1. HG 2016 Workshop Design of Metallic Subwavelength Structures for Wakefield Acceleration Xueying Lu, Michael Shapiro, Richard Temkin Plasma Science and Fusion Center, MIT 06/07/2016

2. Outline Motivation Metallic subwavelength deep corrugation structure Metallic metamaterial (MTM) wagon wheel structure Conclusions

3. Why metallic WFA?

4. Novel structures for metallic WFA Two metallic subwavelength structures will be introduced sequentially. –‘Conventional’ deep corrugation structure –Metamaterial (MTM) wagon wheel structure Deep corrugation structureWagon wheel structure

5. An array of metallic subwavelength cavities Two methods of analysis: –Analytical theory of wakefield in a single cell for scaling study –CST Particle Studio to simulate a multi-cell structure Deep corrugation structure

6. Simulation of wakefields Calculation results from the CST Wakefield solver (WAK) The decelerating wakes following the drive bunch: –travel outward –bounce at the metal wall into accelerating wakes –travel inward and focus at the beam axis to accelerate a witness bunch Beam Decelerating Ez Accelerating Ez z

7. Analytical wakefield calculation in a single cavity A single cavity with radius R and length d excited by a point charge with charge Q traveling at v 0 Maxwell’s equations Boundary condition p s is the s th zero of the J 0 function. The (s, n) term represents TM 0sn mode.

8. Equations of wakefields Longitudinal wakefield for the point charge where Gaussian bunch excitation with rms length σ z,,

9. The two methods are in good agreement. Scaling study can be done with the analytical model efficiently, without running the CST WAK for each data point. Benchmark analytical theory with CST WAK

10. Scaling of gradient Only one parameter is varied in every plot. Higher gradient is achieved with –Shorter bunch (Fig. a) –Shorter structure period (Fig. b) –Smaller beam hole (Fig. c) –No direct dependence on beam pipe radius or beam energy (c)(a)(b)

11. Nominal design with ANL beam parameters Drive bunch charge10 nC Drive bunch σ z 0.6 mm Drive bunch energy70 MeV Waveguide radius9.8 mm Single cavity length2 mm Cavity wall thickness0.5 mm Beam hole radius0.6 mm Fundamental frequency11.7 GHz Shunt impedance Maximum gradient200 MV/m Decelerating Accelerating

12. Comparison with dielectric WFA- ANL Compare with the dielectric tube experiment at ANL DielectricDeep Corrugation Drive bunch charge75 nC Drive bunch σ z 2 mm Drive bunch energy15 MeV Waveguide radius7.49 mm Beam hole radius1.9 mm PeriodN/A1 mm Plate thicknessN/A0.4 mm Gradient100 MV/m300 MV/m

13. Comparison with dielectric WFA- SLAC Compare with the dielectric tube experiment at SLAC DielectricDeep Corrugation Drive bunch charge2.24 nC Drive bunch σ z 2 μm Drive bunch energy28.5 GeV Waveguide radius162 μm Beam hole radius50 μm PeriodN/A10 μm Plate thicknessN/A2 μm Gradient16 GV/m25 GV/m

14. Summary of deep corrugation structure Deep corrugation structure is a promising candidate of collinear metallic WFA. A design for the Argonne Wakefield Accelerator Facility is shown to generate a maximum accelerating gradient of 20 MV/m/nC. An analytical model has been developed and it agrees with the CST WAK code. Scaling study has been performed, and higher gradient can be achieved with –Smaller beam aperture, smaller period –Smaller bunch length The deep corrugation structure can generate a higher gradient than a dielectric tube with the same beam aperture and the same outer waveguide radius when excited by the same bunch

15. Wagon wheel structure Deep corrugation structure is designed for a collinear WFA experiment. –Propagation in the longitudinal direction and cell-to-cell coupling are not necessary in the collinear regime. The metamaterial approach: –Enable a propagating wave below the TM 01 cut-off frequency of an empty waveguide –Metamaterials: Subwavelength periodic structures Often referred to as a structure with a negative group velocity Bigger parameter space for dispersion engineering and optimization Enhanced wave-beam interaction

16. Previous MTM experiment in Argonne A MTM-loaded waveguide was tested with a 6 MeV bunch. Measured wakefield spectrum has a peak in the ‘negative’ band. Antipov 2008

17. Unit cell design nx rod R out R in ttztz pFrequencyShunt impedance 418.101.6211311.7 GHz R out R in t p tz x rod

18. Negative group velocity in the fundamental mode Below-cut-off –TM 01 mode of an empty waveguide w/ 8.10 mm radius: 14.17 GHz –Interaction frequency 11.7 GHz 11.7 GHz Dispersion diagram

19. Power extractor with wagon wheel structure A power extractor is designed at 11.7 GHz Scaling law is different: Output port 1 (higher power port) Beam Output port 2 Collinear WFAPower extractor Sum of contribution from all the modes is optimized Interaction of the beam and the fundamental mode is optimized Smaller beam aperture helpsBigger beam aperture with more charge Shorter bunch helpsNo need to have a super short bunch

20. Single bunch excitation Structure length: 9 cm, 30 cells, beam hole radius: 1.62 mm Excited by a single Gaussian bunch with 40 nC, rms length 1 mm 140 MW power from the side-coupling slot Backward wave at 11.7 GHz, higher power from port 1 Time lag = structure length / |group velocity (-0.15 c)|

21. Bunch train excitation Structure length: 9 cm, 30 periods, beam hole radius: 1.62 mm Excited by 15 bunches each with 40 nC, rms length 1 mm Bunch rep rate 1.3 GHz, output frequency 11.7 GHz (9 th harmonic) 2 GW power from side-coupling slots

22. Summary of wagon wheel structure A wagon wheel MTM structure is designed to allow wave propagation below the waveguide TM 01 frequency. The fundamental mode has a negative group velocity. A power extractor working at 11.7 GHz is designed. –140 MW output power with a single 40 nC bunch –2 GW output power with a train of 15 bunches each with 40 nC charge, bunch rep rate 1.3 GHz

23. Conclusions Two structures have been designed for the Argonne Wakefield Accelerator Facility. Deep corrugation structure for a collinear metallic WFA experiment –20 MV/m/nC Wagon wheel structure for a MTM-based power extractor experiment –2 GW

24. Acknowledgement MIT staff William Guss Sudheer Jawla Ivan Mastovsky Guy Rosenzweig Michael Shapiro Jacob Stephens Richard Temkin Paul Woskov MIT students Sergey Arsenyev Sam Schaub Alexander Soane Haoran Xu This research is supported by the Department of Energy.

25. Backup Beam Decelerating Ez Accelerating Ez z Beam