1. examples of dual-mode (3 GHz + 6 GHz) cavities
Presentation at X-BAND RF STRUCTURSES, BEAM DYNAMICS AND SOURCES WORKSHOP – XB-10 Cockcroft Institute, Daresbury, UK, Nov. 30 – Dec. 3, Multi-mode, multi-harmonic cavities to increase RF breakdown threshold*,**
Y. Jiang,1 S.V. Kuzikov,2,3 and J. L. Hirshfield1,2
1Beam Physics Laboratory, Yale University, 272 Whitney Ave., New Haven, CT 06511, USA
2Omega-P, Inc., 258 Bradley St., New Haven, CT 06510, USA
3Institute of Applied Physics, RAS, Nizhny Novgorod, Russia
Contents of talk:
motivation
examples of dual-mode (3 GHz + 6 GHz) cavities
dual frequency experimental test stand
summary
*Research supported in part by US DoE –Office of High Energy Physics.
**Pertinant recent references:
“Asymmetric bimodal accelerator cavity for raising RF breakdown thresholds,” by S.V. Kuzikov,
S.Yu. Kazakov, Y. Jiang, and J.L. Hirshfield, Phys. Rev. Lett. 104, (2010).
“High-gradient two-beam accelerator structure,” by S.Yu. Kazakov, S.V. Kuzikov, Y. Jiang, and
J.L. Hirshfield, Phys. Rev. ST – Accel. Beams 13, (2010).

2. Motivation: Why bother with more than one cavity mode?
Superimposing harmonically-related cavity modes can shorten the exposure times on metallic cavity surfaces to the peak RF electric fields during each RF cycle;
2. Superimposing harmonically-related cavity modes can yield RF electric fields that point into metallic cavity surfaces to be always smaller than fields that point away from the surfaces; and
Superimposing harmonically-related modes can cause the exposed areas on the cavity surface where RF magnetic fields have peak values to shrink and sweep around the surface during each RF cycle;
All these might contribute to raising RF breakdown thresholds.
However, in general, these are not three isolated phenomena,
but will probably occur together when more than one mode is used.

3. Example of bimodal harmonic cavity
Parameters for bimodal harmonic cavity

4. Example of bimodal harmonic cavity – field maps

5. Example of bimodal harmonic cavity optimization of field ratio definition of coordinates
Following slides show distributions of E-field and
square of H-field along the cavity periphery,
at equal time intervals within an RF cycle.

6. a b c d E
S (mm)

7. a b c d E
S (mm)

8. a b c d H
S (mm) 2

9. a b c d H
S (mm) 2

10. Two-frequency test stand at Yale Beam Physics Lab

11. Second-harmonic frequency multiplier

12. Computational predictions for second-harmonic frequency multiplier

13. Design parameters for 2nd harmonic multiplier

14. Demountable bimodal cavity test cell

15. Coupling into bimodal cavity

16. Acceleration structure comprising bimodal cavities
with double-helix waveguide feeds
A double-helix waveguide structure is suggested for coupling along a structure composed of individual bimodal cavities, maintaining
correct synchronization for each frequency:
Idea: Fast wave in waveguides propagate on longer helical path to match the phase of the test beam passing along the structure axis.

17. Phase advance in waveguide: 2π/3 Phase advance of particle: 2π/3
Multi-harmonic excitation and synchronization
via double helical waveguide
Bunch frequency: GHz
Phase advance in waveguide: 2π/3
Phase advance of particle: π/3
External rf: 3 GHz
Test beam
2010 Advanced Accelerator Concepts Workshop

18. External rf: 6 GHz test beam
Multi-harmonic excitation and synchronization
via double helical waveguide
External rf: 6 GHz
test beam
2010 Advanced Accelerator Concepts Workshop

19. Summary
Use of bimodal cavities may allow an increase in RF breakdown threshold, due to:
a. Reduced exposure times to high fields;
b. Cathode-like fields being weaker than anode-like fields;
c. Migration of field patterns around cavity periphery.
A two-frequency synchronous multi-MW RF source and a demountable test cavity are being built at Yale for breakdown studies of bimodal cavities, at 2.85 and 5.7 GHz.
When/if bimodal cavities are proven to allow an increase in RF breakdown thresholds, inventive coupling schemes will be needed; a double-helix scheme has been illustrated.

20. Bimodal cavity with beam tunnels

21. Bimodal test cavity with beam tunnels