Statistics – Applications
Scientific paper
Aug 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aipc.1039..233l&link_type=abstract
PARTICLE ACCELERATION AND TRANSPORT IN THE HELIOSPHERE AND BEYOND: 7th Annual International Astrophysics Conference. AIP Confer
Statistics
Applications
Flares, Particle Emission, Solar Wind, Planetary Bow Shocks, Interplanetary Shocks, Interplanetary Magnetic Fields, Particle Acceleration, Applications Of Monte Carlo Methods, Turbulence
Scientific paper
In impulsive SEP events, electrons and ions are accelerated at the Sun in a small region, during a short period and then ``injected'' into the solar wind, propagating to 1 AU and are observed by various spacecraft. Their propagation in the solar wind is a competing process between magnetic focusing due to large scale magnetic field geometry and pitch angle scattering due to small scale turbulence in the magnetic field. In a collisionless plasma like the solar wind, the effect of the pitch angle scattering is to alter particle pitch angles in a random but continuous manner during their propagation. Here we briefly discuss a direct Monte-Carlo method that solves the transport equation by following individual particle trajectories. Mathematically, the approach can be understood under the framework of stochastic differential equation method. By casting the underlying Fokker-Planck equation to a set of equations consisting of deterministic pieces and stochastic pieces, one can treat the Lorentz force of the large scale magnetic field and a stochastic force arising from turbulence in the magnetic field separately. Physically, the stochastic pieces describe a diffusion process in particle pitch angle and the rate of particle pitch angle change is readily evaluated through the power of the turbulence.
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