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

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