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This paper pointed out that the usual gyrocenter transform, which implementssingle-parameter Lie transform perturbation theory on Lagrangian differential1-form of the orbit of charged particles immersed in a strong magnetic field,is not a near identical coordinate transform, and further causes someunphysical terms in the eventual orbit equations.

On the gyrocenter transform implemented on Lagrangian differential 1-form with the existence of magnetic perturbation