind directly interacts with the ionosphere and upper atmosphere, promoting plasma loss from the dayside and magnetotail (Nagy et al. 2004).However, local crustal magnetic fields, primarily distributed in the southern hemisphere, exert complex influence on the Marssolar wind interaction (Acuña et al. 1998;Connerney et al. 2005;Liemohn et al. 2006;Brain et al. 2007;Ma et al. 2014;Xu et al. 2014;Dong et al. 2015), altering plasma boundary locations (Brain et al. 2005;Edberg et al. 2008;Xu et al. 2016;Fang et al. 2017).Additionally, the local crustal magnetic fields inhibit or promote the process of plasma transport (Brain et al. 2006;Cao et al. 2019;Li et al. 2022aLi et al. , 2022b)).
The crustal fields also exert important effects on the structure of the dayside ionosphere of Mars.Compared with that of Venus, the ionosphere of Mars is magnetized by the solar wind-induced magnetic fields because the low ionospheric thermal pressure cannot balance the total pressure in the overlying magnetic pileup boundary (MPB; Nagy et al. 2004).However, the locally enhanced magnetic pressure due to the crustal sources contributes to the pressure balance, resulting in the upward spread of the ionosphere (Dubinin et al. 2019;Fowler et al. 2022) and shape change of the ionopause (Duru et al. 2006(Duru et al. , 2020)).The ionopause is an occasionally observed upper boundary of the Martian ionosphere.Its location has been previously identified using different parameters, such as the horizontal line at frequencies below 0.4 MHz (∼2•10 9 m −3 ) in the MARSIS radar observations (Duru et al. 2009;Chu et al. 2019), the sharp decrease in the total-ion density by at least a factor of 10 over an altitude range of at most 30 km (Vogt et al. 2015), the dramatic variability in values of electron temperature and density (Sánchez-Cano et al. 2020), and the location where the total electron density drops below a threshold of 10 3 cm −3 (Han et al. 2014).However, identifying the ionopause in the near-terminator region or above the strong crustal sources is challenging (Chu et al. 2019;Duru et al. 2020;Sánchez-Cano et al. 2020).Due to the dynamic solar winds and rotating crustal fields, the altitude of the ionopause is highly variable.The altitude of the ionopause is between 180 and 800 km, being generally higher near the terminator (Schunk & Nagy 2009).Recently, an observational study based on the Mars Express (MEX) data showed that the average altitude of the Martian ionopause is between 500 and 700 km on the dayside (Duru et al. 2020).However, research based on the Mars Atmosphere and Volatile Evolution (MAVEN) data showed a lower ionopause altitude of 363 ± 65 km (Chu et al. 2019;Sánchez-Cano et al. 2020).The mechanism of the location change of the ionopause remains unclear.
Owing to the importance of plasma transport on the ionosphere structure above an altitude of 200 km, the influence of the crustal fields on the dayside plasma transport probably alters the ionosphere structure.On the one hand, observational studies have reported the upward spread of the ionosphere and an increase in O + flux in the southern hemisphere (Lundin et al. 2011;Dubinin et al. 2019), especially above the strong crustal source (Fowler et al. 2022).Li et al. (2022a) indicated that the upward motion of O + is caused by the high magnetic inclination angle on the crustal field areas.On the other hand, the day-to-night plasma transport and impact ionization by precipitating electrons are important sources of the nightside ionosphere (Cui et al. 2015;Girazian et al. 2017;Adams et al. 2018).In the presence of the crustal fields, the tailward transport of heavy ions from the southern hemisphere strongly deviates near the terminator rather than flowing to the magnetotail (Lundin et al. 2011;Xu et al. 2017a).Based on the zonal transport model, Cao et al. (2019) estimated the mean day-to-night transport velocity to be 2.2 ± 0.4 km s −1 on the northern hemisphere and 1.5 ± 0.4 km s −1 on the southern hemisphere, which are consistent with the values reported by previous observational studies (Withers et al. 2012;Cui et al. 2015).Moreover, Cao et al. (2019) estimated the effective plasma transport velocity over the southern hemisphere to be 50% lower than that over the northern hemisphere.These effects result in a decreased heavy-ion loss rate in the magnetotail, which has been reported by multispecies magnetohydrodynamic (MHD) numerical simulations (Fang et al. 2010(Fang et al. , 2015;;Ma et al. 2014Ma et al. , 2015)).However, whether meridional transport could be neglected remains unknown.Consequently, the effect of the crustal fields on the dayside horizontal plasma (zonal transport and meridional transport) is worth investigating.
