Wavevector spectral signature of decay instability in space plasmas

Identification of a large-amplitude Alfvén wave decaying into a pair of ion-acoustic and daughter Alfvén waves is one of the major goals in the observational studies of space plasma nonlinearity. In this study, the decay instability is analytically evaluated in the 2-D wavenumber domain spanning the parallel and perpendicular directions to the mean magnetic field. The growth-rate determination of the density perturbations is based on the Hall MHD (magnetohydrodynamic) wave–wave coupling theory for circularly polarized Alfvén waves. The diagrams of the growth rates versus the wavenumber and propagation angle derived in analytical studies are replaced by 2-D wavenumber distributions and compared with the corresponding wavevector spectrum of density and magnetic field fluctuations. The actual study reveals a perpendicular spectral pattern consistent with the result of a previous study based on 3-D hybrid numerical simulations. The wavevector signature of the decay instability observed in the two-dimensional wavenumber domain ceases at values of plasma beta larger than β=0.1. Growth-rate maps serve as a useful tool for predictions of the wavevector spectrum of density or magnetic field fluctuations in various scenarios for the wave–wave coupling processes developing at different stages in space plasma turbulence.