Interpreting Mars ionospheric anomalies over crustal magnetic field regions using a 2-D ionospheric model
使用二维电离层模型解释火星地壳磁场区域电离层异常

2.1 Input and Boundary Conditions
2.1 输入和边界条件

The model takes as input a diurnally fixed neutral atmosphere derived from lower boundary (homopause) mixing ratios of CO₂, O, CO, Ar, N₂, and H₂ taken from the Mars Climate Database (version 5.1) using solar minimum conditions at 120–150° solar longitude, 42°S latitude and 15°E longitude [Forget et al., 1999; Lewis et al., 1999; Millour et al., 2014]. Solar minimum flux input at Mars is generated by the Solar Irradiance Platform [Tobiska, 2004] for Earth and is then scaled to Mars' location. Plasma temperatures are derived from Viking Lander 1 measurements [Hanson et al., 1977; Hanson and Mantas, 1988], with the electron temperature extrapolated downward and adjusted for local conditions as described in Mendillo et al. [2011]. A slice along the meridian of the magnetic field morphology representative of a strong crustal magnetic field region was then used to investigate plasma dynamics in the ionosphere, as will now be described.
该模型以来自火星气候数据库（5.1版）的CO ₂ 、O、CO、Ar、N ₂ 和H ₂ 的下边界（同温层）混合比为输入，这些混合比取自太阳赤经120-150°、南纬42°和东经15°的太阳最小条件[Forget等人，1999；Lewis等人，1999；Millour等人，2014]。火星上的太阳最小通量输入由地球的太阳辐射平台生成[Tobiska，2004]，然后根据火星的位置进行缩放。等离子体温度来自维京1号着陆器的测量数据[Hanson等人，1977；Hanson和Mantas，1988]，电子温度向下推算，并根据Mendillo等人[2011]描述的当地条件进行调整。然后，我们使用代表强地壳磁场区域的磁场形态子午线切片来研究电离层中的等离子体动力学，下文将对此进行描述。

Components of the magnetic field at Mars have been measured by Mars Global Surveyor (MGS) during its mapping orbit at 400 km altitude [Acuña et al., 2001]. Using these measurements, models have been used to generate global magnetic field maps that cover altitudes down to the surface [Purucker et al., 2000; Connerney et al., 2001; Arkani-Hamed, 2001, 2004; Voorhies et al., 2002; Cain et al., 2003; Langlais et al., 2004; Morschhauser et al., 2014]. At ionospheric altitudes, the characteristics of a strong crustal magnetic field are analogous to those of a dipole. Using the computational simplification of an ad hoc regional dipole field with a magnetic moment of 1.5×10¹⁰ JT⁻¹, placed 100 km below the surface, as shown in Figure 1, adequately simulates the magnitude and direction of an observed strong crustal field within the model spatial boundaries [e.g., Brain et al., 2003; Arkani-Hamed, 2004].
火星全球勘测器（MGS）在400公里高空的测绘轨道上测量了火星磁场的组成部分[Acuña等人，2001]。利用这些测量数据，研究人员通过模型绘制了全球磁场图，其覆盖范围从高空一直延伸到地表[Purucker et al., 2000; Connerney et al., 2001; Arkani-Hamed, 2001, 2004; Voorhies et al., 2002; Cain et al., 2003; Langlais et al., 2004; Morschhauser et al., 2014]。在电离层高度，强地壳磁场的特性与偶极子相似。如图1所示，通过计算简化，模拟出位于地表以下100公里处、磁矩为1.5×10 ¹⁰ JT ⁻¹ 的特设区域偶极子磁场，可以充分模拟出模型空间边界内观测到的强地壳磁场的强度和方向[例如，Brain等人，2003；Arkani-Hamed，2004]。