This study aims to simulate the interaction between the solar wind and Mars using a multispecies MHD numerical model.A 110°spherical harmonic model developed by Gao et al. (2021) is included to describe the crustal fields.Instead of the Cartesian coordinate velocity components V x , V y , and V z , the spherical-coordinate velocity component V r is chosen to describe the vertical plasma motion in the Martian ionosphere, and both the components V θ , and V j are chosen to describe the horizontal plasma motion there.This work determines the plasma velocity from tens of R M to 100 km above the Martian surface, while the dominant component of the ion changes from the proton in the solar wind to O + and O 2 + in the Martian ionosphere.We aim to quantitatively describe the features and north-south asymmetries in the dayside plasma horizontal transport and ion tailward escape in the presence of crustal fields.We use the threshold of the electron density 10 3 cm −3 to characterize the altitude change of the ionosphere.Our results enhance our understanding of the role of crustal fields in controlling the dayside ionosphere structure and tailward plasma escape.

Model Description
We employ a three-dimensional multispecies MHD model to simulate Mars-solar wind interactions.The model includes a set of four continuity equations for the ion species (H + , O 2 + , O + , and CO 2 + ), with the highest contributions in the Martian ionosphere.This model is based on a set of eight-wave MHD equations and consider a series of ionospheric chemical reactions, including photoionization, ion-neutral reaction, and dissociative recombination.The model is based on the formula proposed by Ma et al. (2004), which integrated MHD equations with the mass conservation equation for individual ion species.
In our model, the mass equations for the four ion species are decoupled from the main MHD equations to facilitate the implementation of the calculation (Li et al. 2021).The decoupled MHD equations, as well as the details of the model setup, refer to the model of Li et al. (2021), which has been shown to roughly describe the plasma environment in the Mars-solar wind interaction without the crustal fields.In our model, the total number of cells in the whole simulation domain is 960,000, with the highest radial resolution reaching 10 km near the inner boundary (100 km), to accurately calculate the structure of the ionosphere (Ma et al. 2004;Fang et al. 2015).The resolutions in longitude and latitude are 3°.6 and 4°.5, respectively.The program is parallelized to improve computing speed.Moreover, the photoionization effect is included by adopting the Chapman function, which has been shown to significantly improve the agreement with plasma density observations (Ma et al. 2015).Our calculations are performed in the Mars Solar Orbital coordinate system, with the x-axis pointing from Mars toward the Sun, the z-axis perpendicular to the x-axis and parallel to the northward normal of the orbit plane of Mars, and the y-axis completing the righthanded coordinate system.The simulation domain is within −24 R M x 8 R M and −16 R M y, z 16 R M , where R M is the radius of Mars (3396 km).The inner boundary of the grid is set to 100 km above the Martian surface.The density and speed of the upstream solar wind are 4 cm −3 and 400 km s −1 , respectively.The interplanetary magnetic field (IMF) is assumed to be along the nominal Parker spiral, as specified by |B| = 3 nT and (BX, BY, BZ) = (−1.6,2.5, 0) nT.
