A high-order electromagnetic gyrokinetic model

Abstract

A high-order extension is presented for the electromagnetic gyrokinetic formulation in which the parallel canonical momentum is taken as one of phase space coordinates. The high-order displacement vector associated with the guiding-center transformation should be considered in the long wavelength regime. This yields addtional terms in the gyrokinetic Hamiltonian which lead to modifications to the gyrokinetic Poisson and Amp\`ere equations. In addition, the high-order piece of the guiding-center transformation for the parallel canonical momentum should be also kept in the electromagnetic model. The high-order piece contains the Ba\~nos drift effect and further modifies the gyrokinetic Amp\`ere equation.