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Energy transfer equation and universal spectrum of ion–acoustic wave turbulence

The energy transfer equation in wavenumber space of ion–acoustic wave turbulence is obtained through investigation of the effects of turbulent fluctuations on the propagator of a test wave in the plasma. Those turbulent fluctuations whose wavelengths are shorter than that of the test wave give rise to collisional effects, while those with longer wavelengths act to deform continuously the shape of the test wave, thereby producing a diffusive flow of the turbulence energy in k space. Dimensional analysis, coupled with the Kolmogorov hypothesis, is then carried out on the resulting equation; a universal spectrum proportional to in the large k subdivision and to k−4 in the small k subdivision of the inertial domain is thus obtained.