Analysis of the transient process in underwater spark discharges

If water is stressed with a voltage pulse having a rise time of tens of nanoseconds which creates a sufficiently high electric field, streamers develop and a highly conductive channel forms between the electrodes. The intense Joule heating of the plasma in the channel results in the collapse of its electrical resistance from a few Ohms to a few tens of milliOhms with the behavior of the collapse depending on the parameters of the discharge circuit. The rapid decrease of the resistance occurs during the first quarter of the current oscillation in the circuit. During this time, the pressure inside the channel rises to several GPa, causing the channel to expand in water with a velocity of 100 to 1000 m/s driving a high power ultrasound pulse. In the present paper, a phenomenological model is discussed which describes the dynamics of the resistance of underwater spark discharges during its initial stage and allows the pressure in the acoustic pulse to be obtained. The model is based on the plasma channel energy balance equation used by Braginskii and links the hydrodynamic characteristics of the channel and the parameters of the electric driving circuit. The dynamics of the transient cavity during the dissipation of the electrical energy in the plasma channel is described and the analytical results are compared with experimental measurements of the current in the electrical circuit and the acoustic pulse profiles radiated by the transient cavities.