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

Galaxy clusters possess turbulent magnetic fields with a dominant scale length l B ≃ 1-10 kpc. In the static magnetic field approximation, the thermal conductivity κ T for heat transport over distances ≫ l B in clusters is ≃κ S l B / L S (ρ e ), where κ S is the Spitzer thermal conductivity for a nonmagnetized plasma, the length L S ( r 0 ) is a characteristic distance that a pair of field lines separated by a distance r 0 < l B at one location must be followed before they separate by a distance l B , and ρ e 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 L S ( r 0 ). We also determine L S ( r 0 ) using direct numerical simulations of MHD turbulence with zero mean magnetic field. All three approaches, like earlier models, predict that L S asymptotes to a value of order several l B as r 0 is decreased toward l d in the large- l B / l d limit, where l d 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 L S (ρ e ) ≃ 4.5 l B and the Monte Carlo model yields L S (ρ e ) ≃ 6.5 l B in the large- l B / l d limit. Extrapolating from our direct numerical simulations to the large- l B / l d limit, we find that L S (ρ e ) ≃ 5 l B -10 l B , implying that κ T ≃ 0.1κ S -0.2κ 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 resistivity completely reconnects field lines on the timescale l B / u , where u is the rms turbulent velocity, we find that κ T is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions.