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We study a quasi-two-dimensional electrostatic drift kinetic system as a model for near-marginal ion temperature gradient (ITG) driven turbulence. A proof is given of the nonlinear stability of this system under conditions of linear stability. This proof is achieved using a transformation that diagonalizes the linear dynamics and also commutes with nonlinear $Etimes B$ advection. For the case when linear instability is present, a corollary is found that forbids nonlinear energy transfer between appropriately defined sets of stable and unstable modes. It is speculated that this may explain the preservation of linear eigenmodes in nonlinear gyrokinetic simulations. Based on this property, a dimensionally reduced ($inftytimesinfty rightarrow 1$) system is derived that may be useful for understanding dynamics around the critical gradient of Dimits.
A scaling theory of long-wavelength electrostatic turbulence in a magnetised, weakly collisional plasma (e.g., ITG turbulence) is proposed, with account taken both of the nonlinear advection of the perturbed particle distribution by fluctuating ExB f
The local stability of ion-temperature gradient driven mode (ITG) in the presence of a given radial electric field is investigated using gyrokinetic theory and ballooning mode formalism with toroidal effect accounted for. It is found that, zero frequ
A four-dimensional plasma model able to describe the scrape-off layer region of tokamak devices at arbitrary collisionality is derived in the drift-reduced limit. The basis of the model is provided by a drift-kinetic equation that retains the full no
Scaling laws for ion temperature gradient driven turbulence in magnetized toroidal plasmas are derived and compared with direct numerical simulations. Predicted dependences of turbulence fluctuation amplitudes, spatial scales, and resulting heat flux
In the present work the zonal flow (ZF) growth rate in toroidal ion-temperature-gradient (ITG) mode turbulence including the effects of elongation is studied analytically. The scaling of the ZF growth with plasma parameters is examined for typical to