Tempered Lévy walk of charged particles in turbulent magnetic field

Abstract

Abstract. Recently, various diffusion regimes of ions and electrons in interplanetary magnetic field have been recognized from the data collected by different spacecrafts. Particularly for protons, superdiffusion and normal diffusion parallel to the mean magnetic field were declared, simulation also predicts transient superdiffusive behavior. We interpret parallel motion in terms of the one-dimensional tempered Lévy walk process and show that this representation is consistent with the experimental and simulated results.In [1][2][3][4][5][6], different transport regimes of parallel and perpendicular diffusion of charged particles in turbulent magnetic field (TMF) were predicted among which are normal diffusion, ballistic motion, super-and subdiffusion. It is ascertained that the transport of charged particles in turbulent magnetic field is defined by several parameters, such as turbulence level δB/B 0 , turbulence anisotropy, and ratio of Larmor radius R L to correlation length l c . Matthaeus et al. [7] developed the theory of nonlinear guiding center based on the decorrelation hypothesis leading to diffusive motion of guiding centers along magnetic field lines, which undergo random walk in perpendicular direction due to developed turbulence. Perpendicular subdiffusion of particles was reported in [1,8] as a component of the compound diffusion model. The model assumes that guiding centers of CR particles moves along magnetic field lines, so the perpendicular motion is interpreted as a result of combined action of field lines wandering and diffusive back and forth motion along field lines. Similar conclusions about subdiffusion for slab turbulence were achieved by Shalchi and Kourakis [5] by means of analysis of four-order correlations. For the composite model of slab and 2D-turbulence with 80% of fluctuation energy in 2D spectrum, authors [4] obtained normal diffusion for perpendicular transport that is explained by strong exponential wandering of field lines for 2D turbulence. The influence of turbulence anisotropy on particle transport was studied in [9]. For quasi-slab turbulence, parallel superdiffusion and perpendicular subdiffusion take place. For isotropic turbulence, there are parallel superdiffusion and perpendicular normal diffusion that confirms the results of [4]. Superdiffusive regime is obtained also in the composite turbulence model [5]. Pucci et al. [6] indicate very narrow spectral turbulence range used in previous works [9] and consider wide range. Using the p-model, they simulate turbulent magnetic field as a superposition of spatially localized fluctuations of magnetic field on different scales [6]. The obtained spectrum of generated turbulence is isotropic with adjustable spectral index.Authors of [6] calculated time dependencies of diffusion coefficients D ⊥ (t) and D (t) and observed tempered power law form of pdf ρ(τ ) of time between consecutive inversions of parallel velocity sign. The form of D (t) and ρ(τ ) indicate realization of the tempered Lévy