SIMULATION OF SPACE-CHARGE EFFECTS IN THE PROPOSED CERN PS2 ∗

A new proton synchrotron, the PS2, was proposed to re- place the current proton synchrotron at CERN for the LHC injector upgrade. Nonlinear space-charge effects could cause significant beam emittance growth and particle losses and limit the performance of the PS2. In this paper, we report on simulation studies of the potential space-charge effects at the PS2 using three-dimensional self-consistent macro-particle tracking. We will present the computa- tional model used in this study, and discuss the impact of space-charge effects on the beam emittance growth, espe- cially due to synchro-betatron coupling, initial longitudi- nally painted distribution, and RF ramping schemes. accurately model systems with strong space charge as in photoinjectors), an RF linac lattice design code, an enve- lope matching and analysis code, and a number of pre- and post-processing codes. Both parallel particle track- ing codes assume a quasi-electrostatic model of the beam (i.e. electrostatic self-fields in the beam frame, possi- bly with energy binning) and compute space-charge ef- fects self-consistently at each time step together with the external acceleration and focusing fields. The 3D Pois- son equation is solved in the beam frame at each step of the calculation. The resulting electrostatic fields are Lorentz transformed back to the laboratory frame to obtain the electric and magnetic self-forces acting on the beam. There are six Poisson solvers in the IMPACT suite, cor- responding to transverse open or closed boundary con- ditions with round or rectangular shape, and longitudi- nal open or periodic boundary conditions. These solvers use either a spectral method for closed transverse bound- ary conditions (4), or a convolution-based Green function method for open transverse boundary conditions (5). The parallel implementation includes both a 2D domain de- composition approach for the 3D computational domain and a particle-field decomposition approach to provide the optimal parallel performance for different applications on modern supercomputers. Besides the fully 3D space- charge capability, the IMPACT code suite also includes detailed modeling of beam dynamics in RF cavities (via field maps or z-dependent transfer maps including RF fo- cusing/defocusing), various magnetic focusing elements (solenoid, dipole, quadrupole, etc), allowance of arbitrary overlap of external fields (3D and 2D), structure and CSR wake fields, tracking multiple charge states, tracking multi- ple bin/bunches, Monte-Carlo simulation of gas ionization, an analytical model for laser-electron interactions inside an undulator, and capabilities for machine error studies and correction. For the purpose of studying space-charge ef- fects in a synchrotron ring, the IMPACT code was extended to include thin lens kicks for multipole elements and RF cavities, multi-turn simulation, dynamic RF ramping, and lumped space-charge kicks.