The present work considers the stability of a high- $\beta$ , large aspect ratio, circular plasma with diffuse profiles for the safety factor and the angular toroidal frequency (López & Guazzotto, Phys. Plasmas, vol. 24, 032501). An application of the Frieman–Rotenberg formalism results in a system of scalar eigenmode equations whose coupling is retained at the plasma–vacuum transition but is disregarded across the plasma column, which is a standard practice. The solution technique consists of a multidimensional shooting method for the poloidal harmonics; robust initial guesses are constructed by solving the dispersion relation in the static scenario with vanishing magnetic shear. Flow shear appears as a high- $\beta$ toroidal contribution, and we illustrate its destabilizing influence on $n=1$ external kink modes in the presence of ideal and resistive walls. Internal resonances are avoided by means of the selection of appropriate equilibrium parameters. The stabilizing influence of a finite positive average magnetic shear is also exemplified.

中文翻译：

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具有扩散环形旋转的托卡马克等离子体的稳定性

目前的工作考虑了高稳定性 $\beta$ , 大纵横比, 具有扩散轮廓的圆形等离子体, 用于安全系数和角环形频率 (López & Guazzotto,物理。等离子, 卷。24, 032501)。Frieman-Rotenberg 形式的应用产生了一个标量本征模式方程系统，其耦合保留在等离子体-真空过渡处，但在等离子体柱中被忽略，这是一种标准做法。求解技术包括极向谐波的多维拍摄方法；稳健的初始猜测是通过求解具有消失磁剪切的静态场景中的色散关系来构建的。流动剪切表现为高 $\beta$ 环形贡献，我们说明了它的不稳定影响 $n=1$ 存在理想和电阻壁时的外部扭结模式。通过选择适当的平衡参数来避免内部共振。还举例说明了有限正平均磁剪切的稳定影响。