The Influence of Solar Irradiation and Solar Wind Conditions on Heavy Ion Escape from Mars

We apply a recently proposed method to estimate heavy ion escape from Mars. The method combines in situ observations with a hybrid plasma model, which treats ions as particles and electrons as a fluid. With this method, we investigate how solar upstream conditions, including solar extreme ultraviolet (EUV) radiation, solar wind dynamic pressure, and interplanetary magnetic field (IMF) strength and cone angle, affect the heavy ion loss. The results indicate that the heavy ion escape rate is greater in high EUV conditions. The escape rate increases with increasing solar wind dynamic pressure, and decreases as the IMF strength increases. The ion escape rate is highest when the solar wind is parallel to the IMF and lowest when they are perpendicular. The plume escape rate decreases when the solar wind convective electric field increases.


The Influence of Solar Irradiation and Solar Wind Conditions on Heavy Ion Escape from Mars
Qi Zhang 1,2 , Mats Holmström 1 , Xiao-dong Wang 1 , Hans Nilsson 1,2 , and Stas Barabash 1 1 Swedish Institute of Space Physics, Kiruna, Sweden, 2 Department of Physics, Umeå University, Umeå, Sweden Key Points: • Ion escape rate decreases as the strength of the interplanetary magnetic field (IMF) increases • Escape rate is smallest for an IMF perpendicular to the solar wind flow • Ion escape in the plume decreases with increasing magnitude of the solar wind convective electric field

Supporting Information:
Supporting Information may be found in the online version of this article.
There is no consensus on how the solar wind dynamic pressure influences ion escape.With measurements from MEX ASPERA3-IMA, Lundin et al. (2008) reported that low-energy (30-800 eV) heavy ion outflow increases with solar wind dynamic pressure due to enhanced energy and momentum transfer.N. J. T. Edberg et al. (2010b) used MEX data to identify 36 high-pressure events.They found that during these high-dynamic pressure events, the heavy ion escape increases by a factor of approximately 2.5, which they explained in terms of the enhanced momentum transfer from the solar wind to planetary ions.Dubinin et al. (2017b) stated that solar wind dynamic pressure is the main driver of the escape of high-energy O + .Using MAVEN data, Dubinin et al. (2018) observed expanded O + outflow above 450 km with increasing solar wind dynamic pressure.Girazian et al. (2019) computed electron densities representing the total ion densities with MEX Mars advanced radar for subsurface and ionospheric sounding (MARSIS) data under various solar wind dynamic pressure cases derived from the MAVEN Solar Wind Ion Analyzer (SWIA).They described that electrons (ions) were more depleted in the topside ionosphere during high dynamic pressure conditions and explained that there are more ions escaping due to the deeper penetration of the solar wind.In contrast, Ramstad et al. (2018) investigated 10 years of MEX data and showed that the ion escape rate has a weak negative correlation with the solar wind dynamic pressure.Estimates from Nilsson et al. (2021) with MEX data divided into Martian years showed that there is no discernible correlation between heavy ion outflow and dynamic pressure.
Studies on interplanetary magnetic field (IMF) effects on heavy ion escape from Mars are few.Here we discuss some results of Venus studies to provide a comparison with Mars, since both Venus and Mars are unmagnetized planets and have some similarities when interacting with the solar wind.Liu et al. (2009) applied a hybrid model to Venus and found that the x-component of the IMF enhances the O + loss rate.T. L. Zhang et al. (2009) has run an magnetohydrodynamics (MHD) model for extreme cone angle cases at Venus.Their results showed that the escape rate increases from 5.4 × 10 25 s −1 to 9.5 × 10 25 s −1 when the cone angle is reduced from 11° to 0°.There is barely any induced magnetosphere formed in these two parallel IMF cases.However, using Venus Express measurements, Masunaga et al. (2013) indicated that the O + outflow is not affected by IMF direction (cone angle).Egan et al. (2019) has modeled the plasma environment of an unmagnetized exoplanet in the habitable zone of an M-dwarf.The authors indicated that quasi-parallel IMF drives a larger amount of O + and  O + 2 escape flux than quasi-perpendicular IMF.
Previous observational studies are mostly based on averaged observations since in situ observations only observe one location at each time.Moreover, averaging usually overlooks the effects of other parameters when investigating one parameter.Figure 1a shows the solar wind dynamic pressure variations over Martian years (to avoid seasonal effects) from MEX and MAVEN measurements.There is an obvious variation in the MEX data even though it does not perfectly fit the solar cycle.With MAVEN data less than a solar cycle, lower pressure is observed as the solar activity declines.Figure 1b shows that the IMF strength decreases as solar activity decreases.This indicates that, at solar maximum, solar EUV, solar dynamic pressure, and IMF strength are all high.At solar minimum, they are all low.If one wants to investigate any one of these parameters, the others need to be controlled.
In this paper, we use a recently proposed method (Holmström, 2022;Q. Zhang et al., 2023) to perform a parameter dependence study.The advantage of this method is that it makes control of the parameters possible by selecting MAVEN orbits based on specified criteria.Then, a hybrid model is run to obtain the global escape picture of each individual orbit.

