A semi-analytical approach to the design of low energy cylindrically symmetric transport lines

An optimization procedure that determines the best values (i.e., those that minimize beam radius) for the focal distances of solenoidal magnetic lenses in a low-energy cylindrically symmetric transport line is presented. The procedure is based on an analysis of the RMS beam envelope equation, which accounts for space charge as well as emittance effects. Universal beam-spreading curves including emittance effects (a generalization to the well-known space-charge spreading curves) are presented in a form convenient for general use. The results are applied to the design of the gun-to-linac transport channel of the LNLS injector