High-current arc in a pulse power gas switch has a high current rising rate and energy injection in the pre-pump energy of laser inertial confinement fusion

and the dramatic expansion of the arc can produce a huge shock wave overpressure

which may cause serious damage to the switch structure. Consequently

the plasma motion and shock wave theory are combined to establish an arc expansion energy balance equation

and two solutions of constant adiabatic exponent and time self-similarity are adopted to obtain analytical formulas for arc radius that is essentially the same and for temporal and spatial variation of the peak overpressure. It is proven that the peak overpressure in the current rising phase is proportional to the 4/5 th power of the current rising rate. Simulation calculations with different current and switch parameters show that the peak shock wave overpressure decays rapidly in time and space. It is most related to the energy injection rate in the current rising phase

and is also affected by the total energy injection

arc conductivity

gas density

and electrode spacing. By changing the arc current rising rate and other parameters in coordination

the internal overpressure of the switch can be reduced

providing certain theoretical guidance for the maintenance

improvement and development of the high-current impulse switch.