  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 analyze 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 centers in the limit of Hamiltonian dynamics to
random walks on a percolating fractal array and further to nearly diffusive
behavior of the mean-square particle displacement versus time. In all cases, we
find 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.
