Estimation of the pressure in a “slow” spark discharge in a cylindrical water-filled chamber

On the assumption that a spark discharge in water is quasi-steady, its pressure and channel radius are calculated. It is shown that the key discharge parameter is the action integral S=∫ ₀ ^t i ² dt, where i is the current in the channel. The conductivity only slightly affects the computational results and thus can be assumed to be constant. The formulas obtained can be applied to a discharge along the axis of a cylindrical water-filled chamber if the deformation of its walls over the discharge time is negligibly small and the pulse duration is several times greater than the time of sound propagation in water from the axis of the chamber to its wall. At relatively low pressures (P≤10⁸ Pa), P∼R ^−4/3, where R is the chamber radius.