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 variational framework to study its stability in the absence of viscosity effect, and demonstrate for the first time that such a [Formula: see text]-pinch is always unstable. Moreover, we discover a sufficient condition such that the eigenvalues can be unbounded, which leads to ill-posedness of the linearized 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：无粘性情况

[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。我们开发了一个变分框架来研究其在没有粘度效应的情况下的稳定性，并首次证明这种 [公式：见文本]-夹点总是不稳定的。此外，我们发现了一个充分条件，使得特征值可以是无界的，这导致了线性化 MHD 系统的不适定性。