基于动力学熵的分布函数非麦克斯韦性度量：理论与模拟
Kinetic Entropy-Based Measures of Distribution Function Non-Maxwellianity: Theory and Simulations
摘要：
我们研究了等离子体中分布函数的非麦克斯韦性的基于动力学熵的测量，即，局部分布函数与相关麦克斯韦分布函数的偏离的基于熵的测量，该麦克斯韦分布函数具有与局部分布相同的密度、体积流量和温度。首先，我们考虑Kaufmann和Paterson [{ \it J.~ Geophys.~ Res.，} { \bf 114}，A00 D 04（2009）]，评估其性质并导出等效形式。为了提供一个定量的理解，我们推导出三个常见的非麦克斯韦等离子体分布函数的解析表达式。我们表明，有不可取的功能，这种非麦克斯韦措施，包括它可以在各种物理限制发散，并阐明了发散的原因。然后，我们引入了一个新的动力学熵为基础的非麦克斯韦测度的速度空间动力学熵密度，它有一个有意义的物理解释，不发散。我们使用无碰撞粒子模拟的二维反平行磁重联，以评估动力学熵为基础的非麦克斯韦措施。我们发现，区域的非零非Maxwellianity与动力学过程中发生的磁重联。我们还表明，模拟的非Maxwellianity同意相当不错的分布类似的分析计算的预测。这些结果对于应用可能是重要的，因为非麦克斯韦性可用于识别动力学尺度物理或等离子体中增加的耗散的区域。
英文摘要：
We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e., entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow, and temperature as the local distribution. First, we consider a form previously employed by Kaufmann and Paterson [{\it J.~Geophys.~Res.,} {\bf 114}, A00D04 (2009)], assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.
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