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

Abstract

view Abstract Citations (11) References (19) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Legendre expansion of the quasi-linear equations for anisotropic particles and Langmuir waves. Hoyng, P. ; Melrose, D. B. Abstract 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. 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; Plasma-Particle Interactions; Astrophysics full text sources ADS |