Eigenfunction Methods in Magnetospheric Radial-Diffusion Theory

  1. Tom Chang,
  2. M. K. Hudson,
  3. J. R. Jasperse,
  4. R. G. Johnson,
  5. P. M. Kintner and
  6. M. Schulz
  1. Michael Schulz

Published Online: 21 MAR 2013

DOI: 10.1029/GM038p0158

Ion Acceleration in the Magnetosphere and Ionosphere

Ion Acceleration in the Magnetosphere and Ionosphere

How to Cite

Schulz, M. (1986) Eigenfunction Methods in Magnetospheric Radial-Diffusion Theory, in Ion Acceleration in the Magnetosphere and Ionosphere (eds T. Chang, M. K. Hudson, J. R. Jasperse, R. G. Johnson, P. M. Kintner and M. Schulz), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM038p0158

Author Information

  1. Space Sciences Laboratory, the Aerospace Corporation, El Segundo, California 90245

Publication History

  1. Published Online: 21 MAR 2013
  2. Published Print: 1 JAN 1986

ISBN Information

Print ISBN: 9780875900636

Online ISBN: 9781118664216

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Keywords:

  • Magnetosphere—Congresses;
  • Ionosphere—Congresses;
  • Ion flow dynamics—Congresses;
  • Space plasmas—Congresses

Summary

Complete sets of orthonormal basis functions constructed according to a generalization of the quantum-mechanical WKB approximation can be used to generate a nearly-diagonal matrix representation of the radial-transport operator for ring-current ions in the presence of radial diffusion and charge exchange. The resulting eigenfunctions (constructed by weighting the basis functions in proportion to the respective components of the eigenvectors of the matrix representation) and eigenvalues provide a spatial and temporal description of the evolving phase-space density during and following a magnetospheric disturbance (e.g., a magnetic storm). A linear superposition of the basis functions can also be used to eliminate any discrepancy between the steady-state solution of the transport equation and the appropriate WKB approximation of this steady-state solution.