Evolution of a z-pinch with constant dI/dt

The evolution of a linear z-pinch in which the current rises at a constant rate is analysed in terms of a quasi-static pinch model. It is shown that there is a maximum current in hydrogen or deuterium equal to approximately 31/2 times the Pease-Braginskij current which cannot be exceeded because of radiative collapse. Higher currents may be obtained in D-T because heating by the alpha particles prevents collapse until most of the fusion fuel is consumed, at which point the pinch collapses like a star. The implications for the pinch as a fusion system are discussed and it is shown that, if the pinch remains stable while the current is rising, a dense z-pinch in D-T might form the basis of a small fusion reactor.