In Figure 1, a selected region of strong crustal field is compared with the field produced by a simplified dipole. In Figure 1a we show arcade-like looped field lines of a strong crustal field region at Mars [e.g., Riousset et al., 2014], located between 50°S and 68°S, centered at 180°E and spanning ~18° in latitude. The simplified dipole analog shown in Figure 1b has a field strength of ~1000 nT at the lower boundary and ~100 nT at the upper boundary and has a similar spatial extent to the observationally constrained field in Figure 1a. This chosen region of strong crustal field contains both horizontal and vertical field lines. To ensure an open field line cusp-like morphology at the edges, an inclination of ±90° is imposed on the right and left edges of the simulation window (shown in subsequent figures). This is done to capture both closed and open field plasma dynamics. The spatial resolution in the model is 10 km vertically and 100 km horizontally. The analytical expression of a dipole field in Figure 1a is used as the input magnetic field in the model used here.
在图1中，将选定的强地壳磁场区域与简化偶极子产生的磁场进行了比较。在图1a中，我们展示了火星上强地壳磁场区域的拱廊状环形磁场线[例如，Riousset等人，2014]，该区域位于南纬50°和68°之间，以东经180°为中心，横跨纬度约18°。图1b中所示的简化偶极子模拟在低边界处场强约为1000 nT，在低边界处场强约为100 nT，其空间范围与图1a中观测约束的场相似。这个选定的强地壳磁场区域包含水平和垂直磁场线。为了确保边缘处出现开放的场线尖角状形态，在模拟窗口的左右边缘施加了±90°的倾斜度（在后续图中显示）。这样做是为了捕捉闭合和开放场等离子体动力学。模型的空间分辨率为垂直方向10公里，水平方向100公里。图1a中偶极场的解析表达式在此模型中用作输入磁场。

The boundary conditions used in the model simulations are similar to those described in previous works [e.g., Mendillo et al., 2011; Matta et al., 2013, 2014]. In summary, no transport occurs at the lower boundary, and the upper boundary is constrained such that at every topside horizontal grid, ion densities decrease exponentially with a fixed plasma scale height determined by zero velocity conditions. No plasma drifts through the left or right edges of the simulation region due to the imposed vertical field line structure at those boundaries.
模型模拟中使用的边界条件与之前的工作[例如，Mendillo等人，2011；Matta等人，2013，2014]中描述的边界条件相似。总之，下边界没有发生传输，上边界受到约束，使得在每个顶部水平网格处，离子密度以指数形式下降，其下降速度由零速度条件决定的固定等离子体尺度高度决定。由于在模拟区域的左右边缘施加了垂直场线结构，因此不存在等离子体在这些边缘处漂移的现象。

2.2 Processes and Assumptions
2.2 流程和假设

The model runs for a Martian day with a time step of ~0.8 s. For each time step, ions are affected by chemical production and loss. Plasma moves due to density and plasma temperature gradients, gravity, and collisions. In the crustal field region analyzed in this work, the gyrofrequency of electrons and ion species exceeds the corresponding collision frequency above ~130 km, and so plasma transport in the fluid model is additionally affected by gyromotion along field lines. For each point in time in the simulation, the electron density is taken as the sum of all ion densities.
模型以约0.8秒的时间步长运行一个火星日。在每个时间步长内，离子会受到化学反应和损失的影响。等离子体因密度和等离子体温度梯度、重力以及碰撞而移动。在本研究分析的地壳磁场区域，电子和离子种类的自转频率在130公里以上时超过了相应的碰撞频率，因此流体模型中的等离子体传输还受到沿磁场线的自转运动的影响。在模拟的每个时间点，电子密度取为所有离子密度的总和。

The model simulates an ionosphere geographically centered at 50°S latitude, 180°E longitude during Northern Winter, resulting in a solar zenith angle (SZA) diurnal range of 30° to 110°. The solar zenith angle, neutral atmosphere, solar flux, and chemical quantities used as input are assumed to remain constant across the horizontal range for each moment in local time. These assumptions are made to isolate the effects of transport from possibly varying photochemical background conditions. Rectangular coordinates are adopted to represent the simulation window that is small with respect to the planet radius.
该模型模拟了北半球冬季时地理中心位于南纬50°、东经180°的电离层，太阳天顶角（SZA）的日变化范围为30°至110°。太阳天顶角、中性大气、太阳辐射通量和化学量作为输入，在当地时间每个时刻的水平范围内保持不变。这些假设是为了将传输的影响与可能变化的光化学背景条件分开。采用矩形坐标来表示相对于行星半径而言很小的模拟窗口。

