Nonlinear gyrokinetic equations for tokamak microturbulence

Abstract

A nonlinear electrostatic gyrokinetic Vlasov equation as well as a Poisson equation have been derived in a form suitable for particle simulation studies of tokamak microturbulence and associated anomalous transport. This work differs from the existing nonlinear gyrokinetic theories in toroidal geometry, since the present equations conserve energy while retaining the crucial linear and nonlinear polarization physics. In the derivation, the action-variational Lie perturbation method is utilized in order to preserve the Hamiltonian structure of the original Vlasov–Poisson system. Emphasis is placed on the dominant physics of the collective fluctuations in toroidal geometry, rather than on details of particle orbits.

A simple model of intrinsic rotation in high confinement regime tokamak plasmas

“…Thus, to this end, a complementary theoretical path was also followed. Taking the parallel velocity moment of the conservative form of the gyrokinetic equations 18,19 in toroidal geometry, it was shown that magnetic curvature leads to a convective flux ͑i.e., a "pinch," if inward͒ of angular momentum density. 20 Afterwards, it was also pointed out that a part of this flux, the so called turbulent equipartition ͑TEP͒ pinch component, can also be obtained from simple consideration of angular momentum conservation in toroidal geometry.…”

Parallel filtering in global gyrokinetic simulations

“…However, when deriving gyrokinetic equations (see for ex. [3]), other small parameters are introduced:…”

Comment on “Nonlinear gyrokinetic theory with polarization drift” [Phys. Plasmas 17, 082304 (2010)]

“…,N runs over the particles of the distribution function. The primary form of the distribution function yields the continuity equation 4 …”