Heat transport along an inhomogeneous magnetic field. I. Periodic magneticmirrors

Thermal conduction plays a critical role in the evolution of galaxy-cluster gas, and an accurate determination of the thermal conductivity is importan t for determinations of mass accretion rates within clusters. Since cluster s are believed to possess magnetic fields with a dominant length scale I, t hat is much smaller than a typical cluster size, the calculation of the mea n conductivity over cluster scales is extremely complicated. In this paper, we treat a small portion of the general problem: the effects of magnetic m irrors on the diffusion of charged particles along magnetic field lines. Fo r simplicity, we take the held strength to be periodic along field lines. W e derive an analytic expression for the suppression factor as a function of the fractional variation in field strength (for arbitrarily large fraction al variations), and verify our analytic findings with the use of Monte Carl o particle simulations.