At the upper boundary of the simulation window (400 km), the strong crustal field magnetic pressure is larger than the typical solar wind ram pressure [e.g., Dubinin et al., 2008b]. For the conditions simulated in this work, the ionospheric topside plasma is considered to be free of any solar wind interactions.
在模拟窗口的上限（400公里），强大的地壳磁场压力大于典型的太阳风冲压压力[例如，Dubinin等人，2008b]。对于本研究中模拟的条件，电离层顶部的等离子体被认为与太阳风没有相互作用。

2.3 Two-Dimensional Transport
2.3 二维运输

The physical processes implemented in the 1-D version of the BU Mars Ionosphere Model are described in detail in Mendillo et al. [2011]. In this section, we describe the additions to the model that have been incorporated to implement horizontal as well as vertical plasma transport.
Mendillo等人[2011]详细描述了BU火星电离层模型一维版本中实施的物理过程。在本节中，我们将介绍模型中新增的用于实现水平及垂直等离子体传输的功能。

At Mars, ionospheric plasma is considered to be Maxwellian, partially ionized, and collision dominated. The vector equations of motion for electrons and ions are [Banks and Kockarts, 1973]
在火星上，电离层等离子体被认为是麦克斯韦的，部分电离，以碰撞为主。电子和离子的运动矢量方程为[Banks和Kockarts，1973]

(1)

(2)

where subscripts e and i refer to electrons and ions, respectively, v_e and v_i are the electron and ion velocities in cm s⁻¹, t is time in seconds, ρ_e and ρ_i are the electron and ion mass densities m_en_e and m_in_i in gr cm⁻³, P_e and P_i are the electron and ion pressures n_ek_bT_e and n_ik_bT_i in eV cm⁻³, is the acceleration of gravity in cm s⁻², q_e and q_i are the electron and ion charges −e and +e in esu, is the polarization electric field that maintains electrical charge neutrality in the plasma (n_e = ∑n_i), c is the speed of light, is the magnetic field with magnitude in nanotesla, and are the collisional terms of electrons and ions described next, m_e and m_i are the electron and ion masses in grams, n_e and n_i are the electron and ion number densities in cm⁻³, k_b is the Boltzmann constant in eV K⁻¹, and T_e and T_i are the electron and ion temperatures, respectively, in degrees Kelvin.
其中，下标e和i分别代表电子和离子，v _e 和v是电子和离子的速度（单位：厘米/秒 ⁻¹ ），t是时间（单位：秒），ρ _e 和ρ是电子和离子的质量密度（单位：克/厘米 _e ），n _e 和mn是电子和离子的数量（单位：克/厘米 ⁻³ ），P _e 和 P 是电子和离子的压力 n _e k _b T _e 和 nk _b T 是电子伏特厘米 ⁻³ ， 是重力加速度厘米秒 ⁻² ， q _e 和 q 是电子和离子的电荷负电荷和正电荷电子伏特， 是维持等离子体电荷中性的极化电场（n _e = ∑n），c 是光速， 是强度为毫微特斯拉的磁场， 和 是接下来描述的电子和离子的碰撞项，m _e 和 m 是电子和离子的质量（单位：克），n _e 和 n 是电子和离子的数量密度（单位：厘米 ⁻³ ），k _b 是玻尔兹曼常数（单位：电子伏特 K ⁻¹ ），T _e 和 T 分别是电子和离子的温度（单位：开尔文）。

Ion-ion collisions are significant in the Martian ionosphere at altitudes where vertical transport is important [Matta et al., 2013]. Consequently, the collision terms and become
在火星电离层中，离子碰撞在垂直传输非常重要的海拔高度上非常重要[Matta等人，2013]。因此，碰撞项 和 变为

(3)

(4)

where the collision term for electrons ν^′_et includes both electron-neutral and electron-ion collision frequencies in hertz and the collision term for ions ν^′_it includes both the ion-neutral (ν^′_in) and ion-ion (ν^′_ij) collision frequencies.
其中电子碰撞项ν _et 包括电子-中性粒子和电子-离子碰撞频率（单位为赫兹），离子碰撞项ν _it 包括离子-中性粒子（ν _in ）和离子-离子（ν _ij ）碰撞频率。

