1. 2006/9/25-26 ILCDR06, Cornell University 1 DESIGN STUDY OF A MOVABLE COLLIMATOR WITH LOW BEAM IMPEDANCE Yusuke Suetsugu*, Kyo Shibata KEKB Vac. Group Introduction Simulation Test Model Summary (Application to clearing electrode)

2. 2006/9/25-26 ILCDR06, Cornell University 2 Movable Collimator (Mask) –A vacuum component to shut off spent electrons, which circulating out of a nominal orbit Indispensable to reduce background of detector Introduction Beam Bellows Chamber Mask Chamber Bellows Chamber Head [Ex. Collimator Ver.4 in operation at KEKB]

3. 2006/9/25-26 ILCDR06, Cornell University 3 Problems in high current machine –High impedance –Damage of head by beam Introduction Ceramics Metal Beam duct Support Head SiC Beam SiC One idea –Ceramics support + thin conductive layer Little interference with beam No charge up –Ceramics head Little damage by beam Ex. Al 2 O 3 ： R.L. = 75 mm –SiC HOM absorbers Absorption of HOM

4. 2006/9/25-26 ILCDR06, Cornell University 4 Introduction Studied here –RF properties Simulation by Mafia 4.2 [MAFIA] 、 Microwave Studio 6.0 [MWS] f r (resonance frequency), Q, R S, R T (shunt impedance) of trapped modes CBI growth rate (Longitudinal, Transverse) Tolerable conductivity of coating –Estimation of head temperature Input power, temperature –Manufacturing of a test model (atmosphere version) Manufacturing of head, dielectric support (BN, Al 2 O 3 ) Measurement of f r 、 Q of trapped modes, and comparison with calculation Clearing electrode

5. 2006/9/25-26 ILCDR06, Cornell University 5 Simulation Model for MWS Head (W:8 mm,T:7 mm, L:90 mm) –Copper, 10 mm from beam Support –BN (W: 4 mm, T: 6mm)  r = 4.0, tan  = 0.0008 –Al 2 O 3 (W: 4 mm, T: 4mm)  r = 9.0, tan  = 0.0001 –Thin layer (t = 0.1mm) with conductivity (  ), as a coating Duct –  94, L: 300 - 500 mm SiC –Deby first-order dispersion –  s = 110,   = 14,  = 1  10 -9 s Port 1 Port 2 Beam duct Support Head SiC Calculation –S 11 between Port 1 and Port 2 Antenna: 10 mm –Frequency mode Debye type

6. 2006/9/25-26 ILCDR06, Cornell University 6 Beam duct Support Head Beam SiC Simulation Model for MAFIA Head (W: 8 mm, T: 7 mm,L:90 mm) –Copper, 10 mm from beam Support –BN (W: 4 mm, T: 6mm)  r = 4.0 –Al 2 O 3 (W: 4 mm, T: 4mm) e r = 9.0 –Thin layer (t = 0.8mm) with conductivity (  ) as a coating Duct –  94, L: 3200 mm SiC –Deby First-order dispersion –  s = 110,   = 14,  = 1  10 -9 s Calculation –  x= 2mm,  y =1mm,  z =0.8mm –Wake calculation up to 32 m –Beam: x = 0, y = 0 –Bunch length:  z = 4 - 8 mm Debye type

7. 2006/9/25-26 ILCDR06, Cornell University 7 Simulation S 11 spectrum (MWS) –Two modes, Mode-1 and Mode-2 are trapped under the cut-off frequency (1.87 GHz) –Mode-1 disappears for ceramics support Mode 2 ~1.38 GHz TE 111 of  94 pipe Mode 1 ~0.69 GHz 1 0.995 0.99 0.985 0.98 0.975 0.5 1 1.5 2 Frequency [GHz] Amplitude Mode 2 ~1.38 GHz 0.5 1 1.5 2 Frequency [GHz]

8. 2006/9/25-26 ILCDR06, Cornell University 8 Simulation H distribution of modes Current goes up and down along support High impedance f~0.69 GHz I [H][H] Depend on  of support [ Mode-1 (only for metal) ] [H][H] f~1.37 GHz [ Mode-2 (both for metal and ceramics) ] I I Current go and back along head

