Ideal matching of heavy ion beams

A novel technique is developed, and demonstrated via simulations, which allows ideal matching of an ultrahigh-brightness heavy ion beam in a linear focusing channel with general magnetic focusing field profile. Unlike the conventional rms matching used in accelerator design, this technique is based on a new class of corkscrewing elliptic beam equilibria in a linear focusing channel consisting of uniform solenoidal fields, periodic solenoidal fields, and/or alternating-gradient quadrupole magnetic focusing fields in an arbitrary arrangement including field tapering. As an illustration of the effectiveness of this technique, a perfect matching of an ultrahigh-brightness heavy ion beam from an axisymmetric particle source into alternating-gradient quadrupole focusing channel is achieved without beam hollowing and beam halo formation. Discussions are made of how to implement such a perfect beam matching to avoid beam hollowing observed in the LBNL 2-MV Heavy Ion Injector Experiment.