Suppression of the quadrupole mode BBU by using the eccentric fluted beam pipe

1. Suppression of the quadrupole mode BBU by using the eccentric fluted beam pipe H.Sakai, K.Shinoe, (ISSP, Univ. of Tokyo) T.Furuya, K.Umemori, T.Takahashi, S.Sakanaka, T.Suwada (KEK) M.Sawamura (JAEA) ERL07 5/24/2007

2. HOM requirement [M.Liepe, Proc. of the 11th workshop on Superconductivity (SRF2003)] • Monopole mode (Heat load) • 100W heat load at resonant condition • HOM frequencies should be apart from multiples of 2.6 GHz(=1.3GHzx2) • Dipole mode (Beam-breakup(BBU) instabilities) • HOM requirement for 100mA beam current • Quadrupole mode (Quadrupole BBU instabilities) • HOM requirement for 100mA beam current

3. KEK-ERL model-2 cavity • In order to reduce a heat load and to satisfy the BBU threshold of 100mA. Cavity cell shape & beam pipe are optimized from TESLA 9cell cavity for the reduction of Qext of monopole and dipole mode • Enlarge Iris diameter to 80mm, elliptical shape at equator • Beampipe diameter 120mm & 100mm and add absorber • Quadrupole mode cannot propagate ourside the cavity, so far the beampipe diameter is much enlarged. Typical HOMs Propagation mode to beampipe KEK-ERL model-2 cavity (fundamental mode 1.3GHz) TM011: 2.34 GHz TE111: 1.61 GHz TM110: 1.82GHz TE211: 2.23 GHz TM01 TE11 Cut off freq. Cut off freq. TE21 LBP dia.：f120 TE11: 1.46 GHz TM01:1.91 GHz TE21:2.43 GHz SBP dia.：f100 TE11: 1.76 GHz TM01:2.30 GHz TE21:2.91 GHz new idea : eccentric fluted beampipe

4. Basic idea of eccentric-flute Calculation with MAFIA • Quadrupole is transformed to Dipole with eccentric-flute Eccentric-flute Quad mode is changed to dipole and propagate normal flute Quadrupole mode excited on cavity No change and disappeared

5. Fourier Component of Electric Field E-boundary M-boundary • Both modes（M-,E-boundary） are transformed to Dipole modes. • After transformation to Dipole, flute is not necessary？

6. Effect of length of flute Fully damped of two quadrupole modes Length of flute 20mm (fixed) Length of flute How long of the length of flute is needed to extract the transformed dipole mode from quadrupole mode The length of 50-100mm is enough for the quadrupole damping

7. Comparison of 3 types of eccentric flute shift shift & bend no-shift & bend • Similar performance is obtained among 3 types • No-shift & bend type is easy fabrication. We adopt type of no shift & bend bending angle of 25°

8. Beam pipe view on the FLUTE side 6cm 3cm Check: Multipacting Surface treatment Affect into other modes (fundamental, dipole) Now under fabrication of Nb single cell

9. Quadrupole of Model2 E M Quad-BBU 100mA threshold 8π/9 → field in end cell opposite eccentric flute is excited Qext would be lowered by optimization of eccentric flute parameters or adoption of eccentric flutes on both sides.

10. Measurement of low power model with eccentric flute Eccentric flute consists of 7 pieces. Eccentric flute TESLA type cavity (TE211 : 2.29GHz) The flute angle can be changed from 0 to 45 degree by 5-degree step. The flute length and depth are also variable. q (0-45 degree)

11. Loaded Q with eccentric flute No flute Flute 15 deg Flute 30 deg M Roll of ferrite Flute 45 deg Ferrite position Ferrite position (cm) Without eccentric flute, no field inside the beam pipe far from the cell. With eccentric flute, measured QL is reduced and therefore field transmits through the beam pipe. Loaded Q varies with ferrite position by the mismaching the transmission to the ferrite and agree well with the transmission line model. Estimate Qext Ferrite sheet(15cm long, 2mm thick) (μr’=5.10,μr’’=6.29 @2GHz)

12. Field Polarization in Beam Pipe Frequency is 2.29GHz of Quadrupole mode rotate Field inside the beam pipe is DIPOLE mode. Magnetic field FBP

13. Loaded Q for two degenerated modes Flute angle = 25 deg Perturbation can separate TE211 mode into 2 modes (E & M). ⇒Eccentric flute is effective for both modes.

14. Calc vs. measurement Calc External Q Calc Flute angle (deg) • Measurement results are almost agree well with calculation. • - But measurement results of TE211E are a little smaller than calc. More detail analysis will be presented on PAC07 : M.Sawamura, et al.

15. Conclusion • We have designed the 1.3GHz superconducting cavity, which is optimized for ERL operations. Especially, eccentric flute is effective for damping quadrupole modes. • In order to confirm the effectiveness of eccentric flute for damping quadrupole modes, we have made a test cavity with eccentric flute. • Measurement results of Qext almost agree with the calculation, but needs more investigation. • From these results, the eccentric fluted beam pipe works well for the damping of quadrupole mode, if we have optimized the position of the damper.

17. Parameters and cut off frequency Parameters for accelerating mode

18. Eccentric-flute Basic Idea for Quadrupole damping • Quadrupole in Beam Pipe Dipole-like Shift FLUTE TE21 can transmit asTE11?

19. Transverse field due to FLUTE • Does eccentric flute affect fundamental field?

20. Ratio of transverse/longitudinal forces 3cell6.4×10-5 9cell2.1×10-5 Transverse kick is small due to flute.

21. Loaded Q for two degenerated modes (cont.) • For 45-deg flute angle ⇒ TE211E mode hardly couple with eccentric flute. 　　　　⇒ This corresponds to calculation. Q value of TE211M is so low that two modes overlap.

22. Estimation of Qext absorber • When a transmission line is connected with a load of normalized conductance g, • Input admittance of a load viewed from z=0 to z=z, • Assume the input admittance viewed from z=z-dz becomes real, • Input admittance becomes Transmission line model

23. Estimation of Qext (Cont.) • Normalized conductance g is • Loaded Q can be represented as • Qext can be estimated by fitting the measured Qload with unknown parameters

24. Estimation of Qext by fitting QL is well fitted by using fitting function

25. Fiiting results of Q0