In this study, a 110°spherical harmonic model developed by Gao et al. (2021) is included, as it has been demonstrated to describe the crustal magnetic fields of Mars in detail.In this crustal field model, almost all the strong crustal field sources, with the magnetic field strength >10 3 nT near the inner boundary of the model (at the altitude of 100 km), are located predominantly in the middle-to high-latitude areas in the south.The strongest source is located near 45°S, 180°W.However, the crustal field strength in most areas of the Martian northern hemisphere is close to 0 nT.Only a few weak crustal sources, with a magnetic field strength of 100-200 nT near the inner boundary of the model, exist in the north.A case without a crustal field is also run as a control group to clearly demonstrate the effects of the crustal fields.
Furthermore, the cases ignore the Martian rotation and the tilt of the rotational axis (about 25°).In different seasons, the relative locations between the strongest crustal source and solar wind inflow will change.Therefore, the shielding effect will be weaker or stronger, and the tailward plasma escape will be enhanced or inhibited (Ma et al. 2014;Fang et al. 2017).Additionally, the solar radiation received by the geographical southern and northern hemispheres will be different.This effect leads to the north-south asymmetry of the photoionization of the neutral atmosphere.Consequently, to reveal an apparent influence of the crustal fields on the plasma transport and avoid the asymmetry of the photoionization, the subsolar location is set at 180°W and 0°N.The rotation of Mars is also ignored in this study.In Fang et al. (2015Fang et al. ( , 2017)), the static model case may underestimate the ion loss, and the crustal field near the terminator may provide an escape-fostering effect in the plasma escape process.

Results
Figure 1 shows the logarithmic magnetic field lg(|B|) and velocity of solar wind ions |V| in the X-Y and X-Z planes, where the magnetic field B is the vector sum of the induced and crustal magnetic fields.In Figures 1(a) and (b), the location where the impacting solar winds suddenly decelerate in front of Mars represents the location of the bow shock (BS).The impacting solar wind is decelerated and deflected in front of Mars, crossing the terminator and then flowing downstream.In Figures 1(c) and (d), the location where the magnetic field jumps from a low background value (3 nT, blue area in Figure 1) to approximately 10 nT (green area), representing the location of the BS.The magnetic pileup region can be characterized by areas colored yellow and red.Compared with Li et al. (2021), owing to the presence of the crustal fields, the southern magnetosphere expands in Figure 1(c).At night, the draped and extended field lines formed an induced magnetotail with a double-lobe structure.The magnetic field and velocity are self-consistently calculated and concur with previous investigations (Nagy et al. 2004;Li et al. 2021).
In this study, V r is the radial velocity, with the positive direction pointing away from Mars.The positive direction of V θ is along the tangent of any longitudinal line and points to the south, and the positive direction of V j is obtained by the righthand rule.Figure 2 presents the distributions of V r , V θ , and V j at altitudes of 300-700 km on the dayside.Figures 2(a  that in the north (Figure 2(d)), especially below the altitude of 500 km.This result indicates the inhibition of the southward transport in the southern hemisphere.The north-south asymmetry of V θ is the most significant at an altitude of 500 km and gradually disappears at altitudes more than 600 km.Figures 2(e) and (f) show the zonal velocity V j .The value of V j is small in the subsolar area and large near the terminator.In the presence of the crustal fields (Figure 2(f)), local increase and decrease in V j occur on both the northern and southern hemispheres.Cao et al. (2019) obtained the distribution of effective zonal transport velocity at an altitude of 400 km from the observed time evolution of ionospheric total electron content based on the MEX Mars Advanced Radar for Subsurface and Ionospheric Sounding measurements.The value distribution and feature they obtained agree well with our results.
