Abstract
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.
Highlights
Parametric instabilities driven by large-amplitude Alfvén waves have extensively been investigated by analytical studies or numerical simulations in one- or multidimensional approaches
Other studies on the nonlinear interaction of obliquely propagating Alfvén waves confirm that the growth rate of the decay instability in direction oblique to the mean magnetic field is typically smaller than the fieldaligned decay; see, for example, Mjølhus and Hada (1990), Laveder et al (2002), and Nariyuki et al (2008)
The wave–wave coupling of the large-amplitude Alfvén pump wave with a density perturbation of wavevector k and frequency ω is conducting to side-band daughter waves expressed by the relations k± = k±k0 and ω± = ω±ω0, where k± and ω± describe the wavevectors and frequencies of the daughter waves, respectively; k0 = k0e, where k0 is the wavenumber of the Alfvén pump wave; e is the unity vector parallel to the mean magnetic field; and ω0 is the frequency of the Alfvén pump wave
Summary
Parametric instabilities driven by large-amplitude Alfvén waves have extensively been investigated by analytical studies or numerical simulations in one- or multidimensional approaches. A systematic analytical analysis of the multidimensional features of the parametric instabilities has been initiated by Viñas and Goldstein (1991a, b) by applying the Hall magnetohydrodynamic (hereafter, Hall–MHD) theory to a large-amplitude field-aligned Alfvén wave with lefthand and right-hand circular polarization. Propagating daughter waves excited by the decay of a field-aligned Alfvén wave have been observed in 2-D MHD numerical simulations by Ghosh et al (1993) for a low-beta regime. Comisel et al (2019) observed recently a perpendicular spectrum of daughter waves by using field-aligned Alfvén pump waves with circular left-hand polarization and 3-D hybrid simulations. This result was not predicted by previous 2-D numerical simulations. The threedimensional setup was used by Comisel et al (2020) for analyzing the evolution of large-amplitude Alfvén waves into
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