1. TWO-BEAM, MULTI-MODE, DETUNED ACCSELERATING STRUCTURE S.Kazakov 1,2, S.Kuzikov 3, V.Yakovlev 4 J.L. Hirshfield 1,5, 1 Omega-p,Inc., 199 Whitney Ave., New Haven, CT 06511, USA 2 High Energy Accelerator Research Organization, KEK, Tsukuba, Ibaraki 305-0801, Japan 3 Institute of Applied Physics, Nizhny Novgorod, Russia 4 Fermi national Accelerator Laboratory, Batavia, IL 60510, USA 5 Beam Physics Laboratory, Yale University, 272 Whitney Avenue, New Haven, CT o6511, USA AAC08, Santa Cruz

2. Co-author S.Kuzikov recently suggested the intriguing idea of increasing the breakdown limit by decreasing the exposure time to high electric fields. It is possible to do this by using a combination of several modes with different frequencies. The idea is clear from picture: Acceleration by one harmonic Acceleration by three harmonics RF energy is concentrated on the bunch for only short times during bunch transit.

3. 6% 9% 12% To get these mode combinations, we need a cavity with an equidistant spectrum, i.e. fi = i  f 0, where i is an integer. In case of a square of side a, even mode odd mode Operating spectrum for a square box cavity is f, 3f, 5f… and operating modes are TM110, TM330, TM550, etc.

4. To compare different structures, one should use a quantitative criterion of dependence of breakdown probability on electric field and exposure time. Let’s take as criteria the integrals Suppose probability of breakdown depends of combination of electric field and pulse length like: P bd ~ E 2 xT or P bd ~ E 3 xT

5. I2I2 I3I3 These results suggest that an accelerating gradient 1.15 – 1.35 times higher can be sustained for the same probability of breakdown, if three harmonics are employed, rather than one.

6. Here we suggest having two beams in the same cavity. If we reflect the square cavity about any e-wall, we will get a “two-box” cavity with the same spectral properties as one box. E-field in a two-box cavity Convenient place for drive beam – all modes are excited equally, zero magnetic field Place for acc. beam For a cavity without lossFor a cavity with loss

7. - angle between I drive and I acc Transformer coefficient for detuned mode with quality factor Q: Accelerating with one mode Accelerating with two mode

8. Accelerating possible in both directions:

9. Drive beam Accelerated beam Geometry for simulations to be described h = 25 mm for singe mode case, f h = 15 mm for two mode case, f, 3f h = 10 mm for three mode case, f, 3f, 5f For computing mean accel gradient G, the gap height is taken to be h + 3 mm. Copper walls are also assumed for calculating wall losses. Beams are  7 cm apart. Resonant frequency of TM 1,2,0 mode is fixed at 3 GHz, but drive bunch frequency, and TM 3,6,0 TM 5,10,0 TM 1,14,0 and TM 7,2,0 mode frequencies are varied.

10. Q d =8.4 nC G =100 MV/m Q d =8.4 nC G =150 MV/m Q d =16.8 nC G =100 MV/m Q d =16.8 nC G =150 MV/m Q d =33.6 nC G =100 MV/m Q d =33.6 nC G =150 MV/m I drive 25.2 A 50.4 A 100.8 A I acc Q acc 1.2 A 0.4nC 1.2 A 0.4nC 1.2 A 0.4nC 1.2 A 0.4nC 1.2 A 0.4nC 1.2 A 0.4nC transform ratio  7.55.615.111.531.123.6 efficiency35.5%26.4 %35.9 %27.1%36.8%28.0% E_max126 MV/m188 MV/m 126 MV/m 188 MV/m 126 MV/m 188 MV/m df 1 /f 1 4.3E-42.8E-48.7E-45.8E-41.8E-31.2E-3 Two-box cavity, single mode, h = 25 mm, f = 3 GHz, Q 1,2 =1.35E+4

11. Q d =8.4 nC G =100 MV/m Q d =8.4 nC G =150 MV/m Q d =16.8 nC G =100 MV/m Q d =16.8 nC G =150 MV/m Q d =33.6 nC G =100 MV/m Q d =33.6 nC G =150 MV/m I drive 25.2 A 50.4 A 100.8 A I acc 1.2 A transform ratio  6.85.113.810.228.020.2 Efficiency32.2%24.0 %32.7 %24.2%33.2%24.0% E_max 142 MV/m 215 MV/m 142 MV/m 215 MV/m 142 MV/m 215 MV/m df 1 /f 1 7.5E-44.9E-41.5E-31.0E-32.8E-32.0E-3 df 2 /f 2 -2.1E-4-1.4E-4-4.3E-4-2.8E-4-9.2E-4-5.5E-4 Two-box cavity, two modes, h = 15 mm, f 1 = 3 GHz, f 2 = 9 GHz Q 1,2 =9.4E+3, Q 3,6 = 1.6E+4

12. Q d =8.4 nC G =100 MV/m Q d =8.4 nC G =150 MV/m Q d =16.8 nC G =100 MV/m Q d =16.8 nC G =150 MV/m Q d =33.6 nC G =100 MV/m Q d =33.6 nC G =150 MV/m I drive 25.2 A 50.4 A 100.8 A I acc 1.2 A x’form ratio 7.25.314.110.728.021.2 Efficiency 34.1%25.3 %33.4 %25.4%33.2%25.2% E_max 146 MV/m220 MV/m146 MV/m220 MV/m146 MV/m220 MV/m df 1 /f 1 8.7E-45.8E-41.80E-31.2E-33.6E-32.3E-3 df 2 /f 2 -3.4E-4-2.2E-4-6.3E-4-4.3E-4-1.2E-3-8.4e-4 df 3 /f 3 7.3E-44.6E-41.7E-31.0E-32.9E-32.0E-3 Two-box cavity, three modes, h = 10 mm, f 1 = 3 GHz, f 2 = 9 GHz, f 3 = 15 GHz Q 1,2 = 6.8E+3, Q 3,6 = 1.2E+4, Q 5,10 (1,14) (7,2) = 1.5E+4

14. Suggested construction: accelerating structure—a series of cavities—could be milled from six copper blocks, assembled with slots (similar to CLIC structure), to suppress spurious modes and wake-fields

15. Problems:

16. Transient effects: Frequencies of cavity and drive beam are different (detuning). There is beating between two frequencies. Decay time is several Q-times of cavity – very long.

19. Transverse wake-fields: Work is in the progress. First results will be presented in next slides.

20. In this talk we will consider only the growth of horizontal emittance. It supposed that cavity placed horizontally and beams with ideal alignment do not exists vertical wake fields. At the same time horizontal wake fields are existed because the beams shifted from centre of cavity horizontally. Criterion: Estimation of emittance growth: (V.Yakovlev) r.m.s. bunch length (140  m) initial energy in eV (10 10 ) initial relativistic factor (10 4 ) beta-function (8m) drive bunch charge transverse wake potential per length distance from the bunch center

21. Closed copper cavity We need a damping !

22. for Q = 33.6nC (transformer ratio = 31) for Q = 8.4nC (transformer ratio = 7.5) Lossy cavity,  1e-5*cooper

23. Copper cavity with slots for Q = 30nC (transformer ratio = 31) for Q = 8.4nC (transformer ratio = 7.5)

24. for Q = 30nC (transformer ratio = 31) for Q = 8.4nC (transformer ratio = 7.5) 9 cell copper structure with slots

25. Conclusion: New two-beam scheme with detuned cavity is suggested. First results of simulation look promising We understand the problems better. Work is in the progress Approach is still alive.