1. A. D’Elia 1,2,3, T. Higo 4, V. F. Khan, R.M. Jones 1,2, A. Latina 3, I. Nesmiyan 1,2, G. Riddone 3 1 School of Physics and Astronomy, The University of Manchester, Manchester, U.K, 2 The Cockcroft Institute of Accelerator Science and Technology, Daresbury, U.K, 3 CERN, Geneva, Switzerland, 4 KEK, Tsukuba, Japan Beam Dynamics and Wakefield Suppression in Interleaved Damped and Detuned Structures for CLIC HIGH GRADIENT CHALLENGES The main issue entailed in the design of high gradient structures as for CLIC is to provide efficient long range wakefield damping in a short time scale together with a low breakdown rate and, hence, with low surface fields on the structure walls. These two requirements are not independent and are usually antithetical. Based on the experience of the Next Linear Collider (NLC), we proposed a damping scheme using a combination of detuning the frequencies of beam-excited higher order modes (HOMs) and by light damping through slot-coupled manifolds (DDS scheme). Interleaving neighbouring structure frequencies help enhance the wake suppression. Advantages with respect to other damping scheme are a compact mechanical design, inbuilt beam diagnostic and reduction of the damping loads. CLIC_DDS_A In the frame of the Collaboration between CI and CERN, a first DDS prototype, CLIC_DDS_A, has been studied, designed and fabricated in Japan, under the supervision of KEK. This structure will be submitted to high power tests (71MW peak input power) at CERN. Finalization of CLIC_DDS_A Engineering Design Finalization of the Input Power Coupling Cell shape optimization for fields DDS1_C DDS2_E Consequences on wake function Final cell geometry with manifold =1947 =1647 Wakefield Analysis Comparative wakefield analysis of CLIC_DDS_A: in blue the predictions from circuit model and spectral function method (see R.M. Jones, et. al, PRST-AB, 9, 102001, 2006), in red GdfidL simulations including ohmic losses Tests on prototype disks Surface roughness analysis Bonding Tests by BODYCOTE Inc. (FR) Metallographic observation of the bonding zone RF Tests on Morikawa disk prototypes The full stack of 26 disks plus couplers, arrived at CERN on July 2012. The couplers have been brazed and the interfaces machined to connect the couplers to the rest of the structure. The whole assembled structure has been RF checked. The results are satisfying: the frequency is ~ 5MHz off which is fully within the tuning range (~20MHz). The structure has been successfully bonded at BODYCOTE Inc. during this summer and it is expected to be back at CERN in the early autumn. Tuning will immediately follow. High power tests will be scheduled according to CERN Test Stand availability. RF check of the full structure before bonding ACKNOWLEDGMENTS: This research has received funding from European Commission under FP7 Research Infrastructure grant no. 227579. 2  /3 Meas. 2  /3 Des.   5MHz BEAM DYNAMICS STUDY Recent analysis of wakefield induced multi-bunch effect in CLIC has given further limitations on the long-range wakefields: it is not only necessary that the trailing bunches be below a certain limit but there is also a limitation on the total integrated wake produced from the whole 312 bunch train. Here we track the multi-bunch beam down the complete collider, under the influence of transverse wakefields and record the final emittance dilution at the end of the linac. We utilize the code PLACET for all tracking simulations and include systematic and random fabrication errors; the latter are particularly beneficial in reducing the impact of the wakefield on the beam quality. Results of some initial alignment studies are also provided. DDS INTERLEAVED DESIGN A single structure consists of no more than 24 cells and hence will be woefully inadequate in suppressing the wakefield. However, provided the dipole modes are interleaved between successive structures, the wakefield will be well-suppressed. We have found 12-fold interleaving of modes to be sufficient (equivalent to a single structure consisting of 288 cells). PLACET requires the mode frequencies, Q’s, and corresponding kick factors as input parameters to assess the impact of these wakefields. We utilize the peaks in the spectral function and assign these to the modal frequencies, the remaining parameters are obtained by taking the usual modal expansion and performing a non-linear least square error fit. To provide some confidence in the fitting method, we compare the original Fourier transform of the spectral function to the fitted modal sum, and this is displayed in Fig. 2. WAKEFIELD REPRESENTATION IN PLACET CLIC_DDS_A 16-fold Interleaved Structure-6RF cycles IMPACT OF SYSTEMATIC AND RANDOM FREQUENCY ERRORS FINAL REMARKS A damped and detuned structure, with appropriately interleaved dipole mode frequencies, has been shown to be suitable for the CLIC main linacs. Two cases have been investigated, based on a bunch spacing of 6 and 8 rf cycles. The S RMS parameter provides a qualitative indication of the location of the worst-case emittance dilution. Preliminary studies on the dilution due to structure misalignments indicate similar values to the baseline design. MISALIGNMENT STUDY The pre-alignment tolerance on the transverse positions of the components (accelerator structures, BPM, girders) of the CLIC linacs is 10 µm rms over distances of 200 m. Beam-based alignment and emittance tuning bumps are used to ensure the emittance dilution associated with this alignment is kept to acceptable limits. Here we assess the implications of these wakefields on the beam emittance dilution. We performed beam tracking simulations down the complete linac, for a bunch train initially offset by  y (0.5  m). In case of a 12-fold interleaved version of the original design, in which bunches were spaced from their neighbours by 8 rf cycles, the emittance dilution is of 4.4%. In case we maintain the original distribution, but modify the bunch spacing to 6 rf cycles, we discover further interleaving, to the extent of 16-fold, is needed to contain the emittance dilution to acceptable limits (3.6%). This of course has implications on the fabrication tolerances, as the minimum frequency spacing for the latter structure is 3.4MHz. However, these tolerances are still compatible with those assigned to the accelerating mode (< 1 MHz). To provide a more realistic assessment of the beam dynamics we conducted further simulations for both cases, in which systematic and random frequency errors (2MHz RMS spread) were included. In both cases the presence of random errors is beneficial. We also note that S RMS provides a qualitative guide as to the expected worst case region for emittance dilution. CLIC_DDS_A 12-fold Interleaved Structure-8RF cycles ParameterValueParameterValue Initial beam energy, E 0 9 GeV Bunch length,  z 44  m Final beam energy, E1500 GeV Initial  x 550 nm Particles per bunch3.72×10 9 Final  x 660 nm Bunch spacing0.15/0.2m(6/8 rf periods) Initial  y 10 nm Bunch train length156 ns Final  y 20 nm Number of bunches312 Initial  E /E 2% Selected Beam Parameters Figure 2: Envelope of fitted transverse wakefunction (dashed and in black) together with that of the Fourier transform of the spectral. We performed simulations for a case which consists of 16-fold interleaving of mode frequencies and bunches spaced 8 rf cycles from their neighbours. However, the implications of not being able to accommodate 16 structures on a girder are not taken into account, as it is a considerable task to redesign the associated beam optics, and hence it remains a subject for a future publication. Figure 1: Spectral function (a) for a single structure (in blue) and a 12-fold interleaved series (in red), together with the Fourier transforms thereof, the corresponding wakefunctions W t (b). Also shown is twice the kick factor weighted frequency density distribution (2Kdn/df).