An ab initio approach to the heliospheric modulation of galactic cosmic rays

Abstract

In the present study we aim to further our understanding of charged particle transport in a magnetized medium. To this end, we perform direct numerical simulations of particle transport in a turbulent magnetic field. From the particle trajectories we calculate diffusion and drift coefficients. In contrast to previous numerical simulations of this nature, we also consider a background magnetic field that contains a gradient perpendicular to the magnetic field direction. By using a non-uniform background magnetic field, we can investigate the simultaneous large scale drift due to the gradient in the background magnetic field and the diffusion due to the turbulence which is superimposed on this background magnetic field. Upon comparison with the simulated diffusion coefficients, the newly proposed weakly non-linear theory (WNLT) of Shalchi et al. (2004b) seems to be the most appropriate theory for the simultaneous description of parallel and perpendicular diffusion over a wide range of fluctuation amplitude and particle rigidity. As for the effect of large scale drift on perpendicular diffusion, we find that under conditions of small amplitude turbulence and/ or high particle rigidity the transport perpendicular to the background field can exhibit super-diffusive behaviour. Diffusive behaviour seems to be recovered for the cases when the turbulence amplitude is sufficiently large and/ or the particle rigidity is sufficiently small. We furthermore find that both the drift coefficient and the drift speed are reduced from their weak scattering counterparts in the presence of scattering, with the reduction becoming more pronounced with increasing turbulence amplitude. For the drift coefficient in particular, the reduction from its weak scattering counterpart behaves differently for the cases in which the background magnetic field is either uniform or non-uniform. For the former case the reduction is predominantly at small rigidities, while for the latter case the reduction is predominantly at large rigidities. The latter result might be of significance for heliospheric modulation models in which the background magnetic field is highly non-uniform. Finally, we use a two-dimensional steadystate cosmic ray modulation model to see how our improved understanding of the underlying transport processes influences the overall cosmic ray modulation in the heliosphere. We conclude that in the absence of a theory which connects large scale drift with small scale diffusion, any statements about the inadequacy of a two-dimensional steady-state modulation model might be premature.