Two fluid modeling of cylindrical wire array Z-pinches

The numerical simulation of current driven plasmas in which density and resistive gradients are large, such as cylindrical wire array Z-pinches, presents great challenges due to the disparate time and spatial scales resulting from physical parameters such as the electron and ion inertial lengths and the resistivity, as well as a from host of other possibly important phenomena. Going beyond MHD modeling of the global characteristics of Z-pinch plasmas, such as capturing the details and prediction of new phenomena, will likely require both improved physical and numerical robustness of existing codes. Correctly simulating the evolution of the magnetic field topology and the plasma penetration into the vacuum region is, we believe, critical to understanding the energetics and dynamics of the ablation stream. We contend that this can only be done correctly if electron inertial physics is included in a consistent manner. Furthermore we argue that the capability of a numerical code to accurately capture shocks is essential to accurately resolving the energetics of the implosion process. We present initial results from a numerical code that includes resistive MHD and electron inertial effects. The code combines a finite volume TVD relaxation scheme with the generalized Ohm's law including finite electron inertia. Current methods in modeling wire array Z-pinches utilize a resistive MHD model in which the conductivity in the low density regions deviates from the Spitzer model by a large vacuum resistivity. This modification of the conductivity imposes severe time step constraints on the numerical algorithm. In addition to capturing the correct physics, we will show that retaining finite electron inertia in the Ohm's law confines current to the high density plasma region without the need for an anomalously high vacuum resistivity and thus relaxes the need for excessively small time steps.