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).