Linear analysis and 3D hybrid simulation study of Z-pinch instabilities in the presence of non - ideal MHD effects

Abstract

The development of z-pinch instabilities in the presence of the Hall term, finite Larmor radius effects (FLR), and axial magnetic field is being investigated. The linear stage of instability development is studied with linearized magnetohydrodynamic (MHD) equations based on the Hall fluid model. Results for linear growth rates as a function of axial sheared flow, axial magnetic field, and the Hall term, with an emphasis on the sausage and kink instabilities, are reported. We also present simulations performed with the 3D version of the hybrid code based on the CAM-CL algorithm Matthews, AP (1994) These simulations serve the dual purpose of comparing with the linear Hall MHD analysis and of investigating the nonlinear stage of instability development with a kinetic model. The overall aim is to characterize the combined influence of sheared axial flow, the Hall term, axial magnetic field, and finite Larmor radius (FLR) effects on the development of sausage and kink modes. Calculations have been carried out in several regimes with respect to the Hall parameter /spl epsiv/=c//spl omega//sub pi/r/sub 0/ (c is the speed of light, Opi is the ion plasma frequency and r/sub 0/ is the plasma radius), with and without axial magnetic field. The axial magnetic field used in the calculations has been varied from Br/sub 0z/=0 to Br/sub 0z/=0.5, where the amplitude of the axial magnetic field is measured relative to the azimuthal magnetic field created by the axial current in the z-pinch. We have also initiated 3D hybrid simulations to study the time development of density and magnetic field profiles produced in the process of long pulse Z-pinch implosions in Saturn. Apruzese, JP et al. (2001). The 3D hybrid code allows for multiple ion species with multiple charges. This code also contains term with finite resistivity in the magnetic field equation. We can thus model realistic wire array loads with wires composed of different materials, for example Al (95%) and Mg (5%), like in Saturn.