Effect of the Plasma Impedance on the Time Variation of the Inverse Pinch

The effect of the plasma impedance on the transient behavior of the inverse pinch is investigated. The initial value problem of the ordinary differential equation is formulated with respect to the electric current, the magnetic cavity radius, the shock front radius and the density behind the shock front within the frame work of reasonable assumptions. The present treatment is a refinement of the acoustic treatment by the senior author (T.S.) and affords qualitatively reasonable results even for cases where the acoustic treatment breaks down. The solution is obtained numerically by the standard method and the existense of a new type damped oscillation is clarified