Longitudinal phase space tomography with space charge

The tomographic reconstruction of longitudinal phase space density is a hybrid measurement technique which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured bunch profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is now described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of the vacuum chamber parametrized by a single value of distributed reactive impedance and by a geometrical coupling coefficient. This is sufficient to model the dominant collective effects in machines of low to moderate energy. In contrast to simulation codes, binning is not an issue since the profiles to be differentiated are measured ones. Results obtained with and without the inclusion of space charge are presented and compared for a proton beam case in the CERN PS Booster (PSB).