Transfer of free energy from large to small velocity-space scales by phase mixing leads to Landau damping in a linear plasma. In a turbulent drift-kinetic plasma, this transfer is statistically nearly canceled by an inverse transfer from small to large velocity-space scales due to “anti-phase-mixing” modes excited by a stochastic form of plasma echo. Fluid moments (density, velocity, and temperature) are thus approximately energetically isolated from the higher moments of the distribution function, so phase mixing is ineffective as a dissipation mechanism when the plasma collisionality is small.
References
This echo effect could not be captured in the earlier work by Plunk,32 who modelled the effect of turbulence not as nonlinear advection but as a random force in a linear system. There could thus not be any nonlinear modification of the linear response, so the effective damping rate inferred by Plunk differed from the standard Landau damping rate only because the kinetic Langevin system is functionally different from the standard fluid system.10
We ignore here the subtleties of the electron response in ITG turbulence (see, e.g., Ref. 33, sec. J.2)—they do not matter for the inertial-range physics on which we focus here. The response we use is formally correct for electron-temperature-gradient (ETG) turbulence,34 which is described by the same equations with e ↔ i swapped and some irrelevant sign changes (Ref. 12, sec. 2.2.1).