9. 2006/9/25-26 ILCDR06, Cornell University 9 Simulation R S and Q for Mode-1 calculated by MWS Expressed as a function of  (skin depth) / t (thickness) R S is larger for large . Q is also high. At  /t ~1, R S ~ 1k .Q ~ 20. Almost constant at R S /Q ~ 50 Calculation was impossible at  /t >2 –Disappear ! Little dependence on SiC at  /t > 0.2 [MWS]

10. 2006/9/25-26 ILCDR06, Cornell University 10 Simulation MWS and MAFIA At  /t ~1, R S ~ 1 k  (  MWS). But, Q~5 (~1/4 of MWS), R S /Q~200. Little effect of Q: Too short calculation length of wake? At  /t ~1, R S =1 k . R S /Q = 50~200 [MWS] [MAFIA]

11. 2006/9/25-26 ILCDR06, Cornell University 11 Simulation R S and Q of Mode-2 by MWS Q does not so depends on SiC as that for Mode-1 At  /t =1~10, R s =100~10 , Q= 1000~500 (with SiC). At  /t =1~10, R s /Q = 0.1~ 0.02 。 R s /Q decreases at  /t >2. [MWS]

12. 2006/9/25-26 ILCDR06, Cornell University 12 Simulation MWS and MAFIA At  /t =1~10, R s =100~10  (  MWS), but Q ~200 (1/5~1/3 of MWS) At  /t =1~10, R s /Q =0.5~ 0.05 R s /Q decreases at  /t >1. [MAFIA] At  /t =1~10, R S =100~10 , R S /Q=0.5~0.02 [MWS]

13. 2006/9/25-26 ILCDR06, Cornell University 13 Simulation Summary of f r, Q, R S and R T

14. 2006/9/25-26 ILCDR06, Cornell University 14 Simulation Growth rate of Longitudinal CBI –For a uniform bunch filling,  : Mode number e : Electron charge N : Number of electrons in a bunch M : Number of bunches  : Momentum compaction factor T 0 : Revolution time [s] E 0 : Beam energy [J]  s : 2   Synchrotron frequency R S : Shunt impedance [  ] Q 0 : Q value  r : 2   Resonance frequency I b : Beam Current [A] = eNM/T 0

15. 2006/9/25-26 ILCDR06, Cornell University 15 Simulation Tolerable growth rate –KEKB(LER) Damping time = 21.5 msec,  = 3.39  10 -4, f s =2  10 3 Hz  -1 < 50 s -1 (@ 2.6 A) Then,  -1 < 3 s -1 (@ #16 masks) –SKEKB Damping time = 30 msec,  = 2.7  10 -4, f s =3.1  10 3 Hz  -1 < 30 s -1 (@ 9.4 A) Then,  -1 < 1 s -1 (@2.6A, #16,  =3.4  10 -4, f s =2  10 3 Hz)

16. 2006/9/25-26 ILCDR06, Cornell University 16 Simulation Maximum  -1 for a 2.6A beam @KEKB m = 1~5120, M =5120, T 0 =1  10 -5 [s], I b = 2.6 [A]  =3.4  10 -4, E 0 =3.5 [GeV],   : 2  2  10 3 Mode-1 Mode-2 500  200  Maximum within f r  0.1GHz 1 1

17. 2006/9/25-26 ILCDR06, Cornell University 17 Simulation Necessary  /t –Mode 1 R S < 500   /t > 2 –Mode 2 R S < 200  OK if with SiC 、  /t > 3 if without SiC (MWS) For Cu (  = 5.8  10 7  -1 m -1 ),  /t =2 Possible material –1  m Ti coating (  =1.7  10 6  -1 m -1 ), for example ： –  = 1  10 -5 m @1.38GHz –  /t = 10 – R S ~10, R S /Q =0.02 ~ 0.05 (Mode-2)

18. 2006/9/25-26 ILCDR06, Cornell University 18 Simulation Similar discussion can be made for transverse CBI. Tolerable growth rate: –Damping time ~50 turn (SKEKB) –  -1  35 s -1 (@2.6A, #16) Mode 1 –R T 2 Mode 2 –R T 1 if without SiC (MWS) Realized by 1  m Ti coating

19. 2006/9/25-26 ILCDR06, Cornell University 19 Simulation Loss factor (MAFIA) At  /t ~10 (  ~10  -1 m -1 ) 、  z = 4mm, 1/4 of Ver.4 @KEKB But, the loss factor is still large (Without SiC) KEKB Ver.4  =10

