Abstract. 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.