Legendre expansion of the quasi-linear equations for anisotropic particles and Langmuir waves

Details Legendre expansion of the quasi-linear equations for anisotropic particles and Langmuir waves Legendre expansion of the quasi-linear equations for anisotropic particles and Langmuir waves

Dec 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977apj...218..866h&link_type=abstract

Astrophysical Journal, Part 1, vol. 218, Dec. 15, 1977, p. 866-880.

Astronomy and Astrophysics

Astrophysics

4

Electrostatic Waves, Legendre Functions, Nonlinear Equations, Polynomials, Type 3 Bursts, Wave Equations, Anisotropy, Astronomical Models, Astrophysics, Coefficient Of Friction, Diffusion Coefficient, Electron Distribution, Plasma-Particle Interactions

Scientific paper

The quasi-linear 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 quasi-linear 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 quasi-linear 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.

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