Analytic Model to Estimate Thermonuclear Neutron Yield in Z-Pinches Using the Magnetic Noh Problem

Batch burn neutron yield calculations were performed using the magnetic Noh problem, in which the physical solution was anchored to experiments and a particle-in-cell simulation from the open literature. This was done by integrating the time and radially dependent physical solution using fusion reactivity, and included deuterium and deuterium-tritium targets. Achieving agreement between the batch burn yield and the actual data required tuning two parameters that control the physical solution, a timescale tm and a parameter χ, which is an exponent to some of the physical variables used when computed from the self-similar solution. It was found that while agreement could be achieved in all five of the cases reported in the open literature, the high current cases (7.7 MA and greater) with implosion velocities of 400 km/s and higher were the only cases in which the physical solution of density, temperature, and magnetic field in the postshock region were consistent with those of the experiments or the higher fidelity particle-in-cell simulations. Thus, the batch burn yield calculations appear to be a reasonable model reflecting the qualitative trends so long as the neutron yield is primarily thermal in origin and not due to disruption in the pinch due to Rayleigh-Taylor instabilities.