Astronomy and Astrophysics – Astrophysics
Scientific paper
May 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005agusmsp21a..07p&link_type=abstract
American Geophysical Union, Spring Meeting 2005, abstract #SP21A-07
Astronomy and Astrophysics
Astrophysics
2159 Plasma Waves And Turbulence, 7514 Energetic Particles (2114), 7519 Flares, 7843 Numerical Simulation Studies
Scientific paper
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.
Miller Aaron J.
Piscicelli M.
No associations
LandOfFree
Numerical Solution of the 2-D Momentum Diffusion Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Numerical Solution of the 2-D Momentum Diffusion Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Numerical Solution of the 2-D Momentum Diffusion Equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1697497