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Diffusive Fermi acceleration is important in efficient acceleration of cosmic rays. For quasi-perpendicular geometry, in order that the process operates, it is essential that the cosmic ray particles ...can traverse magnetic field lines perpendicularly so that they can travel back and forth between upstream and downstream of the shock. In this paper we study cross-field transport of energetic particles in a two dimensional space by performing test particle simulations. We assume that the magnetic field is strictly perpendicular to the simulation plane, and that it is given as superposition of the d.c. field and power-law, time-stationary fluctuation. When typical particle Larmor radius ($\rho$) is much larger than correlation length of the field fluctuation ($L$), the diffusion is well described by conventional quasi-linear theory. On the other hand, when $\rho ll L$, the particle can gradient-B drift along equi-contour lines of the magnetic field strength, which results in either lqlq trapped orbit" or lqlq percolation orbit", depending on whether the particle is on a closed or open trajectory, respectively. When $\rho$ and $L$ are of the same order, depending on the time scale, both the quasi-linear type and the gradient-B type orbits are observed, and furthermore, due to switching between the percolation orbits, quasi-linear type diffusion is again recovered at a very large time scale. We argue that for a proper description of the cross-field transport, Levy statistics must be invoked, which allows explicit scale dependence to the diffusion properties.続きを見る
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