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, 2010 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 603600 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, 214801 (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, 071303 (2010).

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.

Example of bimodal harmonic cavity Parameters for bimodal harmonic cavity

Example of bimodal harmonic cavity – field maps

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.

a b c d E S (mm)

a b c d E S (mm)

a b c d H S (mm) 2

a b c d H S (mm) 2

Two-frequency test stand at Yale Beam Physics Lab

Second-harmonic frequency multiplier

Computational predictions for second-harmonic frequency multiplier

Design parameters for 2nd harmonic multiplier

Demountable bimodal cavity test cell

Coupling into bimodal cavity

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.

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

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

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.

Bimodal cavity with beam tunnels

Bimodal test cavity with beam tunnels