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A Drift-kinetic formulation with strong E$$times$$B flow

Miyato, Naoaki; Scott, B. D.*; Strintzi, D.*; Tokuda, Shinji

A guiding-centre fundamental 1-form with strong E$$times$$B flow for a single charged particle is derived by the Lie transform perturbation analysis. The symplectic part of the 1-form does not include the E$$times$$B term which is included in the symplectic part in the previous formulations. As a result, it is the same as the standard one without the strong flow formally and gives the standard Hamilton equations even when time evolution of the E$$times$$B flow is allowed. Although the guiding-centre Hamiltonian is more complicated than the previous ones, it can be simplified in well localised transport barrier regions such as a tokamak H-mode edge where the strong E$$times$$B flow is observed. Based on the derived 1-form, a total Lagrangian including both contributions from particles and fields is constructed. The guiding-centre Vlasov and Poisson equations are derived from the variational principle. The conserved energy of the system is obtained from the Lagrangian by the Noether method.

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