On extension of the gyrokinetic quasi-neutrality condition towards the long wavelength regime

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

Although the standard gyrokinetic model is formulated for perturbations with short wavelength and small amplitude, it is used in several global codes treating both long wavelength and short wavelength perturbations recently. In the codes the gyrokinetic (reduced) poisson equation or the gyrokinetic quasi-neutrality condition is used to obtain the electrostatic potential. It is found, however, that the original gyrokinetic quasi-neutrality condition (and the Poisson equation) becomes insufficient for long wavelength perturbations since the polarisation density term with the electrostatic potential in the condition goes to higher order. Then, we have to consider other higher order terms. The polarisation density term stems from the displacement vector associated with the gyro-centre transformation. There is another piece associated with the guiding-centre transformation. By taking into account this piece, we find several additional terms resulting from non-uniformity of magnetic field.