ON HALO FORMATION FROM SPACE-CHARGE DOMINATED BEAMS

In this paper, as in J.S. O'Connell, T.P. Wangler, R.S. Mills and K.R. Crandall, Beam halo formation from space-charge dominated beams in uniform focusing channels, PAC Washington, 1993, the interaction of particles with a zero-emittance, uniform-density beam core is described. When this core is mismatched in a uniform linear focusing channel, its envelope oscillates, just like a matched beam in an alternating gradient channel. As is usual for this kind of channel, the particle evolution in the transverse phase plane has been followed period by period. For a strong core modulation, this analysis clearly shows i) how the particles nearest to the core move to the halo, ii) two stable areas separated from the core, and iii) how trajectories develop along the ''lattice''. Also the halo formation problem is compared with similar phenomena from stellar dynamics in order to demonstrate that it is the mechanism of resonance overlap which leads to the formation of a halo area where the particle trajectories are stochastic. The chaotic behaviour of the particle trajectories in this area is subsequently discussed.