Systematic comparison of position and time dependent macroparticle simulations in beam dynamics studies

Macroparticle simulation plays an important role in modern accelerator design and operation. Most linear rf accelerators have been designed based on macroparticle simulations using longitudinal position as the independent variable. In this paper, we have done a systematic comparison between using longitudinal position as the independent variable and using time as the independent variable in macroparticle simulations. We have found that, for an rms-matched beam, the maximum relative moment difference for second, fourth moments and beam maximum amplitudes between these two types of simulations is 0.25% in a 10 m reference transport system with physical parameters similar to the Spallation Neutron Source linac design. The maximum z-to- t transform error in the space-charge force calculation of the position dependent simulation is about 0.1% in such a system. This might cause a several percent error in a complete simulation of a linac with a length of hundreds of meters. Furthermore, the error may be several times larger in simulations of mismatched beams. However, if such errors are acceptable to the linac designer, then one is justified in using position dependent macroparticle simulations in this type of linac design application.