Convection is neglected for all species. Terms with an electron mass dependence are orders of magnitude smaller than equivalent ion terms and so are also assumed to be negligible. As a result, the equations of motion become
对所有物种而言，对流效应可以忽略不计。与电子质量相关的项比等效离子项小几个数量级，因此也可以忽略不计。因此，运动方程变为

(5)

(6)

where ν_inT is the ion-neutral collision frequency summed over all neutral species. Neutral winds are assumed to be negligible with respect to ion transport velocities.
其中，ν _inT 是所有中性物质的总离子-中性碰撞频率。假设中性风相对于离子传输速度可以忽略不计。

As mentioned above, charged particle motion is confined to flow along field lines in areas of strong crustal fields (as demonstrated in Mendillo et al. [2011]), and we assume that this is a starting point for exploration. Equations 5 and 6 can then be solved for the parallel components to the field lines () that reduce the term for electron and ion equations to zero, giving
如上所述，带电粒子运动仅限于沿强地壳磁场区域中的场线流动（如Mendillo等人[2011]所证明），我们假设这是探索的起点。然后，方程5和6可以求解为与场线（ ）平行的分量，将电子和离子方程的 项减为零，得到

(7)

(8)

The electric field term can be eliminated to give the following:
可以去掉电场项，得到：

(9)

This equation is then solved for the field-aligned velocity and its components projected to get the vertical (toward zenith) and horizontal (parallel to the surface) components v_z and v_x, respectively, for each ion.
然后求解该方程，得到每个离子的场向速度及其投影分量，分别得到垂直分量（朝向天顶）和水平分量（平行于表面），记为v _z 和v _x 。

Assuming dx, dz, and ds to be unit lengths along the horizontal, vertical, and magnetic field line, respectively, the unit vectors of each direction , , and ŝ, respectively, are related as follows:
假设dx、dz和ds分别表示水平、垂直和磁场线上的单位长度，则每个方向的单位矢量 、 和ŝ之间的关系如下：

(10)

(11)

(12)

where I is the inclination angle that the magnetic field line B makes with the horizontal.
其中，i是磁场线B与水平面的夹角。

The pressure gradient along the field line, , can then be expressed as follows:
沿场线 的压力梯度可以表示为：

(13)

and expanded into the horizontal and vertical components
并扩展为水平和垂直组件

(14)

Similarly, the field-aligned gravity vector is projected along x and z as
同样，场对齐的重力矢量 沿x和z方向投影为

(15)

(16)

The velocity vector along the field line is
沿着磁场线的速度矢量是

(17)

As a result, the horizontal and vertical components of 9 become
因此，9的水平和垂直分量变为

(18)

(19)

The pressure terms, P = nk_bT, are dependent on density and temperature both of which vary with altitude (dz) and the former with latitude (dx) as well. These terms are expanded to give the following:
压力项P = nk _b T取决于密度和温度，而密度和温度又随海拔高度（dz）和纬度（dx）的变化而变化。这些术语扩展如下：

(20)

(21)

where T_p is the plasma temperature defined here as T_i + T_e.
其中T _p 为等离子体温度，此处定义为T + T _e 。

If there are N ion species, then equation 20 gives a set of N linear equations for the N values of v_xi at each grid point. These equations can then be solved for the N values of v_xi using matrix methods. Similarly, equation 21 can be solved for the N values of v_zi. At the lower boundary, all velocity components are set to zero. At the upper boundary, v_xi and v_zi are set to a weighted sum of the respective velocities two grids below [Mendillo et al., 2011]. At the left and right boundaries, all v_x are zero and horizontal gradients do not affect the vertical velocities, v_zi.
如果存在N个离子种类，那么方程20给出了N个线性方程组，用于计算每个网格点处v _xi 的N个数值。然后，可以使用矩阵方法求解这些方程，得到v _xi 的N个值。同样，方程21可以求解v _zi 的N个值。在边界下方，所有速度分量都设置为零。在边界上方，v _xi 和v _zi 被设置为各自速度的加权总和，位于下方两个网格中[Mendillo等人，2011]。在左边界和右边界，所有v _x 均为零，水平梯度不会影响垂直速度v _zi 。

