THE MAGNETOSPHERIC WAVE EQUATION IN DIPOLAR COORDINATES

Abstract

Dipolar coordinates alpha equals r/sin square theta, beta equals cos theta/r square, phi equals phi, first introduced by A. Dragt ( Geophysics Research, 66:1642, 1961) in his treatment of hydromagnetic waves in the Van Allen belts, are applied to the vector wave equation for the electric field in an inhomogeneous magneto-ionic medium. For slowly-varying media, in which magnetic gradients dominate polarization charge gradients, the vector wave equation may be approximated by a system of uncoupled scalar wave equations. The latter reduce to a system of second-order ordinary linear differential equations at large distances. The latter are then solved in the WKB approximation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1962
Accession Number
AD0282401

Entities

People

  • William C. Hoffman

Organizations

  • Boeing

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Electric Fields
  • Equations
  • Geophysics
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Partial Differential Equations
  • Polarization
  • Real Variables
  • Wave Equations

Fields of Study

  • Physics

Readers

  • Analytical Mechanics
  • Calculus or Mathematical Analysis
  • Plasma Physics / Magnetohydrodynamics