Analytical and Numerical Solutions of Generalized Fokker-Planck Equations - Final Report
The overall goal of this project was to develop advanced theoretical and numerical techniques to quantitatively describe the spreading of a collimated beam of charged particles in space, in angle, and in energy, as a result of small deflection, small energy transfer Coulomb collisions with the target nuclei and electrons. Such beams arise in several applications of great interest in nuclear engineering, and include electron and ion radiotherapy, ion beam modification of materials, accelerator transmutation of waste, and accelerator production of tritium, to name some important candidates. These applications present unique and difficult modeling challenges, but from the outset are amenable to the language of ''transport theory'', which is very familiar to nuclear engineers and considerably less-so to physicists and material scientists. Thus, our approach has been to adopt a fundamental description based on transport equations, but the forward peakedness associated with charged particle interactions precludes a direct application of solution methods developed for neutral particle transport. Unique problem formulations and solution techniques are necessary to describe the transport and interaction of charged particles. In particular, we have developed the Generalized Fokker-Planck (GFP) approach to describe the angular and radial spreading of a collimated beam and a renormalized transport model to describe the energy-loss straggling of an initially monoenergetic distribution. Both analytic and numerical solutions have been investigated and in particular novel finite element numerical methods have been developed. In the first phase of the project, asymptotic methods were used to develop closed form solutions to the GFP equation for different orders of expansion, and was described in a previous progress report. In this final report we present a detailed description of (i) a novel energy straggling model based on a Fokker-Planck approximation but which is adapted for a multigroup transport setting, and (ii) two unique families of discontinuous finite element schemes, one linear and the other nonlinear.
- Research Organization:
- Univ. of New Mexico, Albuquerque, NM (US)
- Sponsoring Organization:
- USDOE Office of Science (US)
- DOE Contract Number:
- FG07-98ID13634
- OSTI ID:
- 782033
- Report Number(s):
- DOE/ID/13634; TRN: US0103084
- Resource Relation:
- Other Information: PBD: 31 Dec 2000
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ANALYTICAL SOLUTION
CHARGED PARTICLES
ENERGY TRANSFER
FOKKER-PLANCK EQUATION
NEUTRAL-PARTICLE TRANSPORT
NUMERICAL SOLUTION
RADIOTHERAPY
TRANSMUTATION
RADIOACTIVE WASTES
HYDROGEN PRODUCTION
TRITIUM
ACCELERATORS
COLLIMATORS
COLLIMATED BEAM
NUCLEI
ELECTRONS
ELECTRON RADIOTHERAPY
ION RADIOTHERAPY
TRANSPORT THEORY
SOLUTION METHODS
FORMULATIONS
SOLUTION TECHNIQUES
GENERALIZED FOKKER-PLANCK (GFP)