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.

中文翻译：

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空间等离子体中衰变不稳定性的波矢频谱特征

识别衰减成一对离子声和子Alfvén波的大振幅Alfvén波是空间等离子体非线性观测研究的主要目标之一。在这项研究中，在跨平均磁场平行和垂直方向的二维波数域中对衰减不稳定性进行了分析评估。密度扰动的增长率是基于圆偏振Alfvén波的Hall MHD（磁流体动力学）波-波耦合理论确定的。分析研究中得出的增长率与波数和传播角的关系图被二维波数分布代替，并与相应的密度和磁场波动的波矢谱进行了比较。实际研究揭示了与先前基于3-D混合数值模拟的研究结果一致的垂直光谱图。在二维波数域中观察到的衰减不稳定性的波矢特征在大于β = 0.1。增长率图可作为预测空间等离子体湍流不同阶段发展的波波耦合过程在各种情况下密度或磁场波动的波矢谱的有用工具。