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A Modification of the guiding-centre fundamental 1-form with strong E$$times$$B flow

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

A modified guiding-centre fundamental 1-form with strong $${bf E}times{bf B}$$ flow is derived by the phase space Lagrangian Lie perturabtion method. Since the symplectic part of the derived 1-form is the same as the standard one without the strong $${bf E}times{bf B}$$ 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 $${bf E}times{bf B}$$ 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 H-mode edge 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.



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Category:Physics, Multidisciplinary



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