Method
In a hybrid model, ions are treated as individual particles accelerated by the Lorentz force, while electrons are treated as an inertialess charge-neutralizing fluid.The electric field is given by where B is the magnetic field, ρ I is the ion charge density, J I is the ion current density, p e is the electron pressure, η is the resistivity and μ 0 is the vacuum permeability.The Mars model has a sphere centered at the origin with a radius (R m ) of 3,380 km, with the resistivity of 7 × 10 5 Ωm, representing the solid planet body.The resistivity above this sphere is 5 × 10 4 Ωm.A fully absorbing boundary (where precipitating ions are removed) is set at the exobase altitude of 170 km (a spherical obstacle with a radius of 3,550 km).Regions with a plasma density less than 1% of the solar wind density are considered as vacuum regions, with the resistivity of 10 6 Ωm.The ionosphere is composed of upflux of 54% O + , 39%  O + 2 , and 7%  CO + 2 (Q.Zhang et al., 2023).The heavy ions are produced on the dayside from the obstacle boundary, with the initial velocity drawn from a Maxwellian distribution corresponding to a temperature of 200 K.The ion upflux decreases by the cosine of the solar zenith angle from the subsolar point to the terminator.The ion upflux is a free parameter in our model.The model is set up in Mars-Solar-Orbital (MSO) coordinates, with the x-axis pointing to the sun, the y-axis antiparallel to Mars' orbital velocity, and the z-axis completing the right-handed coordinate system.The model cell size is 350 km.The number of macro particles per cell at the inflow boundary is 8 for protons, and 2 for alpha particles.The ionospheric ion macro particles share the same weight with protons.We run the model until the number of heavy ions in the simulation domain remains on average constant.The total escape rate is thereafter calculated by averaging the outflow in the region x < −1.5 R m after a steady state has been reached (about 10 min, depending on the conditions of various orbits).More model details can be found in Q. Zhang et al. (2023), and more details on the hybrid solver itself can be found in Holmström (2010).
Our method combines a hybrid model with MAVEN measurements based on the theory that mass loading determines the bow shock location.First, we input upstream solar wind conditions from MAVEN orbits to the model.The measurements include solar wind density (95% proton and 5% alpha particle number density), solar wind velocity, and solar wind proton temperature (alpha particle temperature is taken to be the same) from SWIA; solar wind electron temperature from the Solar Wind Electron Analyzer (SWEA); and IMF from the Magnetometer (MAG).Second, we set the heavy ion upflux from the obstacle boundary of the model.The higher the obstacle boundary upflux, the more mass loading.We set different obstacle boundary upflux values in several model runs.Then, we run those simulations and compare the bow shock location in the model results to observations.We pick the best fitting run as the one used for further study.This method was first proposed by Holmström (2022).Further development and detailed discussion of the parameters can be found in Q. Zhang et al. (2023).Upstream solar wind changes can affect the magnetosphere configuration in minutes, as can be concluded from the fact that a hybrid Mars simulation reaches a steady state after about 10 min for typical upstream conditions.This makes it possible to study the effects of upstream solar wind conditions on the Martian magnetosphere for individual bow shock crossings.
In this study, we assume that four upstream parameters have effects on heavy ion loss: the solar EUV radiation, the solar wind dynamic pressure (P sw ), the magnitude of the IMF, and the cone angle (θ) between the IMF and solar wind velocity.These upstream parameters can be derived from MAVEN observations.We used data from the MAVEN EUV Monitor (EUVM) Channel A (17-22 nm) to represent the solar EUV radiation (Y.Dong  or read from SWIA data.The cone angle is computed using solar wind velocity from SWIA and IMF from MAG.Note that solar EUV irradiation is not a direct input to our model.However, a required increase in upflux to fit the observed bow shock location can reflect a higher solar EUV intensity. To investigate one of those four parameters, we constrain the other three to have similar values.As a consequence, the change in the escape rate only comes from the remaining parameter.To test this, we examined four MAVEN orbits (Orb. 403,413,530,and 688) that have similar upstream parameters (Figures 2a-2d).They all yield similar escape rate estimates (Figure 2e).This result provides a check on our method's robustness in estimating ion escape rates and studying how different parameters affect them.
To explore the dependence of the escape morphology on the upstream conditions, we here focus on two primary escape channels: tail escape and plume escape, which are defined by a geometric box following the description by Q. Zhang et al. (2023) and shown in Figure 3a. Figure 3b gives an example of the cross section of the tail and plume flux that we use to compute the escape rate of Orb.688.