Figure 2 shows that beyond the subsolar region, the main pattern of the plasma transport is approaching the terminator along the horizontal direction.Chaufray et al. (2014) performed simulations of four solar longitudes cases and three solar activities cases based on the Mars General Circulation Model of Laboratoire de Météorologie Dynamique model.They indicated that the horizontal velocity is lower than 1 km s −1 below an altitude of 300 km.Liemohn et al. (2017) calculated the distribution of the velocity using a multifluid MHD model and found that in the low-and middle-latitude, the meridional velocity increased with the altitude and latitude and dominated the plasma motion beyond the subsolar area.Our velocity distribution regions are consistent with their results.In the case without the crustal fields, V r and V j show a dawn-dusk asymmetry.This may be related to the influence of the quasiparallel BS and quasi-perpendicular BS (Ma et al. 2004) or the magnetic pressure arising from the B X component of the IMF (Regoli et al. 2018).Under the influence of the crustal fields, the distributions of the horizontal velocity V θ and V j show a north-south asymmetry.
To investigate this north-south asymmetry, which is the most significant feature at an altitude of 500 km, we trace the variations in the horizontal velocity components and the crustal field strength along the 180°W longitude line at this altitude.Figure 3 demonstrates the variation in the velocity and crustal field strength along the 180°W longitude line.In Figure 3(a), in cases both with and without the crustal fields, the value of V θ (blue lines) on the meridional direction is much higher than that of V r and V j .In the presence of the crustal fields, the southward velocity (blue solid line) is reduced from a maximum of 8.1 km s −1 to an average value of 2 km s −1 in the southern hemisphere.This result indicates that the strong crustal source may inhibit the meridional transport and lead to the deflection of the plasma flow (Li et al. 2022b).At an altitude of 500 km, the peak value 8 km s −1 of V θ at approximately (40°S, 180°W) agrees well with the numerical results reported by Liemohn et al. (2017).In their study, the meridional velocity is between 0 and 10 km s −1 at altitude of 500 km.These results indicate the importance of the meridional transport in the day-to-night plasma transport.
Owing to the reduction in V θ and local increases and decreases in both V r and V j , the direction of the day-to-night plasma flow will be different from that in the case without the crustal fields, and the distribution of the velocity vectors will be north-south asymmetry.The distribution of the unit flow vectors on the northern and southern hemispheres of Mars shown by Lundin et al. (2011) showed such asymmetry.This effect may result in the observed local increase in the heavy-ion number density above the strong crustal field areas (Dubinin et al. 2019;Weber et al. 2021;Fowler et al. 2022).However, the variations in V r and V j above the strong crustal sources at the southern hemisphere are not obvious.The changes in the V r and V j values also occur in the weak crustal field regions.For example, the absolute V r value between 0°S and 20°S decreases to almost 0 km s −1 , indicating that the radial inflow is inhibited in this area.Furthermore, the absolute V j value between 20°N to 80°N also decreases, indicating that the duskward motion of the plasma is inhibited.However, owing to the increase in the absolute V r and V j values in the other areas, the effects of the crustal field strength on V r and V j are not simply enhancement or inhibition.
Figure 4 shows the variation in V θ and V j on different latitude lines at an altitude of 500 km.From longitudes of 140°( 140°E) to 220°(140°W), V θ dominates the plasma motion.On the southern hemisphere, the southward transport near the 180°W longitude line is inhibited by more than 70% at both low-and middle-latitude areas (Figures 4(a) and (c)), whereas the changes in northward transport (Figures 4(e) and (g)) are less than 5%.These results indicate that the number density of the planetary ions reaching the southern terminator is reduced.Figures 4(b), (d), (f), and (h) show the variation of V j .In the case with the crustal fields, the mean zonal velocity is approximately 1.5-2 km s −1 near the terminator, which agrees with the time-dependent ionosphere model (Cui et al. 2015) and the estimation based on the time evolution of ionospheric electrons and ions observed by MEX (Withers et al. 2012;Cao et al. 2019).On the 30°S latitude line, the dawnward transport (the left part of the V j curves) is inhibited in case with the crustal fields, whereas the duskward transport (the right part of the V j curves) is slightly inhibited between longitudes of 180°a nd 205°and is promoted between longitudes of 205°and 240°.On the 50°S latitude line, both the dawnward and duskward transport processes are inhibited in the case with the crustal fields.In the north, the influence of the crustal fields on V j at latitudes of 30°N and 50°N is similar: the dawnward transport is promoted, whereas the duskward transport is inhibited.The promotion/inhibition of the plasma transport on the zonal direction results in an increase/decrease in the number density of the planetary ions reaching the dawn side and dusk-side terminator.
