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Self Consistent Monte Carlo Method to Study CSR Effects in Bunch Compressors

Description: In this paper we report on the results of a self-consistent calculation of CSR effects on a particle bunch moving through the benchmark Zeuthen bunch compressors. The theoretical framework is based on a 4D Vlasov-Maxwell approach including shielding from the vacuum chamber. We calculate the fields in the lab frame, where time is the independent variable, and evolve the phase space density/points in the beam frame, where arc length, s, along a reference orbit, is the independent variable. Some details are given in [2], where we also discuss three approaches, the unperturbed source model (UPS), the self consistent Monte Carlo (SCMC) method and the method of local characteristics. Results for the UPS have been presented for 5 GeV before [3], here we compare them with our new results from the SCMC and study the 500MeV case. Our work using the method of characteristics is in progress. The SCMC algorithm begins by randomly generating an initial ensemble of beam frame phase space points according to a given initial phase space density. The algorithm then reduces to laying out one arc length step. Assume that at arc length s we know the location of the phase space points and the history of the source prior to s. We then (1) create a smooth representation of the lab frame charge and current densities, {rho}{sub L} and J{sub L}, (2) calculate the fields at s from the history of {rho}{sub L} and J{sub L}, and (3) move the beam frame phase space points according to the beam frame equations of motion. This is then iterated. The UPS calculation is similar except the fields are calculated from a function of s computed a priori from the beam frame equations of motion without the self-fields. The phase space points are then evolved according to the equations ...
Date: January 8, 2008
Creator: Warnock, R.L.; /SLAC; Bassi, G.; Ellison, J.A.; Heinemann, K.A. & U., /New Mexico
Partner: UNT Libraries Government Documents Department

Self-Consistent Computation of Electromagnetic Fields and Phase Space Densities for Particles on Curved Planar Orbits

Description: We discuss our progress on the self-consistent calculation of the 4D phase space density (PSD) and electromagnetic fields in a Vlasov-Maxwell formulation. We emphasize Coherent Synchrotron Radiation (CSR) from arbitrary curved planar orbits, with shielding from the vacuum chamber, but space charge forces are naturally included. Our focus on the Vlasov equation will provide simulations with lower numerical/statistical noise than standard PIC methods, and will allow the study of issues such as emittance degradation and microbunching due to space charge and CSR in bunch compressors. The fields excited by the bunch are computed in the lab frame from a new double integral formula. The field formula is derived from retarded potentials by changes of variables. It is singularity-free and requires no computation of retarded times. Ultimately, the Vlasov equation will be integrated in beam frame coordinates using our method of local characteristics. As an important intermediate step, we have developed a 'self consistent Monte Carlo algorithm', and a corresponding parallel code. This gives an accurate representation of the source and will help in understanding the PSD support. In addition we have (1) studied carefully a 2D phase space Vlasov analogue and (2) derived an improved expression of the field of a 1D charge/current distribution which accounts for the interference of different bends and other effects usually neglected. Bunch compressors will be emphasized.
Date: November 2, 2007
Creator: Ellison, J.A.; Bassi, G.; Heinemann, K.A.; U., /New Mexico; Venturini, M.; /LBL, Berkeley et al.
Partner: UNT Libraries Government Documents Department