Linear instability of Z -pinch in plasma: Viscous 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 scaled variational framework to study its stability in the presence of viscosity effect, and demonstrate that any such z-pinch is always unstable. We also establish the existence of a largest growing mode, which dominates the linear growth of the linear MHD system.