Legendre expansion of the quasilinear equations for anisotropic particles and Langmuir waves.
Abstract
The quasilinear diffusion and friction coefficients for axisymmetric electron distributions interacting with Langmuir waves are evaluated explicitly by expanding the distribution of waves in Legendre polynomials. The quasilinear equations are then reduced to a form in which both the distributions of waves and of particles are simultaneously expanded in Legendre polynomials, and all coefficients are evaluated explicitly. It is argued that such expansions are likely to be justified in practice and that the results obtained should prove useful in discussing quasilinear relaxation under various conditions in three dimensions rather than one dimension. New results are anticipated for the problem of the propagation of electron streams causing type III solar radio bursts. The influence of the magnetic field on the Langmuir waves is neglected.
 Publication:

The Astrophysical Journal
 Pub Date:
 December 1977
 DOI:
 10.1086/155742
 Bibcode:
 1977ApJ...218..866H
 Keywords:

 Electrostatic Waves;
 Legendre Functions;
 Nonlinear Equations;
 Polynomials;
 Type 3 Bursts;
 Wave Equations;
 Anisotropy;
 Astronomical Models;
 Astrophysics;
 Coefficient Of Friction;
 Diffusion Coefficient;
 Electron Distribution;
 PlasmaParticle Interactions;
 Astrophysics