Coherent generation of the auroral kilometric radiation by nonlinear beatings between electrostatic waves

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Abstract
The propagation of electrostatic plasma waves in an inhomogeneous and magnetized plasma is studied analytically. These waves, which are driven unstable by auroral beams of electrons, are shown to suffer a further geometrical amplification while they propagate toward cut‐off. Simultaneously their group velocities tend to be aligned with the geomagnetic field. Then it is shown that the electrostatic energy tends to accumulate at or near ωLH and ωUH, the local lower and upper hybrid frequencies. Due to this process, large amplitude electrostatic waves with very narrow spectra should be observed near these frequencies at any place along the auroral field lines where intense beam driven instability takes place. These intense quasi‐monochromatic electrostatic waves are then shown to give rise by a coherent nonlinear three wave process to an intense electromagnetic radiation. Provided that the ratio ωpe/ωce tends to be smaller than unity, it is shown that the most intense radiation should be observed at 2ωUH in the extraordinary mode.