Nonlinear beam dynamics in a funnel for combining two intense ion beams

The concept of funnels was introduced over the last few years with an endeavor to increase the beam intensity by combining two beams in the following fashion: The beam is, in each case, produced by an rf accelerator and thereby composed of bunches. The beam bunches are made to occupy relatively small fractions of the longitudinal phase in these cases. The bunches form each of the two beams are made to interlace and enter and rf deflector which produced the interlacing of the beams into one beam with twice as many bunches occupying twice the phase. The funnel itself, in one embodiment called the magnetic funnel, is composed of many transport elements with strong transverse focusing produced by quadruple permanent magnetic fields. An occasional rf rebuncher is introduced to recompress the beam longitudinally so the beam occupies the appropriate small fraction of velocity space in the parallel direction. Crucial elements of the funnel are the beam dynamics in the rf rebuncher and the deflector. Beam dynamics in either case must be assessed using an analysis which is described in this paper. Several components in a magnetic funnel have been examined by dint of a full three-dimensional solution to the time-dependent Vlasov-Poisson equations with all image charges included. Specifically, the rms emittance growth of subsystems is examined in detail. 11 refs., 26 figs