1D kinetic study of pinch formation in a dense plasma focus: Transition from collisional to collisionless regimes

The pinch-formation stage of a deuterium dense plasma focus, and associated “shock-flash” neutron yield, is studied using 1D kinetic simulations considering a plasma column with initial pressure P, initial radius R, and the compression to be driven by a constant current I. The relative behavior of the compression is shown to be similar for fixed ratios of the characteristic ion mean free path to the radius of the plasma column at stagnation, λ s t / R s t. This dimensionless parameter is shown to scale like I 4 / ( P 3 R 5 ). The compression ratio, R / R s t, is found to be a minimum when λ s t / R s t ≈ 1 and is the largest in the collisionless limit where λ s t ≫ R s t. This behavior is in contrast to the analogous planar pinch where R / R s t decreases from one constant for λ s t / R s t ≪ 1 to a smaller constant for λ s t / R s t ≫ 1. The yield in the collisionless regime is shown to fall between the two well-known I4 scaling laws. Furthermore, this regime exhibits qualities that potentially make it appealing for radiography applications, such as increased localization in time and space of the neutron formation.