Fluid moments in modied guiding-centre coordinates

A general uid moment in the particle coordinates is represented in terms of uid moments in modied guiding-centre coordinates with strong E × B ow derived by the phase space Lagrangian Lie-transform method [N. Miyato et al., J. Phys. Soc. Jpn. 78, 104501 (2009)]. It is called the push-forward representation of the particle uid moment associated with the guiding-centre transformation. The representation derived is similar to that in terms of gyro-uid moments in the standard gyrokinetic theory in the long wavelength limit. Since the particle coordinates are transformed to gyro-centre coordinates by the two-step transformation in the standard gyrokinetic formulation, two exact push-forward representations are possible. Although the exact representation usually used in the standard gyrokinetic theory has a different form from that in the modied guiding-centre case, the correspondence between the two cases is shown more clearly by considering the alternative form of the push-forward representation for the standard gyrokinetic case.