AbstractWe present a new efficient wave decay channel involving nonlinear interactions between a compressional Alfvén wave, a kinetic Alfvén wave, and a modified ion sound wave in a magnetized plasma. It is found that the wave coupling strength of the ideal magnetohydrodynamic (MHD) theory is much increased when the effects due to the Hall current are included in a Hall–MHD description of wave–wave interactions. In particular, with a compressional Alfvén pump wave well described by the ideal MHD theory, we find that the growth rate is very high when the decay products have wavelengths of the order of the ion thermal gyroradius or shorter, in which case they must be described by the Hall–MHD equations. The significance of our results to the heating of space and laboratory plasmas as well as for the Solar corona and interstellar media are highlighted.
Global well-posedness of the full compressible Hall-MHD equations