  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

Astrophysics;High Energy Physics - Phenomenology;Plasma Physics