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Kinetic ion gradient instability: bifurcation properties of a simple, kinetic ηi-unstable slab model

The so-called ηi instability is driven by the ion-temperature gradient and affects both particle and energy transport. Using a simple kinetic model, first the onset of the instability is investigated by linear theory. In contrast to most treatments in the literature, a non-local analysis is performed. It turns out that the local approximation is only a very rough approximation, and may drastically overestimate the instability conditions. A numerical solution of the full model confirms the non-local stability analysis. In addition, it allows one to follow the nonlinear development of the instability. Using a numerical scheme based on the Lagrange structure of the equations of motion, the saturation values are obtained. A constriction of the density profile is accompanied by a broadening of the ion-temperature profile. The normal form of the bifurcation is obtained, together with the scaling of the anomalous transport (in terms of the deviation from the marginal condition).