Transport Phenomena in Stochastic Magnetic Mirrors

Parallel thermal conduction along stochastic magnetic field lines may bereduced because the heat conducting electrons become trapped and detrappedbetween regions of strong magnetic field (magnetic mirrors). The problemreduces to a simple but realistic model for diffusion of mono-energeticelectrons based on the fact that when there is a reduction of diffusion, it iscontrolled by a subset of the mirrors, the principle mirrors. The diffusionreduction can be considered as equivalent to an enhancement of the pitch anglescattering rate. Therefore, in deriving the collision integral, we modify thepitch angle scattering term. We take into account the full perturbedelectron-electron collision integral, as well as the electron-proton collisionterm. Finally, we obtain the four plasma transport coefficients and theeffective thermal conductivity. We express them as reductions from theclassical values. We present these reductions as functions of the ratio of themagnetic field decorrelation length to the electron mean free path at thethermal speed $V_T=\sqrt{2kT/m_e}$. We briefly discuss an application of ourresults to clusters of galaxies. Key words: magnetic fields: conduction --- magnetic fields: diffusion ---methods: analytical --- plasmasComment: 25 pages, 7 figures, 3 appendice