We employ the Kapchinskij-Vladimirskij envelope Hamiltonian to describe the envelope evolution, and the particle Hamiltonian to describe particle motion in a space charge dominated beam. In a uniform focusing channel, particle motion can encounter parametric resonances arising from the envelope oscillations of a mismatched beam. Large amplitude envelope oscillation can cause global chaos near the vicinity of the beam core, and lead to enhanced halo formation. In a periodic focusing channel, enhancement of halo formation may also arise from structure resonances, i.e. envelope-lattice and particle-lattice resonances. The onset of global chaos exhibits a first order phase transition like behavior when the amplitude of envelope oscillations for a mismatched beam is larger than a critical value. The equations of motion for space charge dominated beams in synchrotron are derived. We find that the space charge force generates an identical defocusing function to the betatron motion and dispersion function. The self-consistent envelope equation obeys the Kapchinskij-Vladimirskij type equation similar to that of the linear transport system. We employ these results to analyze the stability of crystalline beams, and discuss the implication on the high intensity proton driver for the neutron spallation sources. Possible experiments are suggested. ©1998 American Institute of Physics.