Reduction of thermal conduction by stochastic magnetic mirrors

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). We use 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. To obtain the net reduction of the electron thermal conductivity, we average the mono-energetic diffusion over a Maxwellian distribution of electron velocities. As a result, we find that if the magnetic field correlation length in a cluster of galaxies is smaller than the electron mean free path at the thermal speed $V_T=\sqrt{kT/m_e}$, then thermal conduction is generally negligible.