4.1 Plasma in Open Field Regions
4.1 开放区域中的等离子体

Open field regions are regions in the ionosphere where the magnetic field is connected to the planet on one end only. In the model used here, open field regions are the left and right edges of the simulation region and ionospheric plasma can move along these open field lines vertically. In open field regions, the ionosphere is more inflated than in other regions since it is easier here for plasma at lower altitudes to diffuse upward. This is consistent with the Mars Express (MEX) Mars Advanced Radar for Subsurface and Ionospheric Sounding (MARSIS) observations. In subsurface sounding mode, MARSIS obtained total electron content (TEC), a measure of the column of ionospheric electrons between the spacecraft and surface of Mars. For daytime conditions, the model variability was 7.2 to 5.5 TECU (where 1 TEC unit is 10¹⁵ e⁻/m²), consistent with the empirical average of 6 TECU [Mendillo et al., 2013]. For nighttime conditions (shown in the supporting information), the simulated TEC decreases, on average, between vertical and horizontal magnetic field regions, by 88% (from 1.7 to 0.2 TECU) for SZA between 100° and 110°, consistent with observational trends in which the TEC was found to decrease by ~90% from ~0.45 to ~0.05 TECU from vertically to horizontally inclined field regions for a SZA greater than 100° [Safaeinili et al., 2007].
开放区域是指电离层中磁场仅与地球一端相连的区域。在此模型中，开放区域是指模拟区域的左右边缘，电离层等离子体可以沿着这些开放区域线垂直移动。在开放区域，电离层比其它区域膨胀得更大，因为低纬度等离子体更容易向上扩散。这与火星快车（MEX）火星地下和电离层探测高级雷达（MARSIS）的观测结果一致。在次表层探测模式下，MARSIS获得了总电子含量（TEC），这是航天器与火星表面之间电离层电子柱的测量值。对于白天的情况，模型变化范围为7.2至5.5 TECU（其中1 TEC单位为10 ¹⁵ e ⁻ /m ² ），与6 TECU的经验平均值一致[Mendillo等人，2013]。对于夜间条件（如支持信息所示），在100°至110°的SZA范围内，垂直磁场区域和水平磁场区域之间的模拟TEC平均下降88%（从1.7下降到0.2 TECU），这与观测趋势一致，即对于大于100°的SZA，从垂直磁场区域到水平磁场区域，TEC从约0.45下降到约0.05 TECU，降幅约为90% [Safaeinili等人，2007]。

Since there is more plasma in open field regions than in other regions, the density of electrons and ions above 200 km is larger than in other regions, resulting in a higher plasma pressure that can stand off the shocked solar wind plasma at higher altitudes. This is consistent with MGS Magnetometer and Electron Reflectometer measurements that showed the boundary separating ionospheric plasma from the shocked solar wind plasma to be at higher altitudes in regions of strong vertical (open) field regions compared to observations in other regions [Mitchell et al., 2001].
由于开放区域中的等离子体比其他区域多，因此200公里以上的电子和离子密度比其他区域大，导致等离子体压力更高，从而在更高的高度抵御冲击的太阳风等离子体。这与MGS磁强计和电子反射计的测量结果一致，该测量结果显示，与其他地区的观测结果相比，强垂直（开放）磁场区域电离层等离子体与冲击太阳风等离子体的边界位于更高的高度[Mitchell等人，2001]。

