On the Gyrokinetic model in long wavelength regime

Miyato, Naoaki; Scott, B. D.*; Yagi, Masatoshi

The standard gyrokinetic model is formulated for perturbations with short wavelength and small amplitude. In the long wavelength regime, the polarisation density term with electrostatic potential in the gyrokinetic quasi-neutrality equation goes to higher order than usual. Therefore, we should consider the other higher order terms to obtain from the equation. This issue is investigated from the point of view of the push-forward representation of particle density. The polarisation density term stems from the displacement vector. There is another piece associated with the transformation which is not considered in the standard model. The gyrokinetic Hamiltonian is modified by taking into account this piece. The quasi-neutrality equation is derived rigorously from the modified Hamiltonian through a variational method and we find several additional terms resulting from non-uniformity of magnetic field.