Scattering of energetic trapped electrons by very-low-frequency waves

The role of VLF waves in precipitating fast electrons is studied. It is found that, by Doppler-shifting whistler frequencies (1–10 kc/s) up to the local Larmor frequency, a resonant interaction of the type proposed by Dragt and Wentzel (for interaction of protons with hydromagnetic waves) can cause the mirror points of the electrons to move randomly. The conditions for resonance lead to a very characteristic dependence on L of the regions of the magnetosphere where VLF waves can effectively precipitate electrons. In general, one expects to see, in a plot of flux versus L, two peaks separated by a broad minimum, the first peak near L ≃ 1.2 and the second near L ≃ 2. Such peaks have been seen by several experimenters. In certain regions of space it may be that whistlers can dominate the lifetimes of trapped electrons, especially for L ≳ 2.