Quantification of Sub-Grid-Scale Terms in Plasma Turbulence

The notions of DNS and LES are well established in hydrodynamic turbulence. We apply similar ideas to plasma turbulence whose governing equation (i.e., the Vlasov or Fokker-Planck equation) is higher dimensional (generally 6D). Analogously to the Navier-Stokes LES equations, we filter and derive sub-grid-scale terms for the Vlasov equation. It is known in gyrokinetic plasma turbulence that nonlinear interactions in velocity space lead small scales generation of the distribution function up to the collisional scales (see Schekochihin et al., Plasma Phys. Control. Fusion 2008). Because the gyrokinetic description still requires a 5D phase space description, and hence is computationally expensive, our first approach is to quantify the SGS terms in the context of drift kinetic equations in 4D phase space under the electrostatic approximation using high resolutions of up to a billion grid cells. We examine the phenomenology of the SGS terms by a careful quantification using high-order DNS of drift kinetic turbulence. The eventual goal is to develop SGS models for use in under-resolved or LES of plasma turbulence.