Derivation via free energy conservation constraints of gyrofluid equations with finite-gyroradius electromagnetic nonlinearities

Abstract

The derivation of electromagnetic gyrofluid equations is made systematic by using the Hermite polynomial form of the underlying delta-f gyrokinetic distribution function. The gyrokinetic free-energy functional is explicitly used to set up the model. The gyrofluid free energy follows directly. The interaction term in the gyrokinetic Lagrangian is used to obtain the gyrofluid counterpart, from which the polarisation equation follows. One closure rule is decided for taking moments over the kinetic gyroaveraging operator. These steps fix the rest of the derivation of the conservative part of the gyrofluid equations. Dissipation is then added in a form to obtain positive definite dissipation and to obtain the collisional fluid equations in their appropriate limit. Existing results are recovered, with the addition of a completely consistent model for finite gyroradius effects in the nonlinearities responsible for magnetic reconnection.