RELATIVISTIC CHARGE CURRENTS IN OBLIQUE ELECTRIC AND MAGNETIC-FIELDS

Runaway processes on neutron stars leading to the sudden release of large quantities of energy (up to of order 10(40) erg) on time scales as short as a fraction of a second involve plasma heating and particle acceleration in superstrong magnetic fields H (of order 10(12) G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (n(e) less-than-or-similar-to 10(25) cm-3) threaded by both electric (E) and magnetic fields. The evaluation of matrix elements involving solutions to the Dirac equation for such a field configuration is often difficult and sometimes impossible, since no completely normalized wave function has yet been found. Here it is shown that, in the special case of E/H less-than-or-similar-to 10(-4), a simplification of the overlap integrals permits an analytical integration that yields explicit expressions for the relativistic charge currents needed in the computation of the anisotropic conductivity tensor when E.H not-equal 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevatn to a theory of resistive magnetic tearing instabilities in a quantizing field.