Magnetic field line random walk in isotropic turbulence with zero mean field

Abstract

© 2015. The American Astronomical Society. All rights reserved. In astrophysical plasmas, magnetic field lines often guide the motions of thermal and non-thermal particles. The field line random walk (FLRW) is typically considered to depend on the Kubo number R = (b/B0)(ℓ∥/ℓ⊥) for rms magnetic fluctuation b, large-scale mean field B0, and parallel and perpendicular coherence scales ℓ∥and ℓ⊥, respectively. Here we examine the FLRW when R → ∞ by taking B0→ 0 for finite bz(fluctuation component along B0), which differs from the well-studied route with bz= 0 or bz蠐 B0as the turbulence becomes quasi-two-dimensional (quasi-2D). Fluctuations with B0= 0 are typically isotropic, which serves as a reasonable model of interstellar turbulence. We use a non-perturbative analytic framework based on Corrsin's hypothesis to determine closed-form solutions for the asymptotic field line diffusion coefficient for three versions of the theory, which are directly related to the k-1or k-2moment of the power spectrum. We test these theories by performing computer simulations of the FLRW, obtaining the ratio of diffusion coefficients for two different parameterizations of a field line. Comparing this with theoretical ratios, the random ballistic decorrelation version of the theory agrees well with the simulations. All results exhibit an analog to Bohm diffusion. In the quasi-2D limit, previous works have shown that Corrsin-based theories deviate substantially from simulation results, but here we find that as B0→ 0, they remain in reasonable agreement. We conclude that their applicability is limited not by large R, but rather by quasi-two-dimensionality.