Simulations of cosmic-ray particle diffusion

Abstract

The diffusion of charged particles in a stochastic magnetic field (strengthB′) which is superimposed on a uniform magnetic fieldB ₀ k is studied. A slab model of the stochastic magnetic field is used. Many particles were released into different realizations of the magnetic field and their subsequent displacements Δz in the direction of the uniform magnetic field numerically computed. The particle trajectories were calculated over periods of many particle scattering times. The ensemble average$\left\langle {\left( {\Delta z} \right)^2 } \right\rangle$ was then used to find the parallel diffusion coefficient$\left( {{\text{i}}{\text{.e}}{\text{.,}}K_\parallel = {{\frac{1}{2}\left\langle {\left( {\Delta z} \right)2} \right\rangle } \mathord{\left/ {\vphantom {{\frac{1}{2}\left\langle {\left( {\Delta z} \right)2} \right\rangle } {\Delta t}}} \right. \kern-\nulldelimiterspace} {\Delta t}}} \right)$. The simulations were performed for several types of stochastic magnetic fields and for a wide range of particle gyro-radius and the parameterB′/B ₀. The calculations have shown that the theory of charged particle diffusion is a good approximation even when the stochastic magnetic field is of the same strength as the uniform magnetic field.