Abstract
A new analytical approach to cyclotron instability of electron beams with sharp gradients in velocity space (step-like or delta distribution function) is developed taking into account magnetic field inhomogeneity and non-stationary behavior of the electron beam velocity. Under these conditions, the conventional hydrodynamic instability of such beams is drastically modified and second order resonance effects become important. It is shown that the optimal conditions for the instability occur for a non-stationary quasi-monochromatic wavelets whose frequency changes in time. The theory developed permits to estimate the wave amplification and spatiotemporal characteristics of these wavelets. The results obtained are important for interpretation of VLF/ELF triggered and chorus emissions.
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