Thermal Conduction and Particle Transport in Strong Magnetohydrodynamic Turbulence, with Application to Galaxy Cluster Plasmas

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Galaxy clusters possess turbulent magnetic fields with a dominant scale length lB ' 1 10 kpc. In the static magnetic field approximation, the thermal conductivityT for heat transport over distances 3 lB in clusters is '� SlB/LS(� e), whereS is the Spitzer thermal conductivity for a nonmagnetized plasma, the length LS(r0 )i s a characteristic distance that a pair of field lines separated by a distance r0 < lB at one location must be followed before they separate by a distance lB ,a nde is the electron gyroradius. We introduce an analytic Fokker-Planck model and a numerical Monte Carlo model of field-line separation in strong magnetohydrodynamic (MHD) turbulence to calculate LS(r0). We also determine LS(r0) using direct numerical simulations of MHD turbulence with zero mean magnetic field. All three approaches, like earlier models, predict that LS asymptotes to a value of order several lB as r0 is decreased toward ld in the large-lB/ld limit, where ld is the dissipation scale, which is taken to be the proton gyroradius. When the turbulence parameters used in the Fokker-Planck and Monte Carlo models are evaluated using direct numerical simulations, the Fokker-Planck model yields LSð� e Þ' 4:5lB and the Monte Carlo model yields LSð� e Þ' 6:5lB in the large-lB/ld limit. Extrapolating from our direct numerical simulations to the large-lB/ld limit, we find that LSð� e Þ' 5lB 10lB, implying thatT ' 0:1� S 0:2� S in galaxy clusters in the static field approximation. We also discuss the phenomenology of thermal conduction and particle diffusion in the presence of time-varying turbulent magnetic fields. Under the questionable assumption that turbulent re- sistivity completely reconnects field lines on the timescale lB/u ,w hereu is the rms turbulent velocity, we find that � T is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions. Subject headings: galaxies: clusters: general — intergalactic medium — MHD — plasmas — turbulence