Investigation of Z-pinch instability development in the non-ideal MHD regime

The linearized Hall fluid model is used to study the m = 0 sausage and m = 1 kink instabilities in Z-pinch plasmas. A general set of equations that permits the evaluation of axial and azimuthal sheared flow and an axial magnetic field has been employed. The problem is then treated numerically by following the linear development in time of an initial perturbation to the equilibrium state of the plasma. Our results indicate that non-ideal magnetohydrodynamic (MHD) phenomena are important in the analysis of these instabilities. This is illustrated by including the Hall term in the analysis of the m = 0 and m = 1 instabilities in the presence of an axial magnetic field. It is also shown that numerical results are very sensitive to the boundary conditions and initial equilibrium profiles. Methods for reducing numerical inaccuracies in the solutions for growth rates are also discussed.