Hamiltonian formalism for space charge dominated beams in a uniform focusing channel

Halo formation for a test particle in a mismatched KV beam is studied. Parametric resonances of the particle Hamiltonian due to envelope modulation are studied with particular emphasis on period 2 resonance which plays dominant role in halo formation. It is shown that the onset of global chaos exhibits a sharp transition when the amplitude of modulation is larger than a critical value which is a function of a single parameter, /spl kappa/, i.e., the ratio of the space charge perveance to the focusing strength.