The effect of the flow of atoms sputtered from the anode on the flow of current in a vacuum arc

The paper deals with the problem on the effect of atoms sputtered from the anode on the flow of fast cathode ions in a vacuum discharge at relatively low ($\sim100$ A/cm$^2$) values of current density. The problem is solved using a model of instantaneous ionization and a model allowing for the finite ionization length. The calculations result in determining the boundary of the region of stable passage of current depending on the density of arc current, the density of the flow of sputtered atoms, and on their velocity. It is demonstrated that, in the studied range of currents, it is impractical to include the fast ion pressure in the equations of motion and balance for energy, because these ions hardly collide with one another during the time of their transit through the discharge gap. The calculation results enable one to determine the range of validity of the model of instantaneous ionization beyond which one must allow for the dynamics of the process of ionization of atoms in the anode region.