Shock front formation at vacuum arc anodes

A vacuum arc plasma jet between copper electrodes is considered as a supersonic hydrodynamic jet (the primary plasma jet) that bombards the anode and sputters and/or reflects ions (secondary plasma). An initial primary ion jet velocity of v ₀=1.5×10 ⁴ m/s is assumed. The time-dependent interaction between primary and secondary ions is considered for primary ion concentrations of n ₀=10 ¹⁸ and 10 ¹⁹ m ^-3 and for a Cu-Cu self-sputtering yield coefficient of β=0.2. It is found by numerical calculation that the primary jet is decelerated by the collisions with the secondary ions. In the case where the mean free path in the primary plasma is much less than the interelectrode gap (l ₁₁≪L) and the mean free path for the primary-secondary ion collision is much more than the interelectrode gap (l ₁₂≫L), the primary jet decelerates, but initially remains supersonic, while at a later time the deceleration is to a subsonic value, and a shock front appears. For a primary ion concentration of n ₀=10 ¹⁸ m ^-3 and an initial secondary ion velocity ≈0.1×v ₀, a shock front appears at time t≈245×L/v ₀ while for n ₀=10 ¹⁹m ^-3, at t≈135×L/v ₀.