Diffusion of Relativistic Charged Particles and Field Lines in Isotropic Turbulence. I. Numerical Simulations

The transport of nonthermal particles across a large-scale magnetic field in the presence of magnetized turbulence has been a long-standing issue in high-energy astrophysics. Of particular interest is the dependence of the parallel and perpendicular mean free paths λ ∥ and λ ⊥ on rigidity R . We have revisited this important issue with a view to applications from the transport of Galactic cosmic rays (CRs) to acceleration at astrophysical shocks. We have run test particle simulations of CR transport in synthetic, isotropic Kolmogorov turbulence at unprecedentedly low reduced rigidities of r g / L c ≃ 10 −4 , corresponding to R ≃ 10 TV for a turbulent magnetic field of B rms = 4 μ G and correlation length of L c = 30 pc. Extracting the (asymptotic) parallel and perpendicular mean free paths λ ∥ and λ ⊥ , we have found λ ∥ ∝ ( r g / L c ) 1 / 3 as expected for a Kolmogorov turbulence spectrum. In contrast, λ ⊥ has a faster dependence on r g / L c for 10 −2 ≲ r g / L c ≲ 1, but for r g / L c ≪ 10 −2 , λ ⊥ ∝ ( r g / L c ) 1 / 3 . Our results have important implications for the transport of Galactic CRs.