Axial magnetic field and toroidally streaming fast ions in the dense plasma focus are natural consequences of conservation laws in the curved axisymmetric geometry of the current sheath

TL;DR

This paper uses hyperbolic conservation laws in a curved coordinate system to explain the natural emergence of axial magnetic fields and toroidal fast ion streaming in the dense plasma focus, linking geometry to observed phenomena.

Contribution

It extends the hyperbolic conservation law formalism to a curved geometry of the plasma focus, deriving expressions for magnetic and flow components from fundamental conservation laws.

Findings

Derivation of axial magnetic field expressions from conservation laws.

Explanation of toroidal fast ion streaming as a consequence of geometry.

Unified framework for magnetic and ion flow behavior in plasma focus.

Abstract

Direct measurement of axial magnetic field in the PF-1000 dense plasma focus (DPF), and its reported correlation with neutron emission, call for a fresh look at previous reports of existence of axial magnetic field component in the DPF from other laboratories, and associated data suggesting toroidal directionality of fast ions participating in fusion reactions, with a view to understand the underlying physics. In this context, recent work dealing with application of the hyperbolic conservation law formalism to the DPF is extended in this paper to a curvilinear coordinate system, which reflects the shape of the DPF current sheath. Locally-unidirectional shock propagation in this coordinate system enables construction of a system of 7 one-dimensional hyperbolic conservation law equations with geometric source terms, taking into account all the components of magnetic field and flow velocity. Rankine-Hugoniot jump conditions for this system lead to expressions for the axial magnetic field and three components of fluid velocity having high ion kinetic energy.