A mechanism for VLF emissions

The triggering of emissions, particularly by Morse pulses, is considered. Because it seems unlikely that linear theory can account for triggered emissions, the nonlinear effect of the pulse on the electron distribution is studied. This is an isolated but complicated theoretical problem, and some approximations are made. The approach aims at calculating the growth rate as a function of frequency for the disturbed plasma after the pulse has passed. The concepts of Kennel and Petschek (1966) are used, and the ‘diffusion curves’ in velocity space along which the electrons are diffused are calculated. Also following Kennel and Petschek it is assumed that the background hiss can be amplified in a narrow band to give a discrete emission. The results are encouraging, particularly in explaining why dashes are so much more effective at triggering than dots. The mechanism discussed must occur, and orders of magnitude suggests that it is important. The mathematical treatment depends on the ratio of the duration of the pulse to the oscillation period for particles trapped by the wave, and this ratio may be of the order of unity. Here one crude model is presented appropriate to large values of this ratio (long strong pulses) and a less crude model is appropriate to small values (short weak pulses). Qualitatively the results are similar, and in particular they predict enhancements of the growth rate in narrow frequency bands at the edges of the spectrum of the triggering pulse. Qualitative discussion also indicates how hooks and risers can result in the nonuniform geomagnetic field, though the nonuniformity of the field is found to be unimportant in the treatment of the effect of the triggering pulse.