COMPARISON OF FOKKER-PLANCK AND BHATNAGARGROSS-KROOK EQUATIONS,

Abstract

A Fokker-Planck Equation, such as the one used in the theory of Brownian motion, and the Bhatnagar-GrossKrook equation that conserves only number density are compared via their transition probabilities. These two equations have been used in various problems arising in the study of plasmas. It is shown that for time intervals large compared with the average collision time both equations give the same results. For the opposite limit of times small compared with the collision time, the disparity between the two equations increases as the initial velocity of the test particle increases; however, the difference between the two transition probabilities is shown to be reduced if the initial velocity distribution is Maxwellian. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 05, 1964
Accession Number
AD0602960

Entities

People

  • M. S. Grewal

Organizations

  • The Aerospace Corporation

Tags

DTIC Thesaurus Topics

  • Brownian Motion
  • Collisions
  • Disparities
  • Equations
  • Fokker Planck Equations
  • Intervals
  • Mathematics
  • Particles
  • Probability
  • Time Intervals
  • Transitions

Fields of Study

  • Mathematics
  • Physics

Readers

  • Combustion Dynamics and Shock Wave Physics.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Mathematical Modeling and Probability Theory.