Calculation of Space Charge Effects in Beam Transport

Methods of calculating space charge effects which are presently available have as their basis the assumption of uniform charge density over the beam cross section. In design of a high intensity beam transport system, it is important to know how sensitive parameters of the design are to this assumption. This question has been investigated by propagating phase plots along the beam axis for space charge fields from both a uniform charge density and a charge density obeying a normal distribution. Normalization was such that the field from the uniform density was a least-squares fit to the field from the charge density of normal distribution. Results of computations for 20 mA of 3.0 MeV protons indicate that while the phase plot showed considerable distortion from effects of the normal charge density, parameters of the plot which effect design of a transport system were not changed appreciably. From these calculations it seems that unless close matching of an acceptance phase plot is imperative, design of a transport system is relatively insensitive to charge distribution in the beam.