Topology of the warm plasma dispersion relation at the second harmonic electron cyclotron resonance layer

P. L. Joostens, E. Westerhof
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引用次数: 0

Abstract

The Warm Plasma Dispersion Relation, for waves in the electron cyclotron resonance range of frequencies, can be cast into the form of a bi-quadratic equation for $N_\perp$, where the coefficients are a function of $N_\perp^2$ and an iterative procedure is required to obtain a solution. However, this iterative procedure is not well understood and fails to converge towards a solution at the second harmonic resonance layer. In particular at higher densities where the wave can couple to an electron Bernstein wave. This paper focuses on a solution to the poor convergence of the iterative method, enabling determination of the topology of the dispersion relation around the second harmonic using a fully relativistic code for oblique waves. A feed-forward controller is proposed with the ability to adjust the rotation of a step of $N_\perp^2$ within the complex plane, while also limiting the step-size. It is shown that implementation of the controller stabilizes unstable solutions, while improving overall robustness of the iteration. This allows the evaluation of the coupling between the fast extraordinary mode and electron Bernstein waves at the second harmonic electron cyclotron resonance layer, for non-perpendicularly propagating waves.
二次谐波电子回旋共振层热等离子体色散关系的拓扑结构
对于电子回旋共振频率范围内的波,热等离子体色散关系可以转化为双二次方程的形式,其中系数是N_\perp^2$的函数,需要迭代过程才能得到解。然而,这种迭代过程不是很好地理解,并且不能收敛到第二谐波共振层的解。特别是在更高的密度,波可以耦合到一个电子伯恩斯坦波。本文着重解决了迭代法收敛性差的问题,利用斜波的完全相对论编码确定了二次谐波周围色散关系的拓扑结构。提出了一种前馈控制器,该控制器能够在复平面内调整$N_\perp^2$步长的旋转,同时也限制了步长。结果表明,该控制器的实现稳定了不稳定解,同时提高了迭代的整体鲁棒性。这允许对非垂直传播波在二次谐波电子回旋共振层上的快速异常模式和电子伯恩斯坦波之间的耦合进行评估。
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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