Escape Variations With Solar EUV Radiation
Changes in EUV radiation affect ionization rates in the ionosphere.This takes time to affect the magnetosphere, due to the chemistry and transport of the generated ions.In a sense, the state of the ionosphere at an instant of time is an integral of the past EUV insolation (Schmölter et al., 2022).The ionosphere is also relying on the state of the atmosphere and exosphere, which are highly variable in space and time at Mars (Chaufray et al., 2015;Fowler et al., 2022a;Leelavathi et al., 2023).That the EUV insolation affects the state of the magnetosphere on long timescales requires that we look at the effects over times longer than one orbit.To exclude the influence of the other parameters, we set the restriction of 2 nT < |B| < 3.5 nT and 55° < θ < 75°.Thereafter, we chose eight dynamic pressure pairs.For each pair, the main difference in upstream conditions is the EUV value.The escape rate estimates for these 16 orbits are shown in Figure 4. Two extra orbits without pairs (smallest dynamic pressure in low EUV flux and largest dynamic pressure in high EUV flux) are also displayed in Figure 4.
Figure 4 illustrates that the escape rate increases as solar EUV radiation increases.The total escape rate in high EUV radiation is 2-4 times that in low EUV radiation, which is close to observations (Nilsson et al., 2021;Ramstad et al., 2015).The widely accepted reason is that the escape rate is production-limited so that a higher production in high EUV radiation gives a higher escape rate.Figures 5a and 5b show a comparison of the magnetic field in low EUV radiation and high EUV radiation cases.The expanded bow shock during high EUV radiation indicates the higher mass loading (ion production) from the atmosphere.Hall et al. (2016) also noticed that the bow shock terminator distance increases linearly with solar irradiance.In addition, the solar wind electron temperature in high EUV radiation is nearly 1.5 times that in low EUV radiation according to SWEA measurements.Solar reviews (Issautier et al., 2005;Salem et al., 2003) have also found that the solar wind is hotter 10.1029/2023JA031828 6 of 15 (higher electron temperature) during solar maximum.The hotter solar wind could possibly transport heating downstream through wave-particle interaction to the topside ionosphere (Cui et al., 2015;Ergun et al., 2016).The enhanced ionospheric electron temperature can create a stronger ambipolar field, which could be the underlying cause of the enhanced ion loss (Brecht et al., 2017;Ergun et al., 2016) in high EUV radiation.
From our model results, the tail flux increases by a factor of 4-5 during high EUV radiation, similar to what was found by Dubinin et al. (2017a).However, the plume flux does not show clear dependence on EUV radiation.Increased ion supply at low altitude during high EUV radiation results in a larger tail flux.The plume, taking place at high altitude, is mainly controlled by the solar wind.As a consequence, the tail escape is sensitive to EUV radiation while the plume is not.ZHANG ET AL. 10.1029/2023JA031828 7 of 15 minor  CO + 2 component also shows systematically positive correlation with solar EUV irradiance.However, this tendency is only known to occur under certain conditions.Once the IMF strength and cone angle are changed, a different ion may be dominant in the escape.Moreover, the ion composition in the model should also make a difference.

