Space Charge Limited Emission Studies Using Coulomb's Law

Abstract

Child and Langmuir introduced a solution to space charge limited emission in an infinite area planar diode. The solution follows from starting with Poisson's equation, and requires solving a non-linear differential equation. This approach can also be applied to cylindrical and spherical geometries, but only for one-dimensional cases. By approaching the problem from Coulomb's law and applying the effect of an assumed charge distribution, it is possible to solve for space charge limited emission without solving a non-linear differential equation, and to limit the emission area to two-dimensional geometries. Using a Mathcad worksheet to evaluate Coulomb's law, it is possible to show correlation between the solution derived by Child and Langmuir and Coulomb's law.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 2004
Accession Number
ADA424738

Entities

People

  • Christopher G. Carr

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Charge Density
  • Current Density
  • Differential Equations
  • Directed Energy Weapons
  • Electric Fields
  • Emission
  • Emitters
  • Energy
  • Equations
  • Geometry
  • Linear Differential Equations
  • Magnetic Fields
  • Poisson Equation
  • Space Charge
  • Two Dimensional
  • United States
  • United States Naval Academy

Readers

  • Calculus or Mathematical Analysis
  • Pulsed Power and Plasma Physics.

Technology Areas

  • Space
  • Space - Hall-Effect Thruster