The theory of astron ion-ring equilibria is considered from a new point of view. In contrast with previous equilibria, the new equilibria have a distribution of canonical momentum which is invariant to axisymmetric changes in the external magnetic field. As a function of the single particle constants of the motion, the energy β, and the canonical momentum π«Ο, the distribution function, f (β,π«Ο) is written as f=g (π«Ο) β± (β,π«Ο)[π (β,π«Ο)]β1. Here, g (π«Ο) is the invariant distribution function for canonical momentum; π (β,π«Ο) is the area of the poloidal (r,z) plane accessible to a ring particle with constants β and π«Ο; and β± (β,π«Ο) is a nonnegative function having the normalization β± dβ β±=const. The possibility of a third constant of the single particle motion is not included. In contrast with some previous equilibria, f (β,π«Ο) is nonzero only in the regions of the π«Ο,β plane in which there are trapped particle orbits. With this representation of f, it becomes possible to study the adiabatic compression of ion-ring Vlasov equilibria.
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Lovelace et al. (1979) studied this question.
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