Self-similar transport processes in a two-dimensional realization of multiscale magnetic field turbulence

Abstract

We present the results of a numerical investigation of charged-particle transport across a synthesized magnetic configuration composed of a constant homogeneous background field and a multiscale perturbation component simulating an effect of turbulence on the microscopic particle dynamics. Our main goal is to analyse the dispersion of ideal test particles faced to diverse conditions in the turbulent domain. Depending on the amplitude of the background field and the input test particle velocity, we observe distinct transport regimes ranging from subdiffusion of guiding centres in the limit of Hamiltonian dynamics to random walks on a percolating fractal array and, further, to nearly diffusive behaviour of the mean-square particle displacement versus time. In all cases, we find a complex microscopic structure of the particle motion revealing long-time rests and trapping phenomena, sporadically interrupted by the phases of active cross-field propagation reminiscent of Levy-walk statistics. These complex features persist even when the particle dispersion is diffusive. An interpretation of the results obtained is proposed in connection with the fractional kinetics paradigm extending the microscopic properties of transport far beyond the conventional picture of a Brownian random motion. A calculation of the transport exponent for random walks on a fractal lattice is advocated from topological arguments. An intriguing indication of the topological approach is a gap in the transport exponent separating Hamiltonian-like and fractal random walk-like dynamics, supported through the simulation.