Owing to the influence of the crustal fields on the horizontal transport on the dayside, the structure of the ionosphere near the terminator will change.Based on our numerical results, we use the threshold of the electron density 10 3 cm −3 to characterize the altitude change of the ionosphere.The electron number density is equal to the total-ion number density.In Figure 5(a), the threshold surface (with the electron density 10 3 cm −3 ) in the case with the crustal fields (red surface) overlaps with that in the case without the crustal fields (gray surface).Under the influence of the crustal fields, the threshold altitude increases in the red areas and decreases in the gray areas.Figure 5(b) shows the distribution of crustal field strength in the red area in Figure 5(a).In the subsolar area and middle-latitude area near the 180°W longitude line, the location of the threshold surface is raised in the presence of the crustal fields.Numerical studies have reported the upward spread of the ionosphere at these locations (Ma et al. 2004;Li et al. 2022a).On the one hand, the crustal magnetic pressure above the strong crustal sources balances the external pressure and protects the ionosphere from being compressed and lost.On the other hand, Figures 3 and 4 demonstrate that the northsouth transport, which dominates the plasma motion on the dayside, is significantly inhibited, especially in the south.These two effects result in the accumulation of planetary ions in strong crustal areas.This effect may result in the shrinking of the ionosphere above the weak crustal areas surrounding strong crustal areas.
Furthermore, around the terminator, the increase/decrease in the threshold altitude in the presence of the crustal fields is related to the local promotion/inhibition of the horizontal transport.In the northern hemisphere, the threshold altitude increases near the dawn-side terminator and decreases near the dusk-side terminator.In the southern hemisphere, the threshold  altitude increases in the low-latitude region near the dusk-side terminator and decreases in the other near-terminator regions.These results correspond to the promotion and inhibition results of the horizontal transport shown in Figure 4. Specifically, when the zonal and meridional transport is promoted/inhibited, the ionosphere in the near-terminator region at the corresponding longitude or latitude will expand/shrink.Figure 5(c) shows the distribution of the threshold altitude.From low to high latitude, the threshold altitude increases from 350 km to over 400 km.However, the threshold altitude is also more than 400 km in the subsolar area, which may be attributed to the weakening of the radial solar wind inflow in this area due to the crustal fields.
Owing to the inhibition of the southward transport, the planetary ions reaching the southern nightside will be reduced, and the planetary ion loss on the southern magnetotail may be weakened.Figures 6(a + along the white circle with the radius of 6 R M in Figure 6(c).In observational studies, the mean escape flux of each heavy-ion species on the downstream of −1.5 to −3 R M is approximately 10 6 cm −2 s −1 (Dong et al. 2015;Inui et al. 2019), and the expected radial fluxes at 6 R M downstream would be lower.The radial flux shows two peaks near 20°N and 20°S, with the peak values of the red lines being lower than those of the blue lines.The peak values of the red lines are 41.3%, 13.4%, and 33.2% lower than the blue peak values in the south for O 2 + , O + , and CO 2 + , respectively.Additionally, O + dominated the heavy-ion escape in the magnetotail, particularly in the central tail area.These results indicate that the crustal fields on the dayside exerted an inhibitory effect on the heavy-ion escape in the magnetotail, owing to the obvious reduction in the number density reaching the southern magnetotail.

