Long Term Variation of Galactic Cosmic Ray Using a Stochastic Differential Method
Dr. Gang Li
Department of Physics and CSPAR
29 October 2010
218 Shelby Center
3:00 (Refreshements at 2:30)
The propagation of cosmic rays in the solar system is described by the Parker's transport equation. The equation is of diffusive in nature which is characterized by the diffusion tensor, kappa. The strength of the diffusion tensor is decided by the solar wind MHD turbulence and is subject to transient and long term variations in the solar wind. The effect of long term variation such as the solar cycle effect can be best seen from the hysteresis effect of galactic cosmic rays (GCRs) --- i.e. the intensities of GCRs show a clear solar cycle dependence. A recent study by Wiedenbeck et al. (2005) showed that Carbon and Oxygen at 226 MeV/nuc observed at the Earth are consistently higher in the declining solar activity phase than in the rising phase when the corresponding intensities at 64 MeV/nuc are at comparable values. To properly understand this observation requires solving a time dependent transport equation. We discuss here an attempt of solving the time dependent GCR modulation using a stochastic differential equation method. This method can be nicely visualized via the Feynman-Kac formula and is also equivalent to the Green's function method. The method has been used previously to obtain steady state solutions of the transport equation and has been shown to be equivalent to traditional finite difference methods. We restrict ourselves to a simple 1D model to illustrate the essence of the physics.
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