AbstractStarting from nonlinear evolution equations of a three‐dimensional extra‐ordinary wavepacket in a magnetized plasma and introducing a correlation function, equations are derived that describe interaction of a coherent low‐frequency magneto‐acoustic wave with a turbulent spectrum of high frequency extra‐ordinary waves. These equations are used to derive the dispersion relation for a low frequency magnetoacoustic wave in the presence of a spectrum of turbulent high frequency extra‐ordinary waves. In the narrow spectrum case, it is found that a small but finite spread in the spectrum of turbulence has a stabilizing influence on the instability which exists for vanishing spectral width. In the wide spectrum case, the effect of a weak turbulent spectrum of extra‐ordinary waves is to produce a slight shift in frequency of the coherent low frequency magneto‐acoustic wave and to damp or excite the wave.
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