Phenomenological modeling of turbulence in Z-pinch implosions

A phenomenological investigation into the effects of magnetohydrodynamic (MHD) turbulence on the initial stagnation dynamics of aluminum wire array and argon gas puff Z-pinch implosions is performed. The increases that turbulence produces in the plasma viscosity, heat conductivity, and electrical resistivity are modeled by using multipliers for these quantities in one-dimensional (1-D) MHD calculations. The major effect of these increases is to soften the 1-D implosions by decreasing the densities that are achieved on axis at stagnation. As a consequence, a set of multipliers can be found that reasonably duplicates the average electron temperatures, ion densities, and mass of the K-shell emission region that were measured at stagnation for a variety of Physics International aluminum wire array and argon gas puff experiments. It is determined that the dependence of these measured quantities on the multipliers is weak once a level of enhancement is reached, where agreement between calculations and experiments is attained. The scaling of K-shell yield with load mass for a fixed implosion velocity is then reexamined, and the minimum load mass needed to efficiently produce K-shell emission by thermalization of kinetic energy is calculated for aluminum and argon using this phenomenological soft implosion modeling. The results show an upward shift in the minimum mass by a factor of 6 when compared to the original nonturbulent hard implosion calculations.