Modeling enhanced energy coupling of z-pinches to pulsed-power generators

It has been observed over the years that the energy coupled to the load in many zpinch experiments is larger than can be accounted for by the sum of the j×B work and classical Ohmic heating. Moreover, this energy enhancement appears to be a function of the generator design, increasing as the risetime of the current is increased. In recent experiments on the Saturn generator, for example, which was operated at current risetimes in excess of 160 ns, observed energy enhancements were factors of 2 to 4 times the energy input expected from J×B work alone. When Saturn operates with risetimes of less than 90 ns, much smaller energy enhancements over the J×B energy are seen. In the past, it was conjectured that some form of anomalous resistivity was needed to account for the extra energy input, while recently, a new idea was proposed based on the buildup of internally generated tubes of magnetic flux energy. [1,2] It was hypothesized that the growth of the Rayleigh-Taylor instability at the surface of the z-pinch plasma would generate bubbles of magnetic flux-tube energy that deposit their energy in the plasma at a current-to-the-third-power rate. While 0-D modeling of the Saturn experiments shows that an anomalously high load resistance can input the required energy needed to match the x-ray data, an alternate mechanism than magnetic flux-tubes exists for anomalous heating that is based on the production of micro-instabilities at the pinch surface. Both this and the flux-tube model are phenomenological and require guidance from experiments to be implemented. Several issues that arise from these enhanced energy coupling mechanisms are discussed in this paper.