Trajectory of plasma current layer in accelerating and decelerating shock wave in a Mather type plasma focus device

When the shock front (SF) hits the central electrode axis of plasma focus device, a reflected shock wave moves radially outwards. The current sheath (CS) results from ionization of filled gas between two electrodes continues to compress inwards until it hits the out-going reflected SF. In this paper the Lagrangian equations are solved for a parabolic shock trajectory yielding a first and second approximation for the CS path. To determine the accuracy of the approximation, the same problem is solved for a constant speed shock. It is seen that the trajectory of CS and shock wave were almost the same for accelerating velocity of shock wave. The first and second approximation are very close together and also an accelerating shock is controlled more by its piston than is a decelerating shock wave.