Radial evolution of the finite-width plasma sheet in a Z-pinch-a parametric analysis based on conservation laws

An algebraic method to compute the macroscopic radial-averaged quantities (thickness, density, radial velocity) of the plasma sheet in the first compression of simple z-pinches is presented. Following the snowplow model, a set of MHD equations is written in a reference system in which the internal boundary of the plasma sheet is at rest. The magnetic pressure and the energy losses are both modeled as functions of the radius of the sheet, and a time-independent algebraic equation is obtained. Finding the roots of this expression, the thickness of the plasma sheet as a function of its radius can be computed. The temporal evolution of all the quantities of the plasma sheet can also be obtained making an appropriate change to the reference system. Computed values of the temperature of the sheet are in agreement with experimental values. The ranges of validity for the numerical values of the modeling parameters are analyzed.