Stochastic diffusion in inverse square fields - General formulation for interplanetary gas

Details Stochastic diffusion in inverse square fields - General formulation for interplanetary gas Stochastic diffusion in inverse square fields - General formulation for interplanetary gas

Jan 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983p%26ss...31....1h&link_type=abstract

Planetary and Space Science, vol. 31, Jan. 1983, p. 1-10. Research supported by the Science Research Council.

Mathematics

4

Fokker-Planck Equation, Gaseous Diffusion, Interplanetary Gas, Stochastic Processes, Gas Dynamics, Matrices (Mathematics), Normal Density Functions

Scientific paper

The Fokker-Planck equation for small stochastic changes to particles in Kepler orbits has to be formulated in terms of the integrals of motion. The authors generalize the modelling of proton and electron collisional perturbations to gas particles on trajectories through the solar system in order to include both spatial and velocity diffusion. The general solution is obtained in terms of a 4-dimensional normal distribution. Treatment of the singularity in the Fokker-Planck operator reduces the dimensionality by one. In addition to extending earlier results for anisotropic collisional heating in the thermal approximation, the present formulation gives the changes in density due to the mean repulsive force and to perturbations of trajectories (spatial diffusion). The net diffusion is almost everywhere towards the sun and the density increase is significant in the downstream hydrogen wake, particularly where destructive depletion is strong and gravitational focussing weak.

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