1. Novel two beam accelerator structures for CLIC applications L.R.Carver, et al L.R. Carver 1,2,3, Y. Jiang 2, R. M. Jones 1,2,3, J.L. Hirshfield 2,4 1 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 2 Department of Physics, Yale University, New Haven, CT, USA 3 The Cockcroft Institute, Cheshire, United Kingdom 4 Omega-P, Inc., New Haven, CT, USA

2. OUTLINE OF TALK: I.Conceptual overview II.Motivation: - Multi-harmonic cavities - Cavity detuning for collinear acceleration III.Multi-harmonic Accelerator Structure: - HOM’s and wakefields - Future time domain simulations IV.Conclusions L.R.Carver, et al

3. Conceptual overview L.R.Carver, et al How to create an accelerator like CLIC that has drive bunches and test bunches moving collinearly. This is possible by having a cavity frequency that is detuned away from the drive bunch frequency. The resultant phase shift can be calculated from where Can be designed such that a drive bunch sees a low decelerating field, while a test bunch can be phased to arrive π/2 later, seeing a high accelerating field. The transformer ratio can be defined as This detuned cavity structure could also potentially illicit reduced effects from pulsed surface heating and rf breakdown were multiple harmonically related eigenmodes to be excited.

4. Potential energy u of an electron near the surface of a metal with x the distance of electron from surface. may lower the pulsed surface heating. By superimposing two modes (Ideal pillbox η=H 2 max /H 1 max =2) may yield RF electric fields that point into metallic cavity surfaces to be always smaller than fields that point away from the surfaces, thereby inhibiting field emission Superimposing harmonically-related modes Motivation: Use multi-harmonics to suppress breakdown rates L.R.Carver, et al

5. Field profiles in dual-harmonic cavities Anode Cathode axis Peak Electric Field (A.U.) periphery distance s (mm) a b c de b Z ac d e S b a c d S a bc d Magnetic Field H 2 (A.U.) Peak Accelerating FieldAnode-like Peak Surface Field Cathode-like Peak Surface Field Contributed to Breakdown TM010 + TM020 TM010 + TM011 L.R.Carver, et al

6. Dual-Frequency RF Source at Yale University Layout of dual-frequency RF source, shown feeding a bimodal test cavity. 1 – S-band klystron; 2 – variable power splitter; 3 – 3-dB hybrid splitter; 4 – 250-kV gun tank; 5 – variable power splitter and phase shifter; 6 - bimodal test cavity. Power splitting into each frequency component with adjustable amplitude and phase Two sources automatically phase-locked No new modulator or C-band driver needed. 1 2 3 4 5 6 Test of anode-cathode effect: Demountable Bimodal Cavity TM 010 2.856 GHz TM 020 5.712 GHz E E H H L.R.Carver, et al

7. Beam Excitation: Detuned-Cavity Two-Beam Accelerator Fixed Detuning Alternative Detuning +∆ F -∆ F +∆ F -∆ F +∆ F Cavity period Λ +∆ F Every other cavities, detuning flips sign Details in “High-gradient two-beam accelerator structure”, S. Yu Kazakov, S.V. Kuzikov, Y. Jiang, and J. L. Hirshfield, PRSTAB 13, 071303 (2010) L.R.Carver, et al

8. Single Mode TBA Experimental Plan final energy spread of accelerated unbunched beam (1)To measure the transformer ratio by measuring the phase relationship between the drive bunch and the excited wakefield in the detuned accelerator structure. (2)To measure the acceleration gradient by measuring the final energy distribution of DC test beam. I/Q Field Probe Attenuator Oscilloscope I/Q Demodulator Drive Bunch π-mode SW Structure Beam Position Monitor Phase Shifter T3P Δθ=φ Detuning angle L.R.Carver, et al

9. Timing mechanism required for detuned experiment. BPM design is a stainless steel pillbox cavity with 2 SMA ports. Low Q required to minimize the filling time of the cavity, which allows as much of the 1µs bunch train to be utilised for data processing. Currently under fabrication. BPM Time signal from on axis bunch train with σz=1.5mm, q=0.175nC and bunch frequency 2.856 GHz. FFT of time signal: first mode is dominant over all others. Operating π-mode Q L ~ 1400 wide-range tunable Q and frequency with different tuner and coupler position Detuned Pillbox Four Cell Structure coupling loop tuning rod Constructed and Cold-Testing f res =2845 MHz 2Qδ=12 f res =2856 MHz 2Qδ=0 L.R.Carver, et al

