A new shock fitting procedure for the MHD Rankine-Hugoniot relations for the case of small He2+ slippage
A new shock fitting procedure for the MHD Rankine-Hugoniot relations for the case of small He2+ slippage
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小 He2 滑移情况下 MHD Rankine-Hugoniot 关系的新冲击拟合程序
DOI：
10.1029/2005ja011449
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发表时间：
2006-09
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为了研究空间MHD激波，从观测到的等离子体和磁场参数中找到激波参考系是很重要的。这些激波参数必须满足朗肯-雨果尼奥关系。在这项研究中，我们提出了一种新的程序冲击拟合的单流体各向异性Rankine-Hugoniot关系和两个航天器观测之间的时间差的情况下，小氦2+滑移。这里，使用蒙特-卡罗计算和最小化技术。在我们的程序中使用的观测变量包括上游和下游磁场，等离子体密度，等离子体β，等离子体各向异性，W（下游和上游速度之间的差异，W = V-2 - V-1），和Δ t（两个航天器观测之间的时间差），其中V被定义为等离子体的质心速度。定义了基于计算值和观测值之间的差异的损失函数，并通过搜索最小损失函数值来找到最佳拟合解。对于不能很好地拟合的激波，我们在修正的RH关系中引入了两个新的参数，一个在正常的动量通量方程中，另一个在能量通量方程中。这两个参数被解释为相对湿度关系中所需的等效“正常动量”和“热量”通量。它们在系统中提供了两个自由度，并且它们的量可以从我们的过程中估计。几个合成冲击验证我们的程序。我们也适用于两个行星际激波观测的风和Geotail航天器。结果表明，我们的方法适用于合成和真实的冲击。我们已经表明，我们的方法可以提供准确的冲击正常估计垂直和平行冲击以及。考虑到我们的模型是基于RH关系，不包括α粒子（He 2+）滑移的影响，它只能适用于可压缩的滑移压力张量的情况。我们已经调查了压力张量由于α粒子滑移使用风航天器数据。结果表明，一般情况下，滑移压力与系统的热压力相比很小，可以忽略不计。因此，我们的模型可以适用于大多数行星际激波观测附近的黄道平面。当滑移压力较大时，磁共面定理不再成立。一个更一般的模型，涉及滑移压力张量是一个主要的和重要的发展，超出了本研究的范围。
To study MHD shocks in space, it is important to find the shock frame of reference from the observed plasma and magnetic field parameters. These shock parameters have to satisfy the Rankine-Hugoniot relations. In this study we present a novel procedure for shock fitting of the one-fluid anisotropic Rankine-Hugoniot relations and of the time difference between two spacecraft observations in the case of small He2+ slippage. Here, a Monte-Carlo calculation and a minimization technique are used. The observed variables including the upstream and downstream magnetic fields, plasma densities, plasma betas, plasma anisotropies, W (the difference between the downstream and upstream velocities, W = V-2 - V-1), and Delta t (the time difference between two spacecraft observations) are used in our procedure where V is defined as the center of mass velocity of plasmas. A loss function based on a difference between the calculated and the observed values is defined, and the best fit solution is found by searching for the minimum loss function value. For shocks that cannot be fitted well, we introduce two new parameters in the modified RH relations, one in the normal momentum flux and the other in the energy flux equations. These two parameters are interpreted as the equivalent "normal momentum" and "heat" fluxes needed in the RH relations. They provide two degrees of freedom in the system, and their amounts can be estimated from our procedure. Several synthetic shocks are given to verify our procedure. We also apply this procedure to two interplanetary shocks observed by both the WIND and Geotail spacecraft. The results demonstrate that our method works for both the synthetic and the real shocks. We have shown that our method can provide accurate shock normal estimations for perpendicular and parallel shocks as well. Given that our model is based on the RH relations that do not include the effect of alpha particle (He2+) slippage, it can only be applied to the cases with an ignorable slippage pressure tensor. We have investigated the pressure tensor due to alpha particle slippage using the WIND spacecraft data. It is found that in general the slippage pressure is small in comparison with the thermal pressure of the system and can be ignored. Thus our model can be applied to most interplanetary shocks observed near the ecliptic plane. However, when the slippage pressure is large, the magnetic coplanarity theorem is not valid any more. A more general model that involves slippage pressure tensor is a major and important development that is beyond the scope of the present study.
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DOI：
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发表时间：
1970
期刊：
--
影响因子：
--
作者：
J. Chao
通讯作者：
J. Chao
影响因子：
--
作者：
C. Russell;M. Mellott;E. Smith;J. King
通讯作者：
C. Russell;M. Mellott;E. Smith;J. King
影响因子：
--
作者：
J. Chao;B. Goldstein
通讯作者：
J. Chao;B. Goldstein
影响因子：
2.6
作者：
A. Coates;A. Johnstone;R. Kessel;D. Huddleston;B. Wilken;K. Jockers;F. Neubauer;H. Rème
通讯作者：
A. Coates;A. Johnstone;R. Kessel;D. Huddleston;B. Wilken;K. Jockers;F. Neubauer;H. Rème
影响因子：
--
作者：
P. Yoon;A. Lui
通讯作者：
P. Yoon;A. Lui