The ionospheric sounding mode of MARSIS returned topside profiles of electron density down to the peak [Picardi et al., 2005]. The first analysis of MARSIS topside sounder measurements showed oblique echoes to occur in the ionosphere above strong crustal vertical field regions that was attributed to solar wind heating of the ionosphere [Gurnett et al., 2005; Nielsen et al., 2007a]. In a follow up study, these features were characterized to extend, on average, ~20 km above the ionosphere in regions of no vertical crustal fields, when sampled at 1.9 MHz. These features generally occurred in cusp-like regions where the field strength at ~150 km exceeded 150 nT [Duru et al., 2006]. A 1.9 MHz sounding frequency corresponds to a plasma density of 4×10⁴ cm⁻³. In the model simulations, plasma layers with densities of 4×10⁴ cm⁻³, 3×10⁴ cm⁻³, 2×10⁴ cm⁻³, and 1×10⁴ cm⁻³ (shown in Figure 4) vary in altitude across magnetic field structure by 2, 5, 20, and 50 km, respectively. The variability with altitude trends are consistent with MEX topside sounder observations, but the densities whose altitude varies by 20 km with magnetic field inclination differ by a factor of 2 (green line in Figure 4). One reason for this discrepancy may be due to the assumption of fixed electron temperature in the model. If the electron temperature were higher in open field regions than in closed field regions, then the recombination coefficient of ions and electrons—that is inversely proportional to Te^0.7—would therefore decrease, leaving more electrons in open field regions compared with similar altitudes in closed field regions. This would cause the contours in Figure 4 to move to higher altitudes, or equivalently, for the existing contours to correspond to higher densities.
MARSIS的电离层探测模式返回了电子密度峰值的上部剖面[Picardi等人，2005]。对MARSIS顶部探测仪测量数据的首次分析表明，在强地壳垂直磁场区域上方的电离层中存在斜向回波，这是由于太阳风加热电离层所致[Gurnett等，2005；Nielsen等，2007a]。在后续研究中，这些特征被描述为在无垂直地壳场的区域，当以1.9 MHz的频率采样时，平均延伸至电离层上方约20公里处。这些特征通常出现在类似尖顶的区域，其150公里处的磁场强度超过150 nT [Duru等人，2006]。1.9 MHz探测频率对应4×10 ⁴ cm ⁻³ 的等离子体密度。在模型模拟中，密度分别为4×10 ⁴ cm ⁻³ 、3×10 ⁴ cm ⁻³ 、2×10 ⁴ cm ⁻³ 和1×10 ⁴ cm ⁻³ 的等离子体层（如图4所示）在磁场结构中的高度变化分别为2、5、20和50公里。随高度变化的趋势与MEX顶部探测器的观测结果一致，但随磁场倾斜度变化20公里的密度却相差2倍（图4中的绿线）。造成这种差异的一个原因可能是模型中假设的电子温度是固定的。如果开放区域中的电子温度高于封闭区域，那么离子和电子的复合系数（与 Te ^0.7 成反比）就会降低，与封闭区域中相似高度相比，开放区域中会有更多的电子。 这将导致图4中的等值线向更高海拔移动，或者等效地，使现有等值线对应更高的密度。

4.2 Plasma in Horizontal Field Regions
4.2 水平磁场区域中的等离子体

Horizontal field regions are regions in the ionosphere where the magnetic field is parallel or near parallel to the surface. In the model used here, horizontal field regions are the centermost latitudes of the simulation region. In these regions, horizontal drifts due to plasma pressure gradients move plasma particles centerward for both positive and negative inclinations of the field lines. As a result, plasma is pushed toward the local magnetic equator where it gets trapped. The effects of this trapping on plasma density become more apparent above 170 km, where the effects of collisions between plasma and the neutral atmosphere become negligible compared with plasma transport processes. In regions near the simulation latitudes 3–7° and 12–18° in Figures 2, 3a, and 4, plasma is swept toward the inner region of horizontal field lines, depleting the ionosphere in nearby regions. In Figures 2d and 2e, central latitude plasma above the peak is trapped in between the 7° and 12° latitude region creating the dome-like structure above 180 km at centermost latitudes. This is demonstrated in Movie S1 in the supporting information. Due to the meridional symmetry of the dipole magnetic field used here, closed field line plasma remains trapped until the Sun begins to set and the reduced solar flux and chemical recombination reduces its abundance. These results are consistent with both empirical evidence of heavy ion escape fluxes [e.g., Nilsson et al., 2011] as well as MHD modeling results [e.g., Ma et al., 2002] that show less ionospheric plasma escaping over closed magnetic field regions than over other locations on the planet due to trapping along closed field lines.
水平磁场区域是指电离层中磁场与表面平行或接近平行的区域。在此模型中，水平磁场区域是模拟区域的最中心纬度。在这些区域中，由于等离子体压力梯度引起的水平漂移使等离子体粒子向中心移动，无论磁场线的倾斜度是正还是负。因此，等离子体被推向局部磁赤道并被束缚在那里。在170公里以上，这种对等离子体密度的捕获效应变得更加明显，此时等离子体和中性大气之间的碰撞效应与等离子体传输过程相比变得微不足道。在图2、图3a和图4中模拟纬度3-7°和12-18°附近的区域，等离子体被扫向水平场线的内部区域，耗尽了附近区域的电离层。在图2d和2e中，峰值上方的中心纬度等离子体被困在7°和12°纬度区域之间，在最中心的纬度上方180公里处形成圆顶状结构。辅助信息中的视频S1对此进行了演示。由于此处使用的偶极磁场具有子午线对称性，闭合的场线等离子体会一直被困，直到太阳开始落下，太阳辐射通量减少，化学重组降低其丰度。这些结果与重离子逃逸通量的经验证据（例如Nilsson等人，2011年）以及MHD建模结果（例如Ma等人，2002年）相一致，后者表明，由于沿闭合磁场线的捕获作用，电离层等离子体在闭合磁场区域逃逸的数量少于在地球其他位置逃逸的数量。

