A simplified spherical harmonic method for coupled electron-photon transport calculations

Thesis/Dissertation · Sun Dec 01 04:00:00 EST 1996

DOI:https://doi.org/10.2172/459863· OSTI ID:459863

Josef, John A. ^[1]

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1. Pennsylvania State Univ., University Park, PA (United States)

In this thesis we have developed a simplified spherical harmonic method (SP_N method) and associated efficient solution techniques for 2-D multigroup electron-photon transport calculations. The SP_N method has never before been applied to charged-particle transport. We have performed a first time Fourier analysis of the source iteration scheme and the P₁ diffusion synthetic acceleration (DSA) scheme applied to the 2-D SP_N equations. Our theoretical analyses indicate that the source iteration and P₁ DSA schemes are as effective for the 2-D SP_N equations as for the 1-D S_N equations. Previous analyses have indicated that the P₁ DSA scheme is unstable (with sufficiently forward-peaked scattering and sufficiently small absorption) for the 2-D S_N equations, yet is very effective for the 1-D S_N equations. In addition, we have applied an angular multigrid acceleration scheme, and computationally demonstrated that it performs as well for the 2-D SP_N equations as for the 1-D S_N equations. It has previously been shown for 1-D S_N calculations that this scheme is much more effective than the DSA scheme when scattering is highly forward-peaked. We have investigated the applicability of the SP_N approximation to two different physical classes of problems: satellite electronics shielding from geomagnetically trapped electrons, and electron beam problems. In the space shielding study, the SP_N method produced solutions that are accurate within 10% of the benchmark Monte Carlo solutions, and often orders of magnitude faster than Monte Carlo. We have successfully modeled quasi-void problems and have obtained excellent agreement with Monte Carlo. We have observed that the SP_N method appears to be too diffusive an approximation for beam problems. This result, however, is in agreement with theoretical expectations.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
• DOE Contract Number: W-7405-ENG-36
• OSTI ID: 459863
• Report Number(s): LA-UR--97-435; ON: DE97004742
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
97 MATHEMATICS AND COMPUTING
CHARGED-PARTICLE TRANSPORT THEORY
MULTIGROUP THEORY
NUMERICAL SOLUTION
PHOTON TRANSPORT
PHOTON-ELECTRON COLLISIONS
SPHERICAL HARMONICS METHOD