Scaling Z-pinch plasmas with atomic number for a given K-shell emission

A major goal in using z-pinch plasmas as high brightness laboratory sources of x rays is to increase the radiation emission above about 1keV through the use of moderate atomic number (Z = 10 to 36) materials. Two kinds of configuration, single wires and wire arrays or foils, have been investigated in the past. In both cases, it has been observed that optimal x ray emission decreases on a given machine as the atomic number of the z-pitch material is increased. A description is presented of how a previously developed model can be modified and extended to provide predictions of how machine and diode designs must be scaled in order to maintain a given K-shell x ray emission as the plasma atomic number increases in z-pinch array implosions. Simple scaling arguments are developed to show how specification of a desired total K-shell emission can be used to determine the parameters of an imploding array z-pinch plasma as a function of the atomic number of the pinch. The model used ignores all hydrodynamic details of the z-pinch implosion and thermalization processes and assumes that all the plasma mass is imploded and thermalized. The pinch is also assumed to be driven by a prescribed linearly rising current. Scaling laws that are derived from these assumptions, in effect, contain phenomenological scaling parameters whose values will need to be more accurately determined by more detailed theoretical calculations and/or by z-pinch experiments on a variety of different machines.