Sub- and supersonic expansion of an arc channel in liquid

Post-breakdown expansion of a submerged discharge was considered taking into account the curvature of the plasma boundary and the sound and shock wave fronts. Numerical calculations were performed for an inter-electrode gap of 10-5 m, electrical current and voltage of 10 A and 100 V, respectively and a water medium. With an initial temperature of T0 = 2 x 104 K, a subsonic solution was found. The maximum expansion velocity is 1200 m s-1. The electrical current increases up to 9 A during ∼60 ns. With an initial temperature of T0 = 3 x 104 K, the plasma channel expansion starts as subsonic but after ∼5 ns it reaches the sonic velocity and transits it. The maximum velocity of the plasma boundary of about 2000 m s-1 is reached after ∼17 ns, and a shock wave appears in the undisturbed water. At this stage, water intensively evaporates into the plasma cavity. The electrical current jumps at the sonic transition point up to 10 A. The calculated pressure maximum is about 8 x 1010 Pa