  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.
