ECMI Resonance in AKR Revisited: Hyperbolic Resonance, Harmonics, Wave-Wave Interaction

Abstract: Recapitulation of the resonance condition for the fundamental and higher electron cyclotron harmonics in the Electron Cyclotron Maser Instability (ECMI) enables radiation below and confirms the possibility of radiation in a narrow band above harmonics $n>1$. Near $n=1$ resonance on the confined lower X-mode branch, amplification is supported by the decrease of phase and group speeds. Confined slow large-amplitude quasi-electrostatic X-modes nonlinearly modulate the plasma to form cavitons until self-trapped inside them at further increasing wavenumber. They undergo wave-wave interaction, enabling escape to free space in the second harmonic band below $n=2$. At sufficiently large parallel wavenumber (oblique propagation), the fundamental resonance $n=1$ is hyperbolic, a possibility so far missed but vital for an effective ECMI in the upward current region. Here, the resonance hyperbola favourably fits the loss cone boundary, the presumably important ECMI upward-current source-electron distribution, to stimulate ECMI growth at available auroral electron energies.