Weak turbulence theory of ion temperature gradient modes for inverted density plasmas

Typical profiles measured in H-mode ("high confinement") discharges from tokamaks such as JET [Proceedings of the 15th European Conference on Controlled Fusion and Plasma Heating (European Physical Society, Geneva, 1988), Vol. 12B, Part 1, p. 2239] and DIII-D [Phys. Fluids 31, 3738 ( 1988)] suggest that the ion temperature gradient instability threshold parameter η_i(≡d ln T_i/d ln n_i) could be negative in many cases. Previous linear theoretical calculations [Phys. Fluids B 1, 1185 (1989)] have established the onset conditions for these negative η_i modes and the fact that their growth rate is much smaller than their real frequency over a wide range of negative η_i values. This has motivated the present nonlinear weak turbulence analysis to assess the relevance of such instabilities for confinement in H-mode plasmas. The nonlinear eigenmode equation indicates that the three-wave coupling to shorter wavelength modes is the dominant nonlinear saturation mechanism. It is found that both the saturation level for these fluctuations and the magnitude of the associated ion thermal diffusivity are considerably smaller than the strong turbulence mixing-length-type estimates for the more conventional positive η_i instabilities.