Escape Variations With Solar Wind Dynamic Pressure
We chose orbits with solar wind dynamic pressure between 0.2 and 2 nPa.Dynamic pressures lower than 0.2 nPa are too computationally expensive for the hybrid model due to the large simulation domain and the long-time simulation running required to reach a steady state.Pressures higher than 2 nPa are rarely observed, especially during low EUV radiation.To obtain the data pairs, we have to make a compromise to choose the dynamic pressure so that we have both low EUV flux and high EUV flux orbits.We used two sets of data to study how dynamic pressure affects the heavy ion loss, which is the same as in Section 3.1.The first set is during high EUV radiation, with 2 nT < |B| < 3.5 nT and 55° < θ < 75°.The second set is during low EUV radiation, with 2 nT < |B| < 3.5 nT and 55° < θ < 75°.For both sets, the escape rate increases as solar wind dynamic pressure increases, as shown in Figure 4.Not only the tail flux, but also the plume flux responds positively to increasing pressure.A linear least squares fit to the escape rate as a function of solar wind dynamic pressure is shown in dashed lines in Figure 4.The fitted formula in low EUV radiation condition is (4.8 × 10 24 P sw − 4.2 × 10 23 ) s −1 , where P sw is in nPa.The fitted formula in high EUV radiation condition is (1.0 × 10 25 P sw + 3.6 × 10 23 ) s −1 .Figure 6 shows that the escape rates of the different components all increase as the dynamic pressure increases.The dominant escaping ion specie remains the same as the dynamic pressure rises.One possible explanation for the increase in escape rate with dynamic pressure is enhanced energy transfer in high solar wind dynamic pressure (N.J. T. Edberg et al., 2010b;Girazian et al., 2019;Lundin et al., 2008;Martinez et al., 2020).Figures 5b and 5c show clear shrinkage of the induced magnetosphere in a higher solar wind dynamic pressure case.The solar wind penetrates deeper into the induced magnetosphere and interactions become stronger, leading to more escaping ions.For the stronger dynamic pressure, even though the same amount of ions is created in the ionosphere, more ions are extracted upward and escape.Another possible explanation is the enhancement of magnetotail currents that could accelerate the heavy ions.Comparing the 0.5 nPa low-dynamic pressure case and the 1.3 nPa high-dynamic pressure case, Figures 5b  and 5c show an apparent stronger compression in the high-dynamic pressure case in the Y MSO and Z MSO directions than in the X MSO direction, which is shown in Figures 7a and 7i.The magnetic field is less flared in the high- dynamic pressure case.The IMF directions in these two cases are quite close, and ensure that the slices in the plasma sheet are in similar locations.In the lobe and tail region, to balance the increased solar wind compression in the Y MSO and Z MSO directions, the magnetic pressure increases, which causes an increasing magnetic field.With the increased magnetic field and the compressed area, the curl of the magnetic field (∇ × B) increases, meaning the current is strengthened and thereafter the Hall electric field (J × B) is enhanced and eventually accelerates more tail ions to escape energy.Figures 7b and 7g show the stronger electric field in the tail region.In addition, the solar wind-induced electric field penetrates deeper into the Martian atmosphere in high dynamic pressure, leading to lower-altitude heavy ions accelerating and escaping through the plume.This has also been noticed by Sakakura et al. (2022).

