Three-wave interactions of dispersive plasma waves propagating parallel to the magnetic field

Three-wave interactions of plasma waves propagating parallel to the mean magnetic field at frequencies below the electron cyclotron frequency are considered. We consider Alfvén--ion-cyclotron waves, fast-magnetosonic--whistler waves, and ion-sound waves. Especially the weakly turbulent low-beta plasmas like the solar corona are studied, using the cold-plasma dispersion relation for the transverse waves and the fluid-description of the warm plasma for the longitudinal waves. We analyse the resonance conditions for the wave frequencies $ω$ and wavenumbers $k$, and the interaction rates of the waves for all possible combinations of the three wave modes, and list those reactions that are not forbidden.

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