Transport phenomena in stochastic magnetic mirrors

Abstract

Parallel thermal conduction along stochastic magnetic field lines may be reduced because the heat conducting electrons become trapped and detrapped between regions of strong magnetic field (magnetic mirrors). The problem reduces to a simple but realistic model for diffusion of mono-energetic electrons based on the fact that when there is a reduction of diffusion, it is controlled by a subset of the mirrors, the principle mirrors. The diffusion reduction can be considered as equivalent to an enhancement of the pitch angle scattering rate. Therefore, in deriving the collision integral, we modify the pitch angle scattering term. We take into account the full perturbed electron-electron collision integral, as well as the electron-proton collision term. Finally, we obtain the four plasma transport coefficients and the effective thermal conductivity. We express them as reductions from the classical values. We present these reductions as functions of the ratio of the magnetic field decorrelation length to the electron mean free path at the thermal speed $V_T=\sqrt{2kT/m_e}$. We briefly discuss an application of our results to clusters of galaxies. Key words: magnetic fields: conduction --- magnetic fields: diffusion --- methods: analytical --- plasmas