Escape Variations With the Magnitude of the IMF
Seven orbits were selected to study the influence of IMF strength, during a high EUV flux period (December 2014 to March 2015), with solar wind dynamic pressure from 1.2 to 1.6 nPa and cone angle from 45° to 75°.The range of IMF strength is from 1.3 to 13 nT.
Figure 8a illustrates that the total and plume escape rates decrease as the magnitude of the IMF increases.The tail escape also decreases with increasing IMF strength, at least above 3 nT.The magnetosonic Mach number is inversely proportional to the IMF strength (N.J. Edberg et al., 2010a) when the solar wind density and velocity are roughly constant.A large Mach number means that the solar wind compresses the obstacle, causing closer and stronger interaction between solar wind and planetary atmosphere, and is therefore conducive to ion loss.The process is similar to the dependence of escape rate on dynamic pressure.Besides, Figure 9 shows that the stronger the IMF, the stronger and thicker the induced magnetosphere.Stronger IMF builds up larger pile-up regions and induces a stronger magnetosphere to protect the Martian atmosphere.Moreover, the gyroradius is smaller with stronger IMF, which may cause more ions to gyrate into the planet instead of escaping.Since the range of IMF strength in our study is from 1 to 13 nT, the gyroradius could be one order of magnitude different.The range of gyroradius varies from 10 3 to 10 4 km, so the ions could gyrate into the planet, especially for large magnetic field strengths.For large IMF (>10 nT), the escape rates of these three ion species tend to be very close.The reason for this tendency is unknown.

Escape Variations With Cone Angle
Our study of the cone angle (the angle between the solar wind velocity and the IMF) is based on orbits in a high EUV flux period (December 2014 to March 2015), with 0.55 nPa < P sw < 0.65 nPa and 2.5 nT < |B| < 3.5 nT.The range of cone angles is from 15° to 160°.Understanding the physical processes in the extreme cases outside this range would require separate study.) that the highest escape rate occurs in the parallel situation.One possible explanation for this is that the energy transfer from the solar wind ions to the heavy ions is less efficient when the cone angle is large.Gary et al. (1989) presented comet hybrid simulations of the energy transfer dependence on cone angle and found that the rate of fluctuating magnetic field energy decreases as the cone angle increases.This was a one-dimensional simulation, but the same mechanism could be present for the Mars-solar wind interaction, and could explain our results showing a lower escape rate for a perpendicular IMF.Incidentally, Fowler et al. (2022b) discovered that when the cone angle is extremely small (or large), the stronger magnetic fluctuations accompanied by cyclotron waves could potentially enhance the ion loss.
Figure 10b shows that the escape rate of each specie (O + ,  O + 2 , and  CO + 2 ) has the same variation as the total escape: it increases as |90° − cone angle| increases.In addition, when |90° − cone angle| < 20°, the O + and  O + 2 escape rates become closer.While |90° − cone angle| increases, the difference in escape rate between these two species grows.We can also note that  CO + 2 has a slight variation in escape as a function of cone angle.It seems that the dependence on cone angle is larger for species with smaller mass per charge.It is possible that there is a relevant kinetic effect that we do not fully understand so far.

