Data set accompanying: Topology of the Warm plasma dispersion relation at the second Harmonic Electron Cyclotron Resonance Layer

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.<br> 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.<br> 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.<br> 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.针对电子回旋共振频率范围内的波动，暖等离子体色散关系可转化为关于$N_perp$的双二次方程，其系数为$N_perp^2$的函数，求解该方程需采用迭代流程。然而，该迭代方法的物理机制尚未被充分阐明，且在二次谐波共振层处无法收敛至有效解；尤其在等离子体密度较高时，波动可与电子伯恩斯坦波（electron Bernstein wave）发生耦合。 本文聚焦于解决该迭代方法收敛性不佳的问题，借助斜波全相对论数值程序，得以解析二次谐波共振区域附近的色散关系拓扑结构。 本文提出一种前馈控制器（feed-forward controller），可在复平面内调整$N_perp^2$步长的旋转角度，同时对步长幅值进行限制。 研究表明，引入该控制器可稳定迭代过程中的不稳定解，同时提升迭代流程的整体鲁棒性。借此，我们能够针对非垂直传播的波动，求解二次谐波电子回旋共振层处快异常模（fast extraordinary mode）与电子伯恩斯坦波之间的耦合特性。