Linear instability of Z-pinch in plasma: Inviscid case

The z-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 z 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 z-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.

Automated summary

In this study, a variational framework was developed to analyze the stability of the z-pinch system in the absence of viscosity effects, revealing that the z-pinch system is always unstable. Additionally, a sufficient condition for unbounded eigenvalues was discovered, leading to ill-posedness in the linearized MHD system.