基于螺旋度的粒子再标记算符和无耗散不可压缩Hall磁流体力学的简正模展开
Helicity-based, particle-relabeling operator and normal mode expansion of the dissipationless incompressible Hall magnetohydrodynamics
摘要：
从拉格朗日力学的观点研究了不可压缩、无耗散霍尔磁流体动力学介质的动力学行为。混合和磁螺旋出现，分别从应用程序的粒子重标记对称性的离子和电子流的Noether的第一定理，而与该定理相关的运动常数一般是由他们的任意线性组合。此外，与不变作用量相关的积分路径变分通过积分微分算子在参考路径上的运算来表示，该算子的特征函数是双Beltrami流，即运动方程的无力定常解，并提供了一族正交函数基，从而得到了形式非常简单的运动方程的谱表示.在考虑均匀背景磁场和霍尔项效应消失极限的双重Beltrami流中，广义Elsasser变量最适合于避免标准磁流体力学极限中的奇异性问题。
英文摘要：
The dynamics of an incompressible, dissipationless Hall magnetohydrodynamic medium are investigated from Lagrangian mechanical viewpoint. The hybrid and magnetic helicities are shown to emerge, respectively, from the application of the particle relabeling symmetry for ion and electron flows to Noether's first theorem, while the constant of motion associated with the theorem is generally given by their arbitrary linear combination. Furthermore, integral path variation associated with the invariant action is expressed by the operation of an integro-differential operator on the reference path. The eigenfunctions of this operator are double Beltrami flows, i.e. force-free stationary solutions to the equation of motion and provide a family of orthogonal function bases that yields the spectral representation of the equation of motion with a remarkably simple form. Among the double Beltrami flows, considering the influence of a uniform background magnetic field and the Hall term effect vanishing limit, the generalized Elsasser variables are found to be the most suitable for avoiding problems with singularities in the standard magnetohydrodynamic limit.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
