Ion temperature gradient turbulence close to the finite heat flux threshold

The dependence of the heat flux on the temperature gradient length in collisionless ion temperature gradient turbulence has recently been revisited. It has been found that the heat flux is discontinuous at a finite heat flux threshold larger than the (Dimits) interpolated threshold. In this paper, the influence of collisions on the heat flux close to the threshold is investigated. It is found that up to relatively high collision frequencies, relevant to the modern day experiments, a discontinuous behaviour of the heat flux as a function of the gradient length persists. Collisions, however, do lead to a reduction in the gradient length at which the discontinuity is observed. Below the finite heat flux threshold, a state of low turbulence with a vanishing small heat flux persists, which can drive the zonal flow against the collisional dissipation. This state is characterised by the fully developed staircases in the radial ExB shearing profile. Increasing the collision frequency at a fixed gradient length leads to the loss of the fully developed staircase structure with the ExB shearing profile having the form of a sawtooth that allows for avalanche formation and a finite heat flux. At very high collision frequencies or gradient lengths well above the threshold the staircase structure is lost. The simulations indicate that the long wave length zonal flow saturates through a mechanism that directly involves the turbulence intensity.