On the gyrokinetic model in long wavelength regime

The gyrokinetic quasi-neutrality equation is considered from the point of view of the push-forward representation of particle density associated with the guiding-center transformation and the gyro-center transformation involved in the standard gyrokinetic formulation. It is clearly shown that the higher order displacement vector of the guiding-center transformation as well as the gyro-center displacement vector should be taken into account in the long wavelength regime. The higher order displacement vector of the guiding-center transformation yields additional higher order terms related to nonuniformity of magnetic field in the gyrokinetic quasi-neutrality equation. These additional terms may be important when the gradient scale length of electric field can be comparable to that of the magnetic field as in low aspect ratio tokamaks. Also the gyrokinetic Hamiltonian should be modified for consistency.