Self‐Consistent Theory of Triggered Whistler Emissions

Abstract

A kinetic theory of triggered VLF whistler emissions is given that is capable of predicting from a small scale numerical implementation the observed emission forms, and frequency-time characteristics. The present paper focuses on the theoretical developments and the explanation of the triggering process, complete with a demonstration of the threshold behavior (sometimes known as the dot-dash anomaly) and the generation of specific falling frequency emissions that compare quite favorably to typical observations made in the controlled experiments based in Siple Station, Antarctica. The theory that gives these results is a fully self-consistent nonlinear treatment based on kinetic theory and valid in the asymptotic limit when several trapping periods occur within the interaction region. For a typical set of parameters, I = 4.3, n = 400 cm-3 , and amplitude, BT ~ 1.6 pT, for the input wave magnetic field, one has about seven trapping periods in the triggering signal and would expect good results from the asymptotic limit. In this limit the nonlinear dynamics can be reduced to the determination of the time, r, that the resonant particles are trapped. The nonlinear currents can be expressed in terms of this function, r, by simple integrals over the trapped particles' perpendicular velocities alone. Most of the features of the emission process can be determined analytically and properties, such as the rate of change of frequency, related to magnetospheric parameters. For more quantitative predictions such as amplitude and frequency waveforms, a small numerical code which integrates the nonlinear wave equations is used. The theoretical picture of the triggering mechanism i contains the observed threshold behavior wherein short triggering pulses of nominal amplitude BT ~ 1 pT and 100 ms in duration or less cannot generate an emission, whereas those in the 200 ms range and longer do. Similar sensitivity is found with respect to initial frequency, where in some cases 5.5 kHz signals can trigger, but 5.0 kHz signals cannot.Gains in the range of 20 -30 dB are obtained with initial temporal growth rates in the range 100 -200 dB/sec. The emission process requires an inverted population in the perpendicular velocity distribution function but not necessarily linear instability. A sufficient number of high energy electrons is required that the driven currents can offset convection, but provided this is satisfied, a sufficiently long triggering signal will always generate a self-sustaining emission. Interestingly, however, the self-sustaining emission does not depend on the number of these high energy particles or the details of the velocity distribution function but only on bulk magnetospheric parameters such as magnetic field, gradient scale length, and the plasma density in the plasmapause. Also the marginal signals generated just above the threshold are always fallers as is observed. These features have not been explained by existing theories. Unresolved issues include the mechanism of termination, the generation of ri...

Beam-plasma instability in inhomogeneous magnetic field and second order cyclotron resonance effects

“…Wellorganized electron beams can be produced by quasimonochromatic whistler wave packets. 5,6 Such a situation takes place in the Earth's magnetosphere in the case of the socalled triggered ELF/VLF emissions. [7][8][9][10] The beams with a step-like distribution function can appear in space plasma conditions even more often than ␦-functions.…”

Simultaneous observation of whistlers and emissions during a geomagnetically quiet period at low latitude

“…The nonlinear self-consistent interaction of cyclotron resonant energetic electrons with narrow band VLF waves in the Earth's magnetosphere has been used to explain many of the qualitative physical features underlying these types of emissions (Helliwell 1967;Karpman et al 1974;Yoshida et al 1983;Molvig et al 1988;Omura et al 1991;Nunn et al 1997;Trakhtengerts and Rycroft 2000). In spite of tremendous efforts and huge theoretical work published so far; a selfconsistence theory capable of predicting the observed dynamic spectra, threshold behavior and frequency time characteristics has remained elusive.…”

On the electron dynamics in the field of a whistler wave propagating along a magnetic field in a weakly inhomogeneous plasma

“…Similar equations have also been exploited repeatedly in subsequent studies on the nonlinear gyroresonant phenomena in the magnetosphere (e.g. Nunn, 1974;Karpman, 1974;Roux and Pellat, 1978;Bell and Inan, 1981;Molvig et al, 1988;Carlson et al, 1990;Shklyar et al, 1992). In essence, the simplified description of the particle dynamics (Dysthe, 1971) reduces to a change of rigorous equations of motion for equations averaged over the Larmor gyration of the particle.…”