A two-frequency RF cavity for the PSI-XFEL: Design and beam dynamics simulations Jean-Yves Raguin à , Kevin Li, Rene Bakker, Anne Oppelt, Marco Pedrozzi Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland article info Available online 10 May 2008 Keywords: FEL RF cavity RF harmonics Emittance abstract In the frame of conceptual studies for a compact (less than 6 GeV) X-ray FEL at PSI, we report here on the design and beam dynamics simulations of a two-cell two-frequency RF gun-like cavity. The goal of this study is to demonstrate the feasibility and the RF flexibility of such a cavity for manipulating the longitudinal phase space while preserving the initial low transverse emittance. Shaping the longitudinal phase space is mandatory for efficient velocity bunching at an early stage of the accelerator. The cavity, located after the gap of a 500-kV to 1-MV diode, is dimensioned to operate at 1.5 and 4.5 GHz. The RF design of the two-cell cavity and the coupling schemes for both frequencies are presented. Mode separation, which ensures adequate operation, is achieved by profiling the cavity walls. The flexibility of such a design to shape the longitudinal phase space is illustrated with beam dynamics simulations. The transverse emittance is shown to be nearly unchanged by combining emittance compensation and a beam matching scheme. The deleterious effects of the transverse RF fields are consequently reduced to a minimum. & 2008 Elsevier B.V. All rights reserved. 1. Introduction In order to realize compact X-ray free electron lasers, electron sources of very high brilliance and ultra-low emittance are required. Thus the necessary beam energy and undulator length are lowered which considerably reduce the size and costs of the resulting machine. The high brightness of the electron beam is reached by the combination of a low emittance electron source and a beam with a comparatively low initial current to reduce emittance degradation by space charge forces at low energies. The design of the low emittance accelerator incorporates a cold electron source [1] followed by a high gradient DC acceleration gap [2] to alleviate space charge forces directly after emission. A pulsed solenoid together with the two-frequency RF cavity are placed thereafter to allow beam matching and to provide the necessary bunch compression for the injection into the next RF accelerating structure. 2. RF cavity design The two-frequency cavity consists of two cells, the down- stream cell being electrically coupled to a 50-O coaxial line through which the RF power at the fundamental frequency (1498.96 MHz) is injected. The coaxial line incorporates a filter [3] that allows propagation in the TEM mode at the fundamental frequency and that reflects the third harmonic frequency (4496.87 MHz) RF fields fed into the cavity by two standard WR187 rectangular waveguides. These waveguides are diametri- cally located and magnetically coupled to the downstream cell. The cavity is dimensioned to operate in the TM 010Àp mode and in the TM 012Àp mode at the fundamental frequency and third harmonic frequency, respectively. The longitudinal position of the coaxial line inner conductor is adjusted to obtain a coupling factor b of 2 for the TM 010Àp mode. The dimensions of the irises that couple the two waveguides to the cavity’s second cell are optimized to obtain a b of 1 for the TM 012Àp mode. In a first design, the cell walls profile of the two-frequency two-cell cavity is kept straight as presented in Ref. [4]. To obtain a coupling factor b of 1.05 for the TM 012Àp mode, the irises which couple the two waveguides to the downstream cell are 4 mm thick, 5 mm wide and 20.25 mm long with fillets of 1.7 mm. With these dimensions the frequency of the TM 010Àp mode and TM 012Àp mode are 1499.01 and 4496.32MHz, respectively. The coupling factor for the TM 010Àp mode is 2.04. Fig. 1 shows the electric field distribution of the TM 012Àp mode calculated with the driven modal solution option of HFSS v10. However, a frequency scan reveals the presence of an octopole mode (TM 410 , Fig. 2), 23.72 MHz lower than the TM 012Àp mode. As can be seen in Fig. 1 , the modal field pattern purity of the TM 012Àp mode in the coupled cell is affected by the octopole mode. For this design, the required peak powers to achieve a flat-top on-axis peak electric field of 40 MV/m are 4.49 MW and 290 kW for the fundamental and third harmonic frequency, respectively. ARTICLE IN PRESS Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/nima Nuclear Instruments and Methods in Physics Research A 0168-9002/$ - see front matter & 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2008.04.071 à Corresponding author. E-mail address: jean-yves.raguin@psi.ch (J.-Y. Raguin). Nuclear Instruments and Methods in Physics Research A 593 (2008) 125– 128