Emittance growth due to static and radiative space charge forces in an electron bunch compressor

Evolution of short intense electron bunches passing through bunch-compressing beam lines is studied using the UAL (Unified Accelerator Libraries) string space charge formulation [R. Talman, Phys. Rev. ST Accel. Beams 7, 100701 (2004); N. Malitsky and R. Talman, in Proceedings of the 9th European Particle Accelerator Conference, Lucerne, 2004 (EPS-AG, Lucerne, 2004); R. Talman, Accelerator X-Ray Sources (Wiley-VCH, Weinheim, 2006), Chap. 13]. Three major configurations are studied, with the first most important and studied in greatest detail (because actual experimental results are available and the same results have been simulated with other codes): (i) Experimental bunch compression results were obtained at CTF-II, the CERN test facility for the ``Compact Linear Collider'' using electrons of about 40 MeV. Previous simulations of these results have been performed (using TraFiC4* [A. Kabel et al., Nucl. Instrum. Methods Phys. Res., Sect. A 455, 185 (2000)] and ELEGANT [M. Borland, Argonne National Laboratory Report No. LS-287, 2000]). All three simulations are in fair agreement with the data except that the UAL simulation predicts a substantial dependence of horizontal emittance ${ϵ}_{x}$ on beam width (as controlled by the lattice ${\ensuremath{\beta}}_{x}$ function) at the compressor location. This is consistent with the experimental observations, but inconsistent with other simulations. Excellent agreement concerning dependence of bunch energy loss on bunch length and magnetic field strength [L. Groening et al., in Proceedings of the Particle Accelerator Conference, Chicago, IL, 2001 (IEEE, New York, 2001), http://groening.home.cern/groening/csr_00.htm] confirms our understanding of the role played by coherent synchrotron radiation (CSR). (ii) A controlled comparison is made between the predictions of the UAL code and those of CSRTrack [M. Dohlus and T. Limberg, in Proceedings of the 2004 FEL Conference, pp. 18\char21{}21, MOCOS05, available at http://www.JACoW.org], a code with similar capabilities. For this comparison an appropriately new, 50 MeV, ``standard chicane'' is introduced. Unlike CSRTrack (which neglects vertical forces) the present simulation shows substantial growth of vertical emittance. But ``turning off'' vertical forces in the UAL code (to match the CSRTrack treatment) brings the two codes into excellent agreement. (iii) Results are also obtained for 5 GeV electrons passing through a previously introduced ``standard chicane'' [Coherent Synchrotron Radiation, CSR Workshop, Berlin 2002, http://www.desy.de/csr] [of the sort needed for linear colliders and free electron lasers (FEL's) currently under design or construction]. Relatively little emittance growth is predicted for typical bunch parameters at such high electron energy. Results are obtained for both round beams and ribbon beams (like those actually needed in practice). Little or no excess emittance growth is found for ribbon bunches compared to round bunches of the same charge and bunch width. The UAL string space charge formulation (like TraFic4 and CSRTrack) avoids the regularization step (subtracting the free-space space charge force) which is required (to remove divergence) in some methods. Also, by avoiding the need to calculate a retarded-time, four-dimensional field history, the computation time needed for realistic bunch evolution calculations is modest. Some theories of bunch dilution, because they ascribe emittance growth entirely to CSR, break down at low energy. In the present treatment, as well as CSR, all free-space Coulomb and magnetic space charge forces (but not image forces), and also the centrifugal space charge force (CSCF) are included. Charge-dependent beam steering due to CSCF, as observed recently by Beutner et al. [B. Beutner et al., in Proceedings of FEL Conference, BESSY, Berlin, Germany, 2006, MOPPH009], is also investigated.