Symmetry and structure in the “Generalized Plasma Focus problem”

The “Generalized Plasma Focus problem” refers to a generic class of plasma propagation phenomena that share many features of a dense plasma focus device. Its recent theoretical development has been shown to predict some features of the pinch phase in PF-1000 and POSEIDON. The theory attempts to decompose the plasma propagation problem into two weakly interdependent subproblems. This is achieved by expressing every physical variable of an applicable continuum model of the plasma as the product of a scaling parameter, which contains device-related information and represents its numerical magnitude, and a scaled variable that is devoid of device-related information, is of order unity, and represents the spatiotemporal structure of that variable. The first subproblem seeks a traveling surface of revolution whose local normal velocity equals the scaling parameter for velocity and is aligned with the magnetic force density. Spatiotemporal distributions of all the scaled variables must move along with this reference surface by definition. This paper explores the resulting scaling theory and its symmetry properties. A new coordinate transformation results in a formula for the spatiotemporal distribution of the magnetic field of the curved and non-steady plasma sheath. New insights into the snowplow effect are obtained. A current sheath with a rear boundary exists only when the current is decreasing and only when the current carrying plasma is less dense than the fill gas. The current sheath thickness is the same for small and large devices. The geomagnetic flux compression problem has an exact solution.