Parametric instabilities of circularly polarized Alfvén waves in plasmas with beam protons

The proton velocity distribution functions (VDFs) observed in the solar wind often show beam components. In this study, by means of one-dimensional hybrid simulation, parametric instabilities of circularly polarized Alfv́n waves in core proton-electron-beam proton plasmas are discussed. Numerical results show that nonlinear evolution of parametric instabilities in core proton-electron-beam proton plasmas are different from those in core proton-electron plasmas. Furthermore, numerical solutions of the linear dispersion relations suggest the importance of the proton kinetic effects, which agrees with the past studies. In the case that the beams are stable, according to the excitation of the broadband Alfvén waves by the parametric instabilities, protons are diffused in the velocity space, resulting in the scattering and broadening of the beam components. Such time evolution of the proton VDFs changes the wave dispersion relation and affects the properties of the parametric instabilities, in agreement with the past theoretical studies. As a result, even if a decay instability is dominant at the linear stage, the parent wave can mainly be dissipated by the modulational instability at the nonlinear stage. Phase coherent turbulence is generated corresponding to the occurrence of the modulational instability. Parametric instabilities are also observed in plasmas with unstable beams. When left-hand polarized (LH-) Alfvén wave is initially given, both backward propagating right-hand polarized (RH-) and LH- Alfvén waves are excited by the decay instabilities in our runs. As time elapses, phase coherent turbulence is generated by the modulational instabilities, as in the case of stable beams. Some of the beam protons are perpendicularly accelerated by cyclotron resonance with the primary wave.