A steady-state model of current filamentation caused by the electrothermal instability in a fully ionized magnetized plasma

Abstract

A magnetically confined two-fluid plasma is considered in which the Ohmic heating of the electrons by a current driven parallel to an applied magnetic field is balanced by bremsstrahlung and equipartition to the ions. It is found that for a steady state the applied electric field must be below a critical value which in absence of bremsstrahlung is given by where the electrical conductivity is and the total pressure is p. Under this condition it is found that there are two /Futions for T_e/T_i which satisfy the steady electron energy balance equation in a homogeneous, fully ionized plasma. One of these /Futions always has values above the critical value of T_e/T_i (= 132 in absence of bremsstrahlung) for the onset of the electrothermal instability in a fully ionized gas. Inclusion of electron thermal conduction transverse to the magnetic field (with Hall parameter ) yields a wavelength for maximum growth of the instability of about , where a_e is the electron Larmor radius. The steady non linear profiles showing current filamentation have been calculated. Runaway electrons and ion-acoustic instabilities can occur in the spatial maximum of the current density and electron temperature. Inclusion of bremsstrahlung loss reduces the value of T_e/T_i for the onset of the instability, and at T_e = T_i yields a maximum ion temperature obtainable by Ohmic heating in a stable plasma.