What Controls Ion Escape in the Plume?
The plume is generally thought to be generated by the convective electric field −V sw × B (Y. Dong et al., 2017;Dubinin et al., 2017c;Nilsson et al., 2021).But how exactly the plume escape is controlled is still unclear.Here we attempt to answer this question by examining the correlations between all components of the convective electric field (|V|, |B|, and cone angle θ) and the plume escape.
For comparison, we selected orbits during a high EUV radiation period (December 2014 to March 2015), with 0.55 nPa < P sw < 0.65 nPa.Then these orbits were classified into three groups: 1.In group 1, they are confined to 2 nT < |B| < 3 nT and 300 km/s < |V| < 360 km/s.Only the cone angle varies.
The result is shown in Figure 11b.3.In group 3, they are confined to 50° < θ < 70° and 2 nT< |B| < 3 nT.Only the solar wind velocity varies.The result is shown in Figure 11c.
In Figures 11a-11c, sin θ, the IMF strength, and the solar wind velocity all grow roughly linearly with the convective electric field, since the magnitude of the convective field is |V|•|B|• sin θ. Figure 11a shows that, as sin θ increases, the convective electric field increases, the total escape rate decreases, and the plume flux decreases.Figure 11b shows that as the magnitude of the IMF increases, the convective electric field increases, the total and tail escape decrease, and the plume flux decreases.Figure 11c shows that, as the solar wind velocity increases, We gathered results of all the orbits displayed in Figures 11a-11c and plotted the escape rate and convective electric field in Figure 11d.For all these cases, the solar EUV and solar wind dynamic pressure are confined and only the convective electric field varies.Counterintuitively, the plume seems to decrease with increasing convective electric field.A power-law fit has been made between the solar wind convective electric field and the plume escape rate.The plume escape follows lg(Q pesc ) = − 0.87 × lg(E conv ) + 24.21, where the unit of Q pesc is s −1 and the unit of E conv is mV/m.One possible reason for this is that a stronger convective electric field results in a stronger induced magnetosphere.Similar to the interpretation of stronger IMF strength driving less ion escape, a strong magnetic field protects the atmosphere from loss, with the small gyroradius causing ions to fall back to the planet, reducing the escape probability.In this case, a certain electric field is needed to accelerate atmospheric ions to escape energy.Above that, only the escape energy becomes larger while the escaping amount does not change.In future work, it will be interesting to estimate the saturation of the electric field.This process also corroborates the view that the source supply of heavy ions is important to the escape on Mars.
In our hybrid model, we use an adiabatic assumption, resulting in an ambipolar field term that is directed opposite to the charge density gradient.This field will therefore be directed approximately radially outward in the region near the inner boundary (exobase).The strength of this field should be similar, independent of upstream conditions.Thus, for a weak convective electric field, closer to the inner boundary, the ambipolar field term will dominate and ionospheric ions will be accelerated outward more easily.When they get away from the inner boundary they can be picked up by the (weak) convective electric field.On the other hand, for a strong convective electric field that is intensely opposed to the ambipolar field term, ions in the negative field hemisphere will be accelerated into the inner boundary.This could explain the reduction in escape when the solar wind convective electric field is stronger.For more certainty of the exact process, a more detailed study would have to be performed, for example, by tracing some individual ionospheric ions to see their trajectories and how different electric field terms control.
However, tail escape does not show a strong dependence on the convective field.This is reasonable since the tail escape is not only affected by the convective field but also the magnetotail current.

