On the nonlinear stability of a quasi-two-dimensional drift kinetic model for ion temperature gradient turbulence

TL;DR

This paper proves the nonlinear stability of a quasi-two-dimensional drift kinetic model for ion temperature gradient turbulence under certain conditions, providing insights into mode interactions and potential simplifications for complex plasma simulations.

Contribution

It introduces a novel stability proof for the model and derives a reduced system to better understand critical gradient dynamics in plasma turbulence.

Findings

Proof of nonlinear stability under linear stability conditions

A transformation that diagonalizes linear dynamics and commutes with nonlinear advection

A reduced system capturing essential dynamics near the critical gradient

Abstract

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 $E\times B$ 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 ($\infty\times\infty \rightarrow 1$) system is derived that may be useful for understanding dynamics around the critical gradient of Dimits.