A Modification of the Guiding-Centre Fundamental 1-Form with StrongE×BFlow

Abstract

A modified guiding-centre fundamental 1-form with strong E × B flow is derived by the phase space Lagrangian Lie perturbation method. Since the symplectic part of the derived 1-form is the same as the standard one without the strong E × B flow, it yields the standard Lagrange and Poisson brackets. Therefore the guiding-centre Hamilton equations keep their general form even when temporal evolution of the E × B flow is allowed. Compensation of keeping the standard symplectic structure is paid by complication of the guiding-centre Hamiltonian. However, it is possible to simplify the Hamiltonian in well localised transport barrier regions like a tokamak edge in a high confinement regime and an internal transport barrier in a reversed shear tokamak. The guiding-centre Vlasov and Poisson equations are derived from the variational principle. The conserved energy of the system is obtained from the Noether's theorem. Correspondence to low-frequency fluid equations is shown.