Summary
We investigate the influence of the undisturbed upstream conditions on heavy ion escape from Mars by a method that couples MAVEN observations with a hybrid model.Using this method, we can estimate the escape rate orbit by orbit and control the other parameters when studying any given parameter.The conclusions are summarized below: 1.The model results show that the escape rate is higher in high EUV radiation.The total escape rate at solar maximum is 2-4 times that at solar minimum.This is because more ions are produced during solar maximum resulting in a larger escape rate.The tail escape increases by a factor of 4-5 during solar maximum, compared to the solar minimum.The plume escape does not show a large sensitivity to EUV flux change.This could be because the stronger low-altitude ionospheric supply is more important to the tail escape than to the plume escape, which depends more on the solar wind convective electric field.2. Increased solar wind dynamic pressure increases ion escape.Both tail flux and plume flux increase as solar wind dynamic pressure increases.One possible explanation is that the energy transfer is more efficient in higher solar wind dynamic pressure cases.Another is that the tail flux is energized by the compression of the magnetic tail current in stronger dynamic pressure.3. We find that the heavy ion loss is reduced when the IMF strength is increased.A stronger IMF drives stronger magnetic pile-up in front of the planet and generates a thicker and stronger induced magnetosphere, which protects the atmosphere from escaping.At the same time, the small gyroradius associated with large IMF strength could lead to ions falling back to Mars. 10.1029/2023JA031828 13 of 15 4. Heavy ion escape is sensitive to changes in the cone angle.When the solar wind velocity is parallel to the IMF, the escape rate is highest.When it is perpendicular, the escape rate is lowest.5. We also study the relation between the solar wind convective field and the plume escape.The plume is generated by the convective field, but surprisingly they are negatively correlated.6.The composition of the escaping ions shows a dependence on the EUV radiation, IMF strength, and cone angle.At solar maximum, O + escape is dominant, while at solar minimum,  O + 2 escape is dominant.When the IMF strength is lower than 3 nT, O + escape is dominant, but above 3 nT,  O + 2 escape is dominant.When |90° − cone angle| < 20°, O + escape is similar to  O + 2 escape.When |90°− cone angle| > 20°, O + escape is eventually larger than that for  O + 2 .Although we present some hypotheses regarding the phenomena we have observed in the model, the detailed processes still need further investigation.For instance, why does the plume flux decrease when the convective electric field increases?What will the measurements look like?Understanding the dependence of ion escape on upstream conditions is helpful to understand the evolution of the Martian atmosphere and could also offer insight into studies of exoplanet atmospheric escape (Egan et al., 2019).We can note that the findings in this paper are related to the question: Does a magnetic field protect a planet (Brain et al., 2012;Ramstad & Barabash, 2021)?That question is posed in terms of an intrinsic magnetic field.Our findings show that ion escape decreases when the strength of the solar wind magnetic field increases at Mars.If we extrapolate this finding we could speculate that the stellar wind magnetic fields protect unmagnetized planets.For exoplanets close to the host star, the upstream conditions are extreme: they exhibit intensive solar EUV radiation, high dynamic pressure, strong IMF, and small cone angle.Study of these extreme parameter regimes could better represent the environment of earlier Mars and some exoplanets.

Figure 1 .
Figure 1.(a) The solar wind dynamic pressure varying over time is calculated by   2  both from Mars Express (MEX) (black line) and Mars Atmosphere and Volatile Evolution (MAVEN) (red line).The median values are shown for each Martian year.The lower dynamic pressure in MEX is due to the lower solar wind density measured by MEX.The blue line sharing the y-axis is the solar F10.7 index derived from OMNI data, which represents the solar cycle.It is also averaged per Martian year.(b) The red line shows the median value of the interplanetary magnetic field strength per Martian year measured by MAVEN.The blue line is the same as the one in panel (a).Error bars are given by standard errors.Note that the error bar of F10.7 index is too small to be visible.
al., 2017).The solar wind dynamic pressure can be calculated by   2

Figure 2 .
Figure 2. The black lines in (a)-(d) show the distribution of extreme ultraviolet, solar wind dynamic pressure, interplanetary magnetic field strength, and cone angle of all Mars Atmosphere and Volatile Evolution orbits with upstream data from 2014 to 2019.The color bars represent the parameters of the four tested orbits (some are too close to be distinguishable).(e) Total escape rates of these four orbits.

Figure 3 .
Figure 3. (a) Illustration of how tail and plume escape are defined in this study.The size of the box is X MSO = ± 1.6R m and Y MSO , Z MSO = ± 1.7 R m .The flux passing through the Y MSO − Z MSO face of the box along −X MSO we define as the tail flux (the blue arrow).The flux passing through the X MSO − Z MSO and X MSO − Y MSO faces of the box is defined as the plume flux (the orange arrows).The direction of the convective electric field determines the direction of the plume flux.(b) An example of the distribution of the tail and plume flux of Orb.688.The leftmost panel shows the tail flux at X MSO = −1.6Rm , and the other two show the plume flux at Y MSO = − 1.7R m and Z MSO = + 1.7R m .The thickness of the cross section of every side is one layer of cell size.The black arrows indicate the direction of the flux.We see longer arrows in plume panels than in the tail panel, meaning that the plume velocity (or energy) is larger than the tail velocity (or energy).Notice that for this simulation there is no plume flux through the +Y MSO or −Z MSO sides.

