Theory of Longitudinal Adiabatic Invariant in the Helical Torus

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  • Theory of Longitudinal Adiabatic Invari

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The theory on the longitudinal adiabatic invariant valid for the helical magnetic field is developed on the basis of the variable transformation from the guiding center variables to the new adiabatic variables. The theory uses the Hamiltonian formalism with non canonical variables. Under the assumption that the rotational transform per period is small, the adiabatic invariant is defined by integral along the toroidal direction, not along the field line. The first order correction to the adiabatic invariant with respect to the expansion parameter is obtained. The transition between the passing and the ripple trapped states is investigated. The jump of adiabatic variables takes place in the transition process, which causes the diffusion of the adiabatic invariant. The transformation of distribution function associated with the variable transformation is also discussed.

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