Plasma Energy Loss by Cathode Heat Conduction in a Vacuum Arc: Cathode Effective Voltage

The importance of understanding the energy loss specifics by the cathode for vacuum arc metallic plasma generation and its applications were emphasized. To this end, the heat conduction losses per unit current were characterized by the cathode effective voltage <i>u_ef</i>, which is weakly dependent on the current. In this paper, a physical model and a mathematical approach were developed to describe the energy dissipation due to heat conduction in the cathode body, which is heated by energy outflowed from the adjacent plasma. The arc plasma generation was considered by taking into account the kinetics of the heavy particle fluxes in the non-equilibrium layer near the vaporizing surface. The phenomena of electric sheath, heat and mass transfer at the cathode were taken into account. The self-consistent numerical analysis was performed with a system of equations for a copper cathode spot. The transient analysis starts from the spot initiation, modeled by the plasma arising at the initial time determined by the kind of arc triggering, up to spot development. The results of the calculations show that the cathode effective voltage <i>u_ef</i> is determined by the cathode temperature as a function of spot time. The calculated evolution of the voltage <i>u_ef</i> shows that the steady state of <i>u_ef</i> is approximately 7 V, and it is reached when the cathode temperature reaches a steady state at approximately one microsecond. This essential result provides an explanation for the good agreement with the experimental cathode effective voltage (6–8 V) measured for the arc duration from one millisecond up to a few seconds.