Benton et al: Computer calculations of effect of space charge computer calculations of effect of space charge on longitudinal beam dynamics in proton linear accelerators

A machine program for calculating the effect of space charge on the longitudinal motion in a proton linac was presented at the 1966 Los Alamos Linear Accelerator Conference. This program assumes a uniformly charged ellipsoidal bunch of constant transverse semi-axes throughout the calculation. Since then, numerical results for transmitted current and longitudinal beam quality have been obtained with this program. These results showed that with increasing current, the assumption of a uniformly charged ellipsoidal bunch becomes less and less justified. It was, therefore, decided to also try other space charge force models which would allow for any longitudinal charge distribution. Three additional models, assuming cylindrical symmetry and a fixed transverse beam radius, were programmed. In all of these, the charge density is assumed to vary only longitudinally and the bunch can, therefore, be represented by a succession of thin disks, each uniformly charged. In the point-disk (PD) program, the contributions of the individual disks to the force at a point on the axis are summed the point-diskimage (PDI) (model used by Morton ) is obtained in the same way but includes the effects of image charges induced on drift tubes and the influence of neighboring bunches; the disk-disk (DD) calculation starts from the force between two coaxial charged disks and sums the contribution from all other disks to the force on any one of them. All computations were done on the CDC 6600 computer at the Brookhaven National Laboratory.