Modelling of space charge effects in the CERN Proton Synchrotron

A new computer code is described for calculating the incoherent tune spreads and the beam envelopes in linear coupled synchrotron lattices in the presence of transverse and longitudinal space charge fields. This work is based on an existing theory devised at DESY (Deutsches Elektronen-Synchrotron) using the six-dimensional phase space formalism. It has been extended to deal with the nonuniform charge density within the bunches. The application to high intensity beams at present in operation in the CERN PS (Proton Synchrotron) is discussed.<>