1. Deflecting Cavities for Advanced Accelerator Applications Kwang-Je Kim ANL ICFA Mini-Workshop Deflecting/Crabbing Cavity Applications in Accelerators April 23-25, 2008 SSRF, Shanghai

2. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 2 Contents EM Fields of a Deflecting Mode Applications of Deflecting Cavities

3. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 3 Deflecting Mode in a Pill-Box Cavity TM 110 Standing wave: Deflecting force: R Aberration terms

4. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 4 Multi-Cell Pillbox,  -Mode - 3λ/4 -λ/2-λ/4λ/43λ/4 λ/2 z = 0 -ℓ-ℓ ℓ Θ(z) = +1 Θ(z) = -1Θ(z) = +1Θ(z) = -1 Θ(z) = +1 -λ λ

5. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 5 Multi-Cell Pillbox,  -Mode (cont’d) V ┴ : kick voltage Transit time factor 

6. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 6 Multi-Cell Pillbox: Off-Set of Bunch Center Independently by J. Power (simulation) & D. Edwards (calculation) Large for low energy application such as 15 MeV emittance exchange experiment Probably not important especially when + & - deflections are added (integer)

7. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 7 Canceling the Bunch Off-Set Off-set vanishes if - + -

8. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 8 Multi-Cell Pillbox with Holes: HEM Mode Solution of Maxwell Equation of the form B.C. on beam hole: B y z x E-field due to a hole - - - + + + + + + B BB

9. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 9 Traveling Wave Solution Take real part of the complex solution No bunch off-set The quadratic terms cancel out  No aberration! SLAC S-band deflector in 60’s. (G. Lowe, …) (H. Hahn, Y. Garault. referred by G. Lowe)

10. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 10 SLAC S-Band Deflector (LOLA II & III, LOLITA I) 3  /2 mode traveling wave

11. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 11 HEM Standing Wave (Most Cases) Complex solution Construct No-vanishing bunch off-set → cancel by adjusting the end-cell length, or radius Aberration terms do not cancel

12. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 12 HEM, Cont’ued Off-set vanishes when: Or when:

13. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 13 Simulation of Bunch Offset in Real Cavity (John Power) Confirms bunch off-set & vanishing of off-set for some  ℓ, but not for a  LeLe gmgm gege r2r C.L. gege a a b end b middle b end LeLe

14. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 14 Applications of Deflecting Cavities Particle separation Temporal beam diagnostics Crab-crossing in colliders X-ray pulse compression Emittance exchange

15. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 15 Deflecting Cavity for Longitudinal Phase space diagnostics

16. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 16 Crabbing to Enhance Collider Luminosity Crab angle 

17. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 17 X-ray Pulse Compression

18. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 18

19. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 19 Emittance Exchange Emittance Exchange (EEX): Complete exchange of x- and z-phase spaces: (  x,  z )  (  z,  x ) Applications To improve performance of high-gain FEL… Reduce transverse emittance at the expense of longitudinal To obviate electron damping ring in linear collider Photocathode gun  flat beam transformation  EEX (  x,  y,  z )=(1, 1, 8)  (50,0.02, 8)  (8, 0.02,50)  m

20. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 20 Construction of an Exact Exchange Optics Thin Trasverse Cavity Dog-Leg for generating dispersion McMc B B B B B Exact Exchange (KJK) Approximate Exchange (M.Cornacchia & P. Emma)

21. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 21 EEX Demonstration Experiment at FNAL (  x,  y,  z )=(4, 4,130)  m  (130, 3,3)  m 3.9 GHz, 5-cell, LiN-cooled copper cavity (adopted from CKM)

22. Deflecting Cavities for Ad. Acc. Appl., Shanghai, 4/23-25/08 22 GunLinac ICT1 GV TQ1,TQ2,TQ3 YAG1YAG2 Emittance Exchanger Demonstration Experiment for EEX at Argonne AWA initial  x =9  m  z = 4  m final  x =4  m  z = 9  m AWA- and APS-ANL, NIU, and Tsinghua U collaboration L-band, TM110, (1/2-1-1/2)-cell cavity from Tsinghua U TM 110