Numerical Simulation of Plasma Near the Cathode Spot of Vacuum Arc

Abstract

Kinetic numerical simulation of plasma near the cathode spot (CS) was performed. Two types of possible solutions for the self-sustained CS on copper cathode were found. The firs type of solutions is valid for quasi-stationary spot with radius of about $100~\mu \text{m}$ . Stationary solution in this case is possible with cathode temperature 4.2–4.5 kK, current density $\sim 10^{6}$ A/cm2, and applied voltage 20–25 V. The second type of solution is obtained for the spot with radius of $1~\mu \text{m}$ and spherical geometry of plasma expansion. Possible solutions were obtained for the cathode temperature of above 6.2 kK, current density of about $10^{8}$ A/cm2 and applied voltage of 15–25 V. Transient simulations of the near-cathode plasma expansion have shown that if current density remains less than $10^{9}$ A/cm2 then the plasma expansion has a “quiet” self-similar character. At higher current density the plasma expansion has an essentially nonstationary character. The high-density current leads first to the development of Buneman instability and second to the plasma rupture with the creation of conditions for collective acceleration of ions toward the cathode and toward the anode. The accelerated ions create an additional powerful heat flux to the cathode, which should facilitate the reproduction of the CSs in the spark stage of vacuum discharge.