A new class of self-consistent 6-D phase space stationary distributions is constructed both analytically and numerically. The beam is then mismatched longitudinally and/or transversely, and we explore the beam stability and halo formation for the case of 3-D axisymmetric beam bunches using particle-in-cell simulations. We concentrate on beams with bunch length-to-width ratios varying from 1 to 5, which covers the typical range of the APT linac parameters. We find that the longitudinal halo forms first for comparable longitudinal and transverse mismatches. An interesting coupling phenomenon -a longitudinal or transverse halo is observed even for very small mismatches if the mismatch in the other plane is large -is discovered.

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A realistic treatment of halo formation must take into account 3D beam bunches and 6D phase space distributions. We recently constructed, analytically and numerically, a new class of self-consistent 6D phase space stationary distributions, which allowed us to study the halo development mechanism without being obscured by the effect of beam redistribution. In this paper we consider nonstationary distributions and study how the halo characteristics compare with those obtained using the stationary distribution. We then discuss the effect of redistribution on the halo development mechanism. In contrast to bunches with a large aspect ratio, we find that the effect of coupling between the r and z planes is especially important as the bunch shape becomes more spherical. [S1098-4402(98)00025-1]