Energy transfer to a wire from a surrounding Joule-heated corona

Abstract

This paper considers the early behavior of the current-carrying coronal plasma formed around the relatively colder liquid-vapor core of a wire. This has applications to both a wire array before global effects dominate and a single wire. An analytic, theoretical model is developed where the Joule heating in the coronal plasma is thermally conducted to the cold core. The balance of both energy and pressure are assumed, and it is further assumed that the Hall parameter is much less than one throughout the domain. This last assumption will be violated near the outside radius of the corona where runaway conditions and lower hybrid turbulence can also occur. The nonlinear second-order differential equation for the normalized temperature variation with a normalized radius has only one free dimensionless parameter, which is the ratio of the applied axial electric field to the mean radial temperature gradient (in electronvolts/m). The inverse of this ratio scales essentially as $${{T^2 } \mathord{\left/ {\vphantom {{T^2 } {\sqrt n }}} \right. \kern-\nulldelimiterspace} {\sqrt n }}$$ , thus showing that both a low Hall parameter and a low magnetic Reynolds' number can occur when the mean free path is less than the collisionless skin depth, a criterion for the onset of current or heat-flow driven electrothermal instabilities.