At the centralmost region of the simulation window, vertical transport is inhibited by a horizontal magnetic field. Below 170 km, plasma in this central region is not subject to significant transport in any direction. As a result, the ionosphere in horizontal magnetic field regions appears to be in photochemical equilibrium up to 200 km, well above the typical photochemical boundary of 150–170 km [Mendillo et al., 2011; Matta et al., 2013]. This is consistent with Mariner 9 and Viking Orbiter observations made over induced field regions (these are regions where the magnetic field is induced by the solar wind interaction with the ionosphere and results in a predominantly horizontal field) that report photochemical-like scale heights above the ionospheric peak [Kliore, 1992; Breus et al., 1998; Ness et al., 2000].
在模拟窗口的最中心区域，水平磁场抑制了垂直传输。在170公里以下，中心区域的等离子体不会向任何方向发生显著传输。因此，水平磁场区域的电离层似乎在200公里范围内处于光化学平衡状态，远高于150-170公里的典型光化学边界[Mendillo等人，2011；Matta等人，2013]。这与“水手9号”和“海盗号”轨道飞行器在感应场区域（这些区域中的磁场是由太阳风与电离层相互作用产生的，并导致主要水平磁场）的观测结果一致，这些观测结果报告了电离层峰值上方类似光化学的尺度高度[Kliore，1992；Breus等人，1998；Ness等人，2000]。

In the central regions where the field lines are horizontal, simulation transport velocities above 200 km reach 400 m/s, consistent with results from another model that achieved best agreement with Mariner 9 and Viking Orbiter observations made over induced field regions when an ad hoc horizontal transport velocity of 400 m/s at 210 km was used [Krymskii et al., 1995].
在磁场线水平的中部区域，模拟的传输速度超过200公里，达到400米/秒，这与另一个模型的结果一致，该模型在210公里处使用400米/秒的临时水平传输速度时，与Mariner 9号和Viking Orbiter号在感应磁场区域进行的观测结果最为接近[Krymskii等人，1995]。

4.3 Plasma in Midinclination Field Regions
4.3 中倾场区域的等离子体

Midinclination field regions are considered as regions in the ionosphere where the magnetic field is closed and has an inclination that is neither purely vertical nor horizontal. In the model used here, midinclination field regions are the intermediate regions between the left, central, and right edges of the simulation region.
中倾角场区域是指电离层中磁场闭合且倾角既非垂直也非水平的区域。在此模型中，中倾角磁场区域是指模拟区域左、中、右边缘之间的中间区域。

The topside electron density profiles of various regions of the ionosphere in the simulated dipolar crustal field region are shown in Figure 5a for local noon. The cusp regions have a vertically pointing magnetic field with inclination angle I_B = ±90°. When compared with other magnetized regions, the density of plasma near open magnetic field lines drops off less sharply with altitude. At 170 km, the plasma scale height, averaged over both SZAs shown in Figure 5, is 80 km near open field regions compared to 32 km over closed field regions. It is not practical to compare the model electron density profiles directly against those observed using radio occultation techniques since the latter covers a horizontal region of ~200 km (~3° in latitude), that is, wider than the model horizontal resolution [Tyler et al., 1992].
图5a显示了模拟双极地壳磁场区域中电离层不同区域的顶部电子密度分布。尖角区域具有垂直指向的磁场，倾角I _B = ±90°。与其他磁化区域相比，开放磁场线附近的等离子体密度随高度的降低而下降得较慢。在170公里处，如图5所示，开放磁场区域附近的等离子体平均高度为80公里，而闭合磁场区域为32公里。将模型电子密度分布图与使用无线电掩星技术观测到的电子密度分布图直接进行比较是不切实际的，因为后者覆盖的水平区域约为200公里（纬度约为3°），比模型的水平分辨率更宽[Tyler等人，1992]。

