Closed orbits of MHD equilibria with orientation-reversing symmetry

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-06-16 DOI:10.1016/j.physd.2025.134762

David Perrella

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引用次数: 0

Abstract

As a generalisation of the periodic orbit structure often seen in reflection or mirror symmetric MHD equilibria, we consider equilibria with other orientation-reversing symmetries. An example of such a symmetry, which is a not a reflection, is the parity transformation

(x, y, z) \mapsto (- x, - y, - z)

R^{3}

. It is shown under any orientation-reversing isometry, that if the pressure function is assumed to have toroidally nested level sets, then all orbits on the tori are necessarily periodic. The techniques involved are almost entirely topological in nature and give rise to a handy index describing how a diffeomorphism of

R^{3}

alters the poloidal and toroidal curves of an invariant embedded 2-torus.

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具有方向反转对称的MHD平衡的闭合轨道

作为在反射对称或镜像对称MHD平衡中常见的周期轨道结构的推广，我们考虑了具有其他方向反转对称性的平衡。这种对称的一个例子，它不是反射，是宇称变换（x,y,z）在R3中的（- x, - y, - z）。在任意方向反转等距下，如果假设压力函数具有环面嵌套的水平集，则环面上的所有轨道都必然是周期性的。所涉及的技术在本质上几乎完全是拓扑的，并且产生了一个方便的指标来描述R3的微分同构如何改变不变嵌入2环面的极向和环向曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.