MAGNETIC FIELD LINE RANDOM WALK in ISOTROPIC TURBULENCE with VARYING MEAN FIELD

Abstract

© 2016. The American Astronomical Society. All rights reserved. In astrophysical plasmas, the magnetic field line random walk (FLRW) plays an important role in guiding particle transport. The FLRW behavior is scaled by the Kubo number R = (b/B0 )(ℓ∥/ ℓ⊥) for rms magnetic fluctuation b, large-scale mean field B0, and coherence scales parallel (ℓ∥) and perpendicular (ℓ⊥) to B0. Here we use a nonperturbative analytic framework based on Corrsin's hypothesis, together with direct computer simulations, to examine the R-scaling of the FLRW for varying B0 with finite b and isotropic fluctuations with ℓ∥/ℓ⊥ = 1, instead of the well-studied route of varying for ℓ∥/ℓ⊥ for b ≪ B0. The FLRW for isotropic magnetic fluctuations is also of astrophysical interest regarding transport processes in the interstellar medium. With a mean field, fluctuations may have variance anisotropy, so we consider limiting cases of isotropic variance and transverse variance (with bz = 0). We obtain analytic theories, and closed-form solutions for extreme cases. Padé approximants are provided to interpolate all versions of theory and simulations to any B0. We demonstrate that, for isotropic turbulence, Corrsin-based theories generally work well, and with increasing R there is a transition from quasilinear to Bohm diffusion. This holds even with bz = 0, when different routes R → ∞ to are mathematically equivalent; in contrast with previous studies, we find that a Corrsin-based theory with random ballistic decorrelation works well even up to R = 400, where the effects of trapping are barely perceptible in simulation results.