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 (εe ≲ 1025 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 ≲ 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.

Turbulent excitation of spontaneous reconnection

We explore the long-term nonlinear evolution of a tearing-mode-unstable sheared-field plasma in a turbulent environment. Two different physical configurations are modeled, and a different computational system is used for each. Results of both sets of calculations show that magnetic tearing arises spontaneously provided that the initial turbulence energy level is below the natural saturation level of the tearing instability.We discuss briefly the relationship between our results and those of previous calculations, concluding that there are no significant unexplainable disagreements.

Spectral analysis of turbulent effects on resistivity and the tearing instability

Biskamp and Welter (1983) have defined an anomalous resistivity due to shortwavelength turbulence. They reported that this resistivity can be of either sign, and that negative anomalous resistivity in particular can affect the growth of the tearing instability. We use a spectral numerical-simulation code and ancillary diagnostics to analyse the behaviour of resistive magnetic tearing in the presence of turbulence of the sort postulated by Biskamp and Welter. We find that, in general, the ‘anomalous resistivity’ tends to return quickly towards zero even when artificially supported away from zero, and that its effect on tearing-mode behaviour is not consistent with its interpretation as a resistivity. We investigate analytically the behaviour reported by Biskamp and Welter, and the behaviour we observe. We also argue that, while not meaningful as a true resistivity, the ‘anomalous-resistivity’ parameter is a useful diagnostic showing the energy balance of the System – a property we refer to as Alfvénicity – illustrating, for example, the onset of nonlinearity in the tearing process.