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 1040 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 1012 G). These transient events are interesting from a theoretical standpoint because they require knowledge of particle transport properties in low-density plasmas (ne ≲ 1025cm−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 ≲ 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 ≠ 0. The application of these results to the evaluation of the conductivity is briefly discussed. Among other things, this work is relevant to a theory of resistive magnetic tearing instabilities in a quantizing field.