Hot spots and filaments in the pinch of a plasma focus: a unified approach

To date, no MHD-based complete description of the tiny, relatively stable, well-ordered structures (hot spots, filaments) observed in the pinch of a plasma focus seems to be feasible. Indeed, the large value of electron density suggests that a classification of such structures which is based on the approximation of local thermodynamical equilibrium (LTE) is possible. Starting from an often overlooked, far-reaching result of LTE, we derive a purely analytical description of both hot spots and filaments. In spite of their quite different topology, both configurations are extremals of the same variational principle. Well-known results of conventional MHD are retrieved as benchmark cases. It turns out that hot spots satisfy Taylor's principle of constrained minimum of magnetic energy, the constraint being given by fixed magnetic helicity. Filaments are similar to the filaments of a superconductor and form a plasma with beta= 0.11 and energy diffusion coefficient = 0.88 D-Bohm. Any process - like e.g. radiative collapse - which raises particle density while reducing radial size may transform filaments into hot spots. A well-known scaling law is retrieved - the collisional Vlasov high beta scaling. A link between dissipation and topology is highlighted. Accordingly, a large-current pinch may give birth to tiny hot spots with large electron density and magnetic field.