Time Evolution of the Electron Swarm Energy Distribution Function

Abstract

The approximate theory of the Boltzmann Equation for the energy distribution function of swarm electrons is reviewed. The L, M approximation (essentially the Fokker-Planck approximation) is developed, being valid when average fractional energy loss per energy transfer collision is small, as is approximately the case in N2 and O2. A summary comparison with N2 and O2 swarm transport coefficients is presented showing excellent agreement over more than four orders of magnitude in the reduced electric field E.No. The spread of energy loss rate about the mean in determining the spectrum is shown. The physical reason for the deficiency of the Continuous Slowing Down Approximation (CSDA) is clarified. It is further shown that the CSDA violates detailed balance. The physical meaning of the function forms is made clear by showing its relation to ordinary diffusion convection theory. The time dependent Boltzmann Equation in the L, M approximation is solved numerically for illustrative cases, demonstrating spectral time lag effects when the electric field varies on a time scale comparable with the swarm energy transfer collision frequency. Keywords; Plasmas; Kinetic theory; Distribution function; Energy spectrum; Boltzman equation; Swarm theory.

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Document Details

Document Type
Technical Report
Publication Date
Jun 28, 1989
Accession Number
ADA212967

Entities

People

  • N. J. Carron

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Air Force
  • Boltzmann Equation
  • Coefficients
  • Diffusion Coefficient
  • Distribution Functions
  • Elastic Scattering
  • Electric Fields
  • Electron Energy
  • Electrons
  • Energy
  • Energy Transfer
  • Equations
  • Kinetic Theory
  • Momentum Transfer
  • Random Walk
  • Scattering
  • Steady State

Fields of Study

  • Physics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Plasma Physics / Magnetohydrodynamics

Technology Areas

  • Microelectronics