Discussion
This study investigates the influence of the Martian crustal magnetic field on the horizontal transport and tailward escape processes of heavy ions.The latest 110°spherical harmonic model developed by Gao et al. (2021) is used to calculate the crustal fields.The model can self-consistently calculate plasma and field environments during the interactions between Mars and solar winds.In this study, spherical-coordinate velocity components are adopted to describe the plasma motion in the dayside ionosphere.The distributions of the velocity components indicate that the horizontal transport toward the terminator dominates the plasma transport on the dayside.We observe significant north-south asymmetry of the distributions of V θ and V j .In the presence of the crustal fields, the total horizontal velocity on the southern hemisphere is reduced.Finally, we show the relationship between the horizontal transport and ionosphere structure and the inhibition of the tailward heavy-ion loss in the southern magnetotail.
Strong crustal field sources provide enhanced magnetic pressure on the dayside ionosphere, counterbalancing the forces exerted by the solar wind plasma and protecting planetary ions from the solar wind (Crider 2002;Bertucci et al. 2003;Fang et al. 2015;Ma et al. 2017).Owing to the shielding effect of the crustal fields, the southward velocity V θ above the strong crustal source is reduced by over 70%.Owing to the much higher value of V θ than that of V r and V j , this effect results in the local increase in the ion number density and deviation of the transport direction, as previously observed (Lundin et al. 2011;Dubinin et al. 2019;Fowler et al. 2022).Therefore, the meridional transport cannot be neglected in the day-to-night transport process.However, compared with the obvious relationship between V θ and the crustal field strength, the relationship between V j and the crustal field strength remains unclear.Above the altitude of 200 km, several probable mechanisms drive and influence the horizontal motion of the heavy ions, such as plasma pressure and magnetic pressure gradients (Chaufray et al. 2014;Wu et al. 2019), Hall electric force (Li et al. 2022b), vertical and close magnetic topology near the strong crustal fields (Matta et al. 2015;Wu et al. 2019), and large ballistic flows along closed loops connecting day and night (Xu et al. 2017a(Xu et al. , 2017b;;Weber et al. 2017).Moreover, on Venus, the momentum transfer from the solar wind is generally considered important for the ionospheric flow (Pérez-de-Tejada et al. 2013).Consequently, in the presence of the crustal fields, the reason for the inhibition and promotion of horizontal transport on the dayside of Mars should be further investigated.
Although the ionosphere above the strong crustal source shows an evident expansion, this study shows that the ionosphere in the near-terminator regions may shrink, especially near the southern terminator.Meanwhile, the local promotion/inhibition of the zonal transport may result in the expansion/shrinking of the ionosphere near the dawn-side and dusk-side terminator.Consequently, in addition to the influence on dayside pressure balance, the influence of the crustal fields on the horizontal transport is an important mechanism in altering the ionosphere structure near the terminator.Although the effects of crustal fields on the plasma escape along the Martian magnetotail have been extensively studied using MHD simulations (e.g., Ma et al. 2014;Fang et al. 2015Fang et al. , 2017)), little attention has been paid to day-to-night plasma transport.However, in the presence of crustal fields, many heavy ions remain in the strong crustal field regions, instead of being transported away (Lundin et al. 2011;Matta et al. 2015;Dubinin et al. 2019;Weber et al. 2021).This effect results in the decrease of the heavy-ion number density transported from dayside to magnetotail and reduction in the heavy-ion loss.
Although O + is the main species responsible for heavy-ion loss in the magnetotail, the inhibitory effect is more obvious on the O 2 + and CO 2 + escape.In this study, the effect of the radial flow on the ionosphere structure is not discussed.Under the approximations that the Martian ionosphere is ideally thin with a constant zonal flow velocity at ionospheric altitudes, the radial is considered to be negligible in the day-to-night transport (Cui et al. 2015;Cao et al. 2019).However, radial transport may be important to the ionosphere structure in the subsolar region.Li et al. (2022a) showed the mechanism of the magnetic inclination angle on the radial transport and ion escape on the dayside, which indicates that the variation in the radial velocity is related to not only the crustal field strength but also to the magnetic topology.The magnetic topology may also influence the distribution of V j .Observational studies have investigated the results of in situ measurement of the magnetic topology based on MAVEN (Connerney et al. 2015;Xu et al. 2017a;DiBraccio et al. 2017;Xu et al. 2019).Furthermore, the multispecies MHD model, based on self-consistently calculated plasmas and fields, has been shown to suitably describe the Martian global magnetic structure (Ma et al. 2004;Ulusen et al. 2016;Fang et al. 2018;Xu et al. 2018).Therefore, the influence of the magnetic topology on the dayside plasma transport should be further studied.
