Development and Application of Stochastic Methods for Radiation Belt Simulations

This thesis describes a method for modeling radiation belt electron diffusion, which solves the radiation belt Fokker-Planck equation using its equivalent stochastic differential equations, and presents applications of this method to investigating drift shell splitting effects on radiation belt electron phase space density. The theory of the stochastic differential equation method of solving Fokker-Planck equations is formulated in this thesis, in the context of the radiation belt electron diffusion problem, and is generalized to curvilinear coordinates to enable calculation of the electron phase space density as a function of adiabatic invariants M, K and L. Based on this theory, a three-dimensional radiation belt electron model in adiabatic invariant coordinates, named REM (for Radbelt Electron Model), is constructed and validated against both known results from other methods and spacecraft measurements. Mathematical derivations and the essential numerical algorithms that constitute REM are presented in this thesis. As the only model to date that can solve the fully three-dimensional diffusion problem, REM is used to study the effects of drift shell splitting, which gives rise to M-L and K-L off-diagonal terms in the radiation belt diffusion tensor. REM simulation results suggest that drift shell splitting reduces outer radiation belt electron phase space density enhancements during electron injection events. Plots of the phase space density sources, which are unique products of the stochastic differential equation method, and theoretical analysis further reveal that this reduction effect is caused by a change of the phase space location of the source to smaller $L$ shells, and has a limit corresponding to two-dimensional local diffusion on a curved surface in the (M,K,L) phase space.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Natural Sciences

Grantor

Rice University

Year dc:date.issued

2015

Author dc:creator

• Zheng, Liheng

Advisor dc:contributor.advisor

• Chan, Anthony A

Committee members dc:contributor.committeemember

• Wolf, Richard A
• Dugan, Brandon

• radiation belt
• electron diffusion
• Fokker-Planck equation
• stochastic differential equation
• modeling

Statement dc:rights

• Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/1911/88411

OAI identifier oai:identifier

oai:repository.rice.edu:1911/88411