Phase density distribution in a six-dimensional phase space for intense ion beams

Dynamics of particles in linear ion accelerator is investigated. Self-consistent distribution of phase density is obtained for intense ion beams in which longitudinal dimensions of buncher by far exceed the transverse ones. Inconsistency is considered of the beam initially consistent in a 4-dimensional phase space, resulting from initial inconsistency in 6-dimensional phase space. The critical frequency spectrum is obtained for linearized equations of envelopes. It is concluded, that the result obtained unifies ''microcanonical'' distribution for the case of particle oscillation in all three space coordinates