Theory of ion temperature gradient instabilities: Thresholds and transport

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Abstract
An investigation of the ion temperature gradient instability that focuses on the behavior of the mode when it is weakly unstable is presented. It is shown that ηi= (2)/(3) is the threshold for long wavelength instability, ηi being the ratio of the density gradient scale length to the ion temperature gradient scale length. For ηi>0.902, a short wavelength mode is concomitantly unstable. The transport resulting from both the short and the long wavelengths is shown to constitute a ‘‘soft’’ turn on of anomalous transport for ηii=2 represents a ‘‘hard’’ threshold for transport: Beyond this point, large, collisionless transport over all wavelengths is precipitated. A nonlocal collisional theory as well as a kinetic theory with a Krook collision operator are presented to describe the progression from weak to strong instability. Transport estimates, based on mixing length arguments, are given for the various regimes incorporated by the critical points ηi= (2)/(3) , 0.902, and 2.