Emittance growth from merging arrays of round beamlets

摘要

The cost of an induction linac for Heavy Ion Fusion (HIF) may be reduced if the number of channels in the main accelerator is reduced. There have been proposals to do this by merging beamlets (perhaps in groups of four) after a suitable degree of preacceleration. In the process of merging, space charge forces cause transverse acceleration, filling in the gaps and rapidly increasing the emittance. The maximum change in mean-square emittance is proportional to the excess electrostatic energy (free energy) in the array when the merging begins. In some designs, it may be desirable to reduce the emittance growth below that produced by a basic 2x2 array. For this, a general understanding is helpful. Therefore, we investigate three factors affecting the normalized free energy U(sub n) of an array of charged interacting beamlets: (1) the number of beamlets N in the array; (2) the ratio (eta) of beamlet diameter to beamlet spacing; and (3) the shape of the array. For circular arrays, we obtain an analytic expression showing that U(sub n)(approximately)NE(sup -1) in the large-N limit, i.e., the emittance growth can be made arbitrarily small. We show that this is not true for square or rectangular arrays, which have larger free energy with a lower limit determined by the non-circular format. Free energy in square arrays can be reduced by omitting comer beamlets; in the case of a 5 x 5 array, the reduction factor is as large as 3.3.