A model for ablated-plasma distribution and width for wire-array Z-pinch implosions.

A one-dimensional radial magnetohydrodynamic model of the plasma ablated from a multi-MA wire-array Z pinch is developed. The model is used to compute the mass weighted-density width δ of the plasma at the end of the ablation phase. The wire-array cores are represented as a prescribed source of plasma injection. The plasma, beyond a thin boundary layer, is approximated as a perfect conductor experiencing only magnetic forces and negligible pressure gradients. Assuming that the current driving the Z-pinch implosion increases linearly with time t during the ablation phase, and that the mass-ablation rate varies as tν, it is shown that the density width δ is a function of the dimensionless parameter λ=ua(ta)ta/r0, where ua is the ablation velocity, ta is the total ablation time, and r0 is the initial wire-array radius. The velocity ua is defined such that its product with the mass-ablation rate equals the magnetic force at r0, which is assumed to be the mass injection point. A solution is obtained for the plasma flow in semianalytical form when the current is an exponential function of time, and ua is constant. The ablated plasma density width δ obtained under these two sets of conditions is compared. In addition, assuming that the plasma sheath at stagnation is proportional to the width δ, scaling relationships for the peak x-ray power radiated when the pinch stagnates on axis are suggested. [ABSTRACT FROM AUTHOR]