Our conclusions are conducive to further understand the north-south asymmetry of heavy-ion escape and ionosphere structure under the influence of crustal fields and contribute new insights to the mechanism that the complex distributed crustal fields alter the plasma environment of Mars.However, Mars-solar wind interactions are dynamic and influenced by the rotation of crustal fields with Mars (Ma et al. 2014, Fang et al. 2015;Ma et al. 2015;Fang et al. 2017).To verify our conclusions under other solar conditions, seasons, and local times, the relevant cases will be calculated and discussed in further studies.
), (c), and (e) show the simulation results without the crustal field for comparison with Figures 2(b), (d), and (f), which are derived with the crustal field.In Figures 2(a) and (b), inflow dominates the subsolar area and low-latitude area.With the increase in altitude, two outflow regions are detected on the middlelatitude areas of both the northern and southern hemispheres.Figures 2(c) and (d) show the distribution of the meridional velocity V θ .Without the crustal fields, the distribution of V θ is north-south symmetric (Figure 2(c)).However, in the presence of the crustal fields, the value of V θ is obviously lower in the middle-to high-latitude areas of the southern hemisphere than

Figure 1 .
Figure 1.Distributions of velocity in the (a) X-Z plane and (b) X-Y plane and the logarithmic magnetic field in the (c) X-Z plane and (d) X-Y plane.Black solid lines with arrows represent streamlines in (b) and magnetic field lines in (d).White and black solid quasi-parabolas represent the mean locations of MPB and BS from Vignes et al. (2000), respectively.

Figure 2 .
Figure 2. Distributions of V r , V θ , and V j at altitudes of 300, 400, 500, 600, and 700 km on the dayside.(a) V r without crustal field; (b) V r with crustal field; (c) V θ without crustal field; (d) V θ with crustal field; (e) V j without crustal field; (f) V j with crustal field.The three coordinate axes in the figure are longitude, latitude, and altitude, with ranges of 90°(dawn side) to 270°(dusk side), −90°( south) to 90°(north), and 300-700 km, respectively.

Figure 3 .
Figure 3. Variations in the distributions of V r (red lines), V θ (blue lines), and V j (green lines) (a) and crustal field strength (b) along the 180°W longitude line at an altitude of 500 km.The case with/without the crustal field is represented by the solid/dashed lines.

Figure 4 .
Figure 4. Variations of V θ (a, c, e, and g), and V j (b, d, f, and h) along the 30°S (a, b), 50°S (c, d), 30°N (e, f), and 50°N (g, h) latitude line at an altitude of 500 km.Solid/dashed lines represents the case with/without the crustal field.
), (b), and (c) show the logarithmic number density distributions of O 2 + , O + , and CO 2 + in the X-Z plane, respectively, with the influence of the crustal field.The distributions of O 2 + and CO 2 + are similar, whereas the lighter O + has a higher number density in dayside high-altitude areas and the distant magnetotail.Figures 6(d), (e), and (f) show the radial flux Q r of O 2 + , O + , and CO 2

Figure 5 .
Figure5.The isosurfaces of total-ion number density = 1000 cm −3 in cases with (red surface) and without (gray surface) the crustal fields (a), and the same isosurfaces with the distribution of the crustal field strength on them (b).The two isosurfaces are created in the three-dimensional spherical-coordinate system and overlap with each other in both (a) and (b).The observing direction is from high to low altitude, along the altitude axis.(c) The isosurfaces of total-ion number density = 1000 cm −3 in cases with the crustal fields, colored by the distribution of altitude and superposed with the isolines.