Figure 6
Figure 6 shows that O + escape is dominant in high EUV radiation and  O + 2 is dominant in low EUV radiation.Less tail flux in low EUV radiation results in a higher percentage of plume. O + 2 has a larger gyroradius and is found predominantly in the plume (Y.Dong et al., 2022).When the plume escape in low EUV radiation becomes important,  O + 2 is dominant.When the tail escape in high EUV radiation becomes important, O + is dominant.The

Figure 4 .
Figure 4.The escape rates of different extreme ultraviolet (EUV) radiation and solar wind dynamic pressure cases under the constraints of 2 nT < |B| < 3.5 nT and 55° < θ < 75°.The dots represent the total escape rate.The dashed lines are linear fits to the total escape.The solid dot lines show the plume escape rate and the dashed dot lines show the tail escape rate.The black and blue colors correspond to the high and low EUV periods, respectively.

Figure 5 .
Figure 5.The configuration of the magnetic field in the Y MSO -Z MSO plane sliced at X MSO = 0.All three cases satisfy 2 nT < |B| < 3.5 nT and 55° < θ < 75°.The extreme ultraviolet radiation is different in (a) and (b).The solar wind dynamic pressure is different in (b) and (c).

Figure 6 .
Figure 6.The escape rates of three heavy ion species during different extreme ultraviolet (EUV) flux and solar wind dynamic pressure conditions, under the constraints of 2 nT < |B| < 3.5 nT and 55° < θ < 75°.The solid lines are during the high EUV radiation, while the dashed lines are during low EUV radiation.The black lines are the total escape of O + , the red lines are the total escape of  O + 2 , and the green lines are the total escape of  CO + 2 .

Figure 7 .
Figure 7.The magnitude of the magnetic field, the total electric field strength, and the magnitude of three components of electric field in the X MSO -Y MSO plane sliced at Z MSO = 0 for two different solar wind dynamic pressure cases.(a) and (f) show the magnitude of the magnetic field.(b) and (g) show the electric field.(c) and (h) show the motional electric field (−V × B).(d) and (i) show the Hall electric field (J × B).(e) and (j) show the ambipolar electric field.Note that the blank area on the nightside region in these three electric field terms has a nonzero resistivity term in our hybrid equation (Q.Zhang et al., 2023).

Figure 8 .Figure 9 .
Figure 8.(a) The escape rate of different interplanetary magnetic field (IMF) strength cases under the constraint of high extreme ultraviolet flux period, 1.2 nPa < P sw < 1.6 nPa and 45° < θ < 75°.The black line shows the total escape rate for seven cases.The red line represents the tail escape.The blue line represents the plume escape.(b) The escape rate of three heavy ion species in different IMF strength cases.The black line is the total escape of O + , the red line is the total escape of  O + 2 , and the green line is the total escape of  CO + 2 .

Figure 10 .
Figure 10.The escape rates for different cone angle cases under the constraints of high extreme ultraviolet radiation, 0.55 nPa < P sw < 0.65 nPa, and 2.5 nT < |B| < 3.5 nT.(a) The black line shows the total escape rate of the nine cases.The red line represents the tail escape.The blue line represents the plume escape.(b) The black line is the total escape of O + , the red line is the total escape of  O + 2 , and the green line is the total escape of  CO + 2 .

Figure 11 .
Figure 11.The escape rates of all cases under the constraint of a high extreme ultraviolet period and 0.55 nPa < P sw < 0.65 nPa.The black, red, and blue lines represent the total, tail, and plume escape rates, respectively.In each case, the green dashed line sharing the y-axis with the escape rate is the magnitude of the convective electric field.(a) Different cone angle cases under the extra constraints of 2 nT < |B| < 3 nT and 300 km/s < |V| < 360 km/s.(b) Different interplanetary magnetic field strength cases under the extra constraints of 100° < θ < 120° and 300 km/s < |V| < 350 km/s.(c) Different solar wind velocity cases under the extra constraints of 50° < θ < 70° and 2 nT < |B| < 3 nT.(d) The escape rates of all cases (orbits) in (a), (b), and (c).The blue dashed line is the least squares fit of the blue dots.