Theory of triggered VLF emissions

Abstract

A theory is presented to explain the origin of triggered discrete VLF emissions that is more complete than earlier theories, in that it is not restricted to the discussion of kinematical relations but evaluates the dynamics of the problem. Resonant electrons are phase correlated with the wave magnetic field by a finite length whistler train moving in the opposite direction. The time for phase correlation is of the order of the period of oscillation of a particle in the effective ‘potential well’ of the wave. It is recognized that the wave acceleration due to the inhomogeneous magnetic field of the earth must be small enough for the particle to stay trapped in the potential well. The phase-correlated electrons are subject to an instability in the form of an emitted whistler with a growth rate γ/ω ∼ (n/no)2/5(υ⊥/c)2/5 (ωp/Ω)2/5, where (n/no) is the fractional density of the resonant particles, υ⊥ is their mean transverse velocity, and ωp and Ω are local cold plasma and gyrofrequencies. The emitted frequency varies according to ω = k(ω)υ∥ − Ω, where υ∥ is the zero order longitudinal velocity of the resonant electron, and the wave vector k is a function of frequency ω through the whistler dispersion relation. The theory is in good agreement with observation.