Abstract

Based on a stochastic microscopic collisional model of the motion of charged particles in a strong external magnetic field, a hierarchy of equations of magnetic hydrodynamics is constructed. The transition to increasingly rough approximations occurs in accordance with a decrease in the dimensioning parameter, similar to the Knudsen number in gas dynamics. The result is stochastic and nonrandom macroscopic equations that differ from the magnetic analog of the Navier–Stokes system of equations, as well as from the systems of magnetic quasi-hydrodynamics. The main feature of this derivation is more accurate velocity averaging due to the analytical solution of stochastic differential equations with respect to the Wiener measure, in the form of which the intermediate meso model is presented in the phase space. This approach differs significantly from the traditional one, which uses not the random process itself but its distribution function. Emphasis is placed on the clarity of assumptions when moving from one level of detail to another, and not on numerical experiments that contain additional approximation errors.

中文翻译：

---

强外部磁场中的随机磁流体动力学层次

摘要

基于带电粒子在强外部磁场中运动的随机微观碰撞模型，构造了磁流体动力学方程的层次结构。与尺寸动力学参数中的克努森数相似，随着尺寸参数的减小，过渡到越来越粗糙的近似值。结果是随机的和非随机的宏观方程，这些方程不同于Navier–Stokes方程组的磁模拟，也不同于磁准流体力学系统。这种推导的主要特征是，由于随机微分方程相对于Wiener测度的解析解，因此速度平均更准确，在相空间中以中间介观模型的形式表示。这种方法与传统方法有很大不同，传统方法不使用随机过程本身，而是使用其分布函数。从一个细节层次转移到另一个细节层次时，重点放在假设的清晰性上，而不是在包含其他近似误差的数值实验上。