Applicability of the hydrodynamic approximation to current-carrying plasma jets during their radial expansion

Supersonic spherically symmetric vacuum-arc plasma jets are considered using a two-liquid model. The jet starts from a radial distance of 3 × 10^-3 m from the cathode surface with a radial directed electric current of 50-1000 A. Joule heating of the electron component and heat transfer to the ion component were calculated. The spatial distribution of plasma density, velocity, and electron and ion temperatures were obtained by numericaily solving the equations of conservation of mass, energy, and momentum. The mean free path for the ion-ion collisions and the Mach number for the ion component of the plasma jet were also calculated as a function of the radial distance. The Knudsen number (Kn) for the ion component of plasma was calculated as a criterion of applicability of the hydrodynamical approximation. It was found that if Kn ≪ 1 at the starting radial distance, it remains much less than unity, in spite of the decrease in the plasma density during the radial plasma expansion.