The [Formula: see text]-pinch is a classical steady state for the MHD model, where a confined plasma fluid is separated by vacuum, in the presence of a magnetic field which is generated by a prescribed current along the [Formula: see text]-direction. We develop a scaled variational framework to study its stability in the presence of viscosity effect, and demonstrate that any such [Formula: see text]-pinch is always unstable. We also establish the existence of a largest growing mode, which dominates the linear growth of the linear MHD system.

中文翻译：

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等离子体中 Z 夹点的线性不稳定性：粘性情况

[公式：见文本]-夹点是 MHD 模型的经典稳态，其中受限等离子体流体通过真空分离，存在由沿 [公式：见文本] 的规定电流产生的磁场]-方向。我们开发了一个比例变分框架来研究其在存在粘度效应的情况下的稳定性，并证明任何这样的 [公式：见文本]-pinch 总是不稳定的。我们还建立了一个最大增长模式的存在，它主导了线性 MHD 系统的线性增长。