A Numerical Solution of the Time-Dependent Boltzmann Equation

Abstract

Interest in gas discharge phenomena for laser, ion source, and plasma processing applications has generated needs for the solution of the time- dependent Boltzmann Equation. An algorithm is developed and tested to compute the electron energy distribution function (EDF), incorporating elastic, inelastic, superelastic, ionization, and electron-electron collisions. A new finite-differencing approach which eliminates low-energy instabilities inherent in previous techniques is developed and tested. An implicit-explicit Euler approximation technique was used for the algorithm to transform the resulting nonlinear differential equation into a system of finite-differenced linear equations. The system is then solved using LU-decomposition for efficient matrix computation. The program developed using this algorithm, MEGABOLTZ, is first put through basic shakedown tests to verify the correctness of the algorithm. Next, the program calculates an EDF for nitrogen gas for electric field to neutral number density ratios (E/N) ranging from 5-40 Townsend. Distributions computed by MEGABOLTZ were compared to previously-reported data from other Boltzmann Equation solvers and experiments, and are found to be in good agreement with them. Future modifications are suggested for MEGABOLTZ to improve robustness and accuracy. A short user's manual for MEGABOLTZ is also included. Keywords: Plasma physics, Electric discharges, Transport properties. (kr)

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1989
Accession Number
ADA216397

Entities

People

  • Gaylord E. Seger Iii

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boltzmann Equation
  • Charged Particles
  • Computational Science
  • Computer Programs
  • Computers
  • Differential Equations
  • Diffusion Coefficient
  • Distribution Functions
  • Electric Fields
  • Electron Energy
  • Electrons
  • Gas Discharges
  • Ionization
  • Operating Systems
  • Transport Properties

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics.
  • Pulsed Power and Plasma Physics.

Technology Areas

  • Directed Energy
  • Microelectronics