Nonlinear evolution of drift instabilities in the presence of collisions

Nonlinear evolution of drift instabilities in the presence of electron--ion collisions in a shear-free slab has been studied by using gyrokinetic particle simulation techniques as well as by solving, both numerically and analytically, model mode-coupling equations. The purpose of the investigation is to determine the mechanisms responsible for the nonlinear saturation of the instability and for the ensuing steady-state transport. Such an insight is very valuable for understanding drift-wave problems in more complicated geometries. The results indicate that the electron E x B convection is the dominant mechanism for saturation. It is also found that the saturation amplitude and the associated quasilinear diffusion are greatly enhanced over their collisionless values as a result of weak collisions. In the highly collisional (fluid) limit, there is an upper bound for saturation with ephi/T/sub e/≅(ω/sub l//Ω/sub i/)/(k/sub perpendicular/ rho/sub s/)2. The associated quasilinear diffusion, which increases with collisionality, takes the form of D/sub ql/≅γ/sub l//k2/sub perpendicular/, where ω/sub l/ and γ/sub l/ are the linear frequency and growth rate, respectively. In the steady state, the diffusion process becomes stochastic in nature. The relevant mechanisms here are related to the velocity-space nonlinearities and background fluctuations. The magnitude of the diffusion at this stage can be comparable to that of quasilinear diffusion in the presence of collisions, and it seems to remain finite even in the collisionless limit