THEORY OF ASTRON EQUILIBRIA

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 ℋ, and the canonical momentum ℘ θ, the distribution function, f(ℋ, ℘θ) is written as f = g(℘θ) ℱ(ℋ,℘θ)[α(ℋ,℘θ) ]-1. Here, g(℘θ) is the invariant distribution function for canonical momentum; α (ℋ,℘θ) is the area of the poloidal (r,z) plane accessible to a ring particle with constants ℋ and ℘θ; and ℱ(ℋ, ℘θ) is a nonnegative function having the normalization ∫ dℋℱ = const. The possibility of a third constant of the single particle motion is not included. In contrast with some previous equilibria, f (ℋ,℘θ) is nonzero only in the regions of the ℘θ,ℋ 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. © 1979 American Institute of Physics.