Shear flow stabilization of Z -pinches

A z-pinch plasma is in principle an efficient and cost-effective way of heating a small amount of matter to high temperatures, while also achieving high densities. In practice, the heating and compression are very nonuniform because z-pinches are very unstable. One of the proposed means of stabilization of the most dangerous magnetohydrodynamic (MHD) instability modes, the m=0 ("sausage") and m=1 ("kink"), is to use sheared plasma flow to tear off the instability structure.;A detailed study of the linear and nonlinear development of the m=0 instability in the presence of sheared axial flows has been performed in this dissertation. For this purpose we have used a two-dimensional MHD numerical code, MHRDR, to solve the ideal set of single-fluid magnetohydrodynamic equations. In order to accurately study shear flow stabilization of a z-pinch, the code was modified to include periodic boundary conditions and a monotonic van Leer advection algorithm. Linear growth rates obtained with MHRDR were in good agreement with the linear theory (<10% difference). Nonlinear mode coupling and saturation of the sausage instability have been studied for plasma equilibria with and without sheared flows. It was found that sheared flows changed the m=0 development by reducing the linear growth rates, decreasing the saturation amplitude, and modifying the instability spectrum. High spatial frequency modes were stabilized to small amplitudes, and only the long wavelengths continued to grow. Full stabilization was predicted for supersonic plasma flows.