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)similar or equal to1-10 kpc. In the static magnetic field approximation, the thermal conductivity kappa(T) for heat transport over distances much greater thanlB in clusters is similar or equal tokappa(S)l(B)/L-S(rho(e)), where kappa(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 rho(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(pi(e))similar or equal to 4.5l(B) and the Monte Carlo model yields L-S(rho(e))similar or equal to 6.5l(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(rho(e))similar or equal to 5l(B)-10l(B), implying that kappa(T)similar or equal to 0.1 kappa(S)-0.2 kappa(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 kappa(T) is enhanced by a moderate amount relative to the static field estimate for typical cluster conditions.