10. III. Beam driven accelerating cavity Cavity parameters and HOM’s Longitudinal and Transverse Wakefield Ongoing simulations on Transformer Ratio and Pulsed Surface heating. Multi Harmonic Accelerator Structure L.R.Carver, et al

11. The drive frequency is 11.9942 GHz Detuning angle is 85.58 degree, 2Qδ=12.9 The chokes at either end of the structure Each mode normalised to 100MV/m Beam driven multi-harmonic structure TM011 2π-mode TM010 π-mode Fundamental TM010Second Harmonic TM011Unit Frequency1200324003MHz Transit-time factor 0.770.78 Power dissipation 8182257kW Q882710328 Shunt impedance 128.645.0MOhm/m r/Q107.833.4Ohm Maximum H364283681209A/m Maximum E207.4351.4MV/m With a/λ=0.15, the drive current needs to be 17 A to have 100 MV/m acceleration gradient with drive bunch length of 0.5 mm, or 25 A to have 150 MV/m. New TBA paradigm? L.R.Carver, et al

12. Goal: (1) minimize the ratio of peak magnetic fields and the ratio of peak electric fields (2) maximize the ratio of shunt impedances between the second mode to the first one and balanced with design goal for both harmonics (3) minimize peak magnetic field and peak electric field (4) maximize the shunt impedance Pulsed Surface Heating Reduction normalized at the same acceleration gradient 100 MV/m Single mode and two mode superposition The preliminary design shows it can lower the pulse heating by about 20% at the cost of increasing maximum electric field by 20%, and satisfy the constraint: (1)surface electric field Max(E surf )<260 MV/m (2)pulsed surface heating ΔT max <56 o C Ideal pillbox E 2, m /E 1,m ~2, H 2,m /H 1,m ~2 L.R.Carver, et al

13. Dispersion Curves L.R.Carver, et al In both cases, red points are single cell simulation results, with blue curves as circuit model prediction. The dashed line is the light line The indices give the type of coupling used for best fit. 1 = Nearest neighbour coupling 2= Mode coupling 3= Next nearest neighbour coupling Monopole 1 2 3 2 Monopole ModeDipole Mode 2 2a 2b 3

14. L.R.Carver, et al Wakefield for test bunch with 1% charge of drive bunch will be extremely high due to bunch spacing of 0.25 RF Cycles. Need to explore effect of increased bunch spacing on transformer ratio if a structure with acceptable transverse wakefields is to be designed. Longitudinal Transverse Wakefields Blue line is GdfidL simulation for full 9-cell structure, red line is single cell wakefield from synchronous mode decomposition. σ z =1mm, Q=1pC Quarter of cavity simulated with HH (longitudinal) and EH (transverse) boundaries

15. Ongoing Study - Time Domain Simulations Time domain simulations using PIC solver in CST and (soon to be) ACE3P. Excite multi-harmonic structure with both long bunches (fundamental mode only) and short bunches (multi-harmonic excitation). L.R.Carver, et al Transformer ratio can be calculated by Black points drive bunches, blue points test bunches. Also allows detuning angle to be measured. Bunch spacing can be varied to see Transformer Ratio behaviour. Peak gradient can be scaled to 100MV/m, allowing for surface heating comparison between single and multi- mode

16. Summary Dual-harmonic operation of acceleration cavities may allow suppression of RF breakdown and possible increase in acceleration gradient. (1)TM010+TM020, exhibits anode-cathode effect that could increase acceleration gradient without raising the surface cathode field. (2)TM010+TM011, exhibits smaller surface pulsed heating than TM010 alone. Detuned single-mode cavity two-beam structure shows high transformer ratio, and high beam-to-beam efficiency. Detuned bimodal cavity two-beam structure could have the same virtues with the additional benefit of reduced surface pulsed heating. Lower drive beam current (17A vs 100A) for 100 MV/m acceleration gradient could lead to a new paradigm for a co-linear TBA. Time domain and wakefield studies are underway to determine effect of HOM’s and bunch spacing on the transformer ratio. Optimisation software currently being created in order to design a structure with the greatest benefit. L.R.Carver, et al