Emission and Absorption of Langmuir Waves by Anisotropic Unmagnetized Particles

Abstract

The emission and absorption coefficients for Langmuir waves due to anisotropic unmagnetized particles are reduced to two complementary forms: one involving integrals over momentum p and pitch angle ex; the other involving an integral over p and a sum over Legendre polynomials. The quasilinear diffusion coefficients are reduced to the former. It is also shown how the absorption coefficient may be reduced to forms involving neither a p derivative nor an ex derivative. The absorption coefficient is evaluated explicitly for five idealized anisotropic distributions, called a 'forwardcone' anisotropy, a 'semi-cos2 ex' anisotropy, a loss-cone anisotropy, a P, anisotropy and a P2 anisotropy respectively. All except the P2 anisotropy can lead to growth of Langmuir waves, but only if the distribution function is an increasing function of p at the resonant phase speed, e.g. only for gap distributions. The results have important implications in connection with the theory of solar radio bursts.