A Model for Ablated Plasma Width Applied to Peak X-Ray Power Scaling for Z-Pinch Wire Array Implosions

Summary form only given. We present the solution of a 1D radial MHD model of the plasma ablated from multi-MA wire array implosions extending a recently obtained steady state solution [J.P. Chittenden, et al. Phys. Plasmas 11, 1118 (2004)] to a driving current that is exponential in time. We obtain a solution for the flow in almost analytical form by reducing the partial differential equations to a set of ordinary differential equations with a single parameter. We compute the mass weighted density width, and find the regime in which it agrees to a few percent with that of a simpler approximation to the ablated plasma flow, for which the driving current is linear in time, and the flow velocity constant. Assuming that the density width at the end of the ablation period is proportional to width of the plasma sheath at stagnation, we obtain a scaling relationship for peak X-ray power. We compare this relationship to experimental peak X-ray powers for tungsten wire arrays on the Z pulsed power generator of Sandia National Laboratories, and to previously proposed scaling hypotheses. We also use this scaling to project peak X-ray powers on ZR, a higher peak current modification of Z, presently under design