We therefore analyze instead observations obtained with the MARSIS active ionospheric sounder instrument to compare with model results. Several hundred topside ionospheric profiles were measured over regions of varying strong crustal field inclination angles when the spacecraft was near 500 km altitude above the surface. In several of these observations, the electron density profile decreased from the characteristic exponential decay with increasing altitude above the peak, as shown in the yellow line of Figure 5b. This observation of a lower density at higher altitudes (noted by a decrease in number density by ~ 10% from an exponentially decaying profile) over the main part of the magnetic arcade, where the inclination angle is between 10° and 80° in strong magnetic field regions, occurred in 37% of 208 profiles analyzed, compared with an occurrence of less than 15% of the time in 356 profiles measured over other regions. A comparable feature is also seen in the simulation results as shown in the yellow profile of Figure 5a, where plasma in these regions is depleted as it is swept away from higher to lower magnetic inclination regions.
因此，我们分析的是用MARSIS主动电离层探测仪获得的观测数据，并与模型结果进行比较。当航天器位于距离地表500公里的高度时，测量了数百个不同强度的地壳磁场倾斜角区域的上层电离层剖面。在几次观测中，电子密度分布随着峰值以上高度的增加而呈指数衰减，如图5b中的黄色线所示。在磁拱的主要部分，即磁场强度为10°至80°的强磁场区域，在208个剖面分析中，有37%的剖面观察到高空密度较低（从指数衰减剖面中可以看出，数量密度降低了约10%），而在其他区域测量的356个剖面中，这种情况只占不到15%。在图5a的黄色剖面图中，模拟结果也显示了类似特征，这些区域中的等离子体从高磁倾角区域被扫到低磁倾角区域时，会逐渐耗尽。

4.4 Open Issues  4.4 待解决的问题

Horizontal transport becomes important above ~170 km. However, vertical transport becomes important above ~150 km [e.g., Mendillo et al., 2011]. This difference in altitude may be physically valid, since transport of plasma depends on gradients of its density and velocity that vary more significantly with altitude than with latitude (equations 20 and 21). Another reason why vertical transport becomes significant at lower altitudes than horizontal transport may be due to the assumption that plasma temperature is the same for all latitudes. As a consequence, transport resulting from horizontal temperature gradients in the simulation is negligible. A more rigorous calculation of plasma temperatures in regions of open and closed field lines is needed to identify any potential discrepancies due to this assumption.
在170公里以上，水平运输变得非常重要。然而，垂直运输在150公里以上变得重要[例如，Mendillo等人，2011]。这种海拔差异可能是有物理依据的，因为等离子体的传输取决于其密度和速度梯度，而密度和速度梯度随海拔变化比随纬度变化更大（公式20和21）。在低海拔地区，垂直传输比水平传输重要的另一个原因可能是由于假设所有纬度的等离子体温度都是相同的。因此，模拟中由水平温度梯度引起的传输可以忽略不计。需要更精确地计算开放和闭合场线区域的等离子体温度，以确定该假设导致的任何潜在差异。

If the plasma temperature were higher at the magnetic equator than at cusp regions of crustal fields, as postulated by Nielsen et al. [2007b], then the horizontal temperature gradient would increase the magnitude of the centerward velocity, enhancing plasma trapping in closed field regions. The simplifications adopted in this work offer guidelines to the relative contribution of horizontal transport to the overall plasma densities.
如果等离子体温度在磁赤道处比在地壳磁场尖角区域更高，正如Nielsen等人[2007b]所推测的那样，那么水平温度梯度将增加向中心方向的流速，从而增强封闭磁场区域中的等离子体捕获。本研究采用的简化方法为水平传输对整体等离子体密度的相对贡献提供了指导。