An Adaptive Runge-Kutta Algorithm for Solving Fokker-Planck Associated Stochastic Differential Equations

Details An Adaptive Runge-Kutta Algorithm for Solving Fokker-Planck Associated Stochastic Differential Equations An Adaptive Runge-Kutta Algorithm for Solving Fokker-Planck Associated Stochastic Differential Equations

Dec 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agufmsh33b0371m&link_type=abstract

American Geophysical Union, Fall Meeting 2005, abstract #SH33B-0371

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2159 Plasma Waves And Turbulence, 7514 Energetic Particles (2114), 7519 Flares

Scientific paper

The momentum diffusion or Fokker-Planck operator describes, at least approximately, the evolution of a distribution of particles interacting with a collection of scattering centers. The interactions can range from Coulomb collisions with particles of the same or another species, to resonant interactions with linear plasma waves, to nonresonant collisions with randomly-moving large-scale (compared to the particle gyroradius) magnetic inhomogeneities. Consequently, this operator is a common feature in descriptions of particle transport and stochastic acceleration by electromagnetic turbulence in a wide variety of astrophysical and space plasma situations. An analytical solution of a kinetic equation involving this operator is intractable in practical instances, and hence numerical solutions must be employed. We demonstrate how to transform the kinetic equation into an equivalent system of Stratonovich Stochastic Differential Equations, and present a high-order adaptive Runge-Kutta algorithm for their solution. This technique can provide accurate solutions of a kinetic equation over long timescales, and is easily adapted to take into account nonstochastic processes. This work was supported by NASA grant NAG5-12794

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