Basic considerations for scaling Z-pinch x-ray emission with atomic number

Two energies are identified that define the x-ray emission characteristics of Z-pinch array implosions. One, the kinetic energy per ion, is intensive, and the other, the kinetic energy per centimeter, is extensive. From a series of one-dimensional axisymmetric hydrodynamic calculations, we have calculated the dependence of the x-ray emission from aluminum implosions above 1 keV on these energies. These calculations are carried out for a specially chosen theoretical case where the kinetic energy that is generated during implosion is converted to thermal energy and x rays during the plasma collision on axis in the absence of current. In this case, we determine the I4 to I2 transition of the scaling of emission with peak current, I, as a parametric function of the kinetic energy per ion. We also determine a functional dependence of the emission on this energy when the mass of the imploded aluminum array is held fixed. It is seen that the ability of the plasma to radiate large amounts of energy in either I4 or I2 regimes is strongly dependent on the mass loading. Finally, some arguments are presented on how the breakpoint between I4 and I2 scaling is expected to scale when the atomic number of the array load is varied.