In ideal MHD, the magnetic flux is advected by the plasma motion, freezing flux-surfaces into the flow. An MHD equilibrium is reached when the flow relaxes and force balance is achieved. We ask what classes of MHD equilibria can be accessed from a given initial state via smooth incompressible ideal motion. It is found that certain boundary displacements are formally not supported. This follows from yet another investigation of the Hahm--Kulsrud--Taylor (HKT) problem, which highlights the resonant behaviour near a rational layer formed by a set of degenerate critical points in the flux-function. When trying to retain the mirror symmetry of the flux-function with respect to the resonant layer, the vector field that generates the volume-preserving diffeomorphism vanishes at the identity to all order in the time-like path parameter.

中文翻译：

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MHD 平衡的刚性使共振表面附近不可压缩的理想运动变得平滑

在理想的 MHD 中，磁通量由等离子体运动平流，将通量表面冻结到流动中。当流动松弛并达到力平衡时，达到 MHD 平衡。我们询问可以通过平滑的不可压缩理想运动从给定的初始状态访问哪些类别的 MHD 平衡。发现某些边界位移在形式上不受支持。这是对 Hahm--Kulsrud--Taylor (HKT) 问题的又一次调查，该问题突出了由通量函数中的一组退化临界点形成的有理层附近的共振行为。当试图保持通量函数相对于共振层的镜像对称性时，产生体积保持微分同胚的矢量场在类时间路径参数中的所有阶的同一性处消失。