Type-III Electron Beams: 3D Quasilinear Effects

Abstract

A conventional model for the generation of Langmuir waves in Type-III radio bursts is based on a one-dimensional (1D) version of the quasilinear equations. In this model a wave with phase velocity $v_{\phi }$ resonates with an electron with velocity $v=v_{\phi }$ , causing the waves to grow at a rate $\propto {\mathrm{d}}F(v)/{\mathrm{d}}v>0$ , where $F(v)$ is the 1D-distribution function. The backreaction on the electrons drives the electrons towards a plateau distribution: $\mathrm{d}F(v)/{\mathrm{d}}v\to 0$ . In the 3D-generalization, none of these features apply: waves with phase speed $v_{\phi }$ can resonate with electrons with speed $v< v_{\phi }$ , depending on the angle between the wave normal and the electron velocity, wave growth occurs only if the distribution function is both an increasing function of $v$ and also has an anisotropic pitch-angle distribution, and the backreaction involves diffusion in both speed $v$ and in pitch-angle $\alpha $ . In this article we discuss implications of the generalization from 1D to 3D on models for Type-III bursts. An effect that is absent in 1D, but may be important in 3D, is scattering of Langmuir waves by turbulence in the ambient plasma. Pitch-angle scattering by the scattered Langmuir waves may play an important role in the evolution of the Type-III beam.