Energy equilibria in the diffuse pinch. Part 1. Classical scalar conductivity and neo-classical models

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Abstract
Numerical solutions of the momentum and energy equilibria in a two-temperature diffuse pinch show that it is possible for the electron temperature to have a radially oscillating component with a wavelength of the order of ae(mi/me)1/2, where ae is the electron Larmor radius. This is also the order of magnitude of the optimum wavelength for growth of an electro-thermal instability in a homogeneous plasma (studied in part 3 of this series) and suggests this kind of instability as a possible primary source of a current filamentation in the plasma. It has also been revealed both analytically and computationally in this strictly steady state model that the pressure of one species (ions or electrons) is finite at the wall boundary; the same study carried out on a neo-classical model shows, however, that strict confinement is possible provided some restrictions are imposed upon its free parameters. This is also found with a model employing classical tensor conductivity (studied in part 2).