RFQ radial matching sections and fringe fields

The entrance radial matching section is an extremely important part of any radio-frequency quadrupole (RFQ) linac. It allows a beam having time-independent characteristics to become adapted to the time-dependent focusing in the RFQ. The matching sections proposed in this paper are defined by a four-term potential function and are very effective over lengths of 3 β lambda or longer. The fringe field at the RFQ exit is mainly of interest because of the time-varying on-axis potential. The beam can either lose or gain energy, depending on the shape of the fringe field. The same four-term potential function can be used for shaping the vanes at the exit so that the fringe fields can be controlled. This formulation also applies to exit radial matching sections, which would be useful if the beam is to enter another RFQ operated at a higher frequency. 4 references, 4 figures