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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.

The diBerential cross section for bremsstrahlung derived in the previous paper is integrated over the direction of the emerging electron. It is found that regions of appreciable polarization occur near both the low energy and high energy ends of the photon spectrum. Calculations are performed for the polarization dependence of the radiation for incident electrons of about 0.1, 0.5, 2.5 Mev with and without approximate shielding corrections calculated for aluminum. The polarization dependence of the differential cross section for pair production and of the cross section integrated over either the electron or positron direction is obtained from the results for bremsstrahlung by the weH-known procedure of changes from positive to negative energy state.

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