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Simulations of cosmic-ray particle diffusion

Authors:	I H Urch

Institution:	(1) University of Waikatoo, Hamilton, New Zealand

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 z 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.

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