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 energyH, and the canonical momentumP&Vthgr;, the distribution function,f(H,P&Vthgr;) is written asf=g(P&Vthgr;)F(H,P&Vthgr;)[A(H,P&Vthgr;)]−1. Here,g(P&Vthgr;) is the invariant distribution function for canonical momentum;A(H,P&Vthgr;) is the area of the poloidal (r,z) plane accessible to a ring particle with constantsHandP&Vthgr;; andF(H,P&Vthgr;) is a nonnegative function having the normalizationF dH F=const. The possibility of a third constant of the single particle motion is not included. In contrast with some previous equilibria,f(H,P&Vthgr;) is nonzero only in the regions of theP&Vthgr;,Hplane in which there are trapped particle orbits. With this representation off, it becomes possible to study the adiabatic compression of ion‐ring Vlasov equilibria.