HR: 0830h
AN: SP21A-07    [Abstracts]
TI: Numerical Solution of the 2-D Momentum Diffusion Equation
AU: * Piscicelli, M
EM: Maxpiscicelli@aol.com
AF: University of Alabama in Huntsville, Department of Physics, Huntsville, AL 35899 United States
AU: Miller, J A
EM: MillerJA@UAH.edu
AF: University of Alabama in Huntsville, Department of Physics, Huntsville, AL 35899 United States
AB: The time-dependent momentum diffusion equation describes the evolution of a particle distribution function in response to resonant wave-particle interactions with plasma turbulence. As such, it is central to treatments of stochastic particle acceleration and transport in space and astrophysical plasmas. In either cylindrical (p_∥,p_⊥) or spherical (p, pitch-angle cosine μ) momentum coordinates, this equation contains a mixed partial derivative, which is highly unstable to numerical finite difference schemes. This in turn precludes the use of many common numerical solution techniques, such as operator splitting or the ADI method. It is for this reason that the momentum diffusion equation is almost always averaged over one degree of freedom, in order to yield a more tractable 1-D equation (typically the pitch-angle averaged momentum diffusion equation, or equivalently the Fokker-Planck equation in energy). Instead, we present a solution that employs stochastic differential equations, which do not suffer from the above numerical instabilities, and which permit us to solve the full 2-D equation without approximation or averaging. The biggest obstacle with this method is taking, basically, the square root of a matrix; however, this can be dealt with effectively using Mathematica. We present results for the case of ions cyclotron resonating with Alfvén waves, and discuss how this numerical method can be easily generalized to include the effects of spatial transport or static electric fields. This work was supported by NASA grant NAG5-12824.
DE: 2159 Plasma waves and turbulence
DE: 7514 Energetic particles (2114)
DE: 7519 Flares
DE: 7843 Numerical simulation studies
SC: Solar Physics Division - AAS [SP]
MN: 2005 Joint Assembly