20. 2006/9/25-26 ILCDR06, Cornell University 20 Simulation Loss factor: Comparison with R S Similar behaviour to R S (Without SiC)

21. 2006/9/25-26 ILCDR06, Cornell University 21 Simulation Heating of Mask head (only results) –Joule loss by wall current ~30 W –Input power from trapped mode (Only Mode-2) ~25 W at most –Heat transfer: Only radiation –Expected temperature: Input ~ 50 W ~600  C for  1 =0.5  1 : emissivity Tolerable range 5000 bunches, 10 A, KEKB

22. 2006/9/25-26 ILCDR06, Cornell University 22 Test Model A test model for air version was manufactured. –Aluminum alloy pipe –Head ： Aluminum 、 Graphite –Support ： Aluminum 、 BN 、 BN+Ti coating, Al 2 O 3 –SiC ： W:20mm  L:90mm  8 pieces Graphite head (Non rectangular) Graphite BN SiC

23. 2006/9/25-26 ILCDR06, Cornell University 23 Test Model S 12 between two antennae was measured Frequency spectrum 、 Q 、 f r of trapped modes were compared to the calculated ones [HP Network Analyzer 8753]

24. 2006/9/25-26 ILCDR06, Cornell University 24 Test Model Frequency spectrum –Mode-1 disappeared for ceramics support as expected S12 Metal Support (Al) Ceramics (BN) Support 0.4 GHz 2 GHz 0.4 GHz 2 GHz Mode 1 (~0.7 GHz) Mode 2 (~1.4GHz) Mode 2 (~1.4GHz)

25. 2006/9/25-26 ILCDR06, Cornell University 25 Test Model Simulation Model for test model SiC Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 f r and Q were measured changing number and position of SiC Al [MWS] Al SiC

26. 2006/9/25-26 ILCDR06, Cornell University 26 Test Model f r and Q (Al support) Difference of f r is within 2.5%. The behaviour is similar, but the change of f r is larger. Q of Mode-2 is also good agreement. Q for Mode-1 is smaller by a factor of 3 - 4. –Due to bad electric contact between support and head, duct Mode-1 Mode-2

27. 2006/9/25-26 ILCDR06, Cornell University 27 Test Model Thin tapes at one side of support Simulation of a thin coating Cu : t = ~30  m,  = 5  10 7  -1 m -1  / t = 0.09 Al -alloy: t = ~50  m,  = 1  10 7  -1 m -1  / t = 0.12 SUS : t = ~40  m  = 1  10 6  -1 m -1  / t = 0.48

28. 2006/9/25-26 ILCDR06, Cornell University 28 Test Model Frequency spectrum: BN→SUS → Al → Cu BN SUS Al Cu 0.4 – 2.0 GHz Case-3

29. 2006/9/25-26 ILCDR06, Cornell University 29 Cold Model Ti coated Al 2 O 3 support Mode-1 disappears for t = 1  m (86  for 30 mm) 0.4 – 2.0 GHz t = 10  m (  /t ~1) t = 1  m (  /t ~10)

30. 2006/9/25-26 ILCDR06, Cornell University 30 Summary Proposal –Head supported by ceramics with a thin coating Simulation –For a case of Al 2 O 3 support with 1  m Ti coating –  / t ~10 @1.38GHz –R S ~10  、 R T ~1 k  m -1 (Only for Mode-2) –Longitudinal, Transverse CBI : OK (for SKEKB) –Loss factor @  z = 4 mm ~ 0.3 V pC -1 (~1/4 of KEKB Ver.4) –Head temperature ~600 ℃ @  1 = 0.5 (~50 W input power) Promising

31. 2006/9/25-26 ILCDR06, Cornell University 31 Summary Test Model –f r and Q (Except for Mode-1) agreed well with calculation –Behavior of Q (Mode-1) against  coincides with calculation –1  m Ti coating actually showed no peak of Mode-1 Next step –Optimization of dimensions of head to reduce loss factor –Trial model for KEB LER is under manufacturing, and will be installed next year.

32. 2006/9/25-26 ILCDR06, Cornell University 32 Summary Plan (under manufacturing)

33. 2006/9/25-26 ILCDR06, Cornell University 33 Summary Application to a clearing electrode –If finite  is ok, the structure can be applied to clearing electrode. –Electrode based on similar concept has been tried in DA  NE Clearing electrode for ion Electrode was supported by ceramics with conductive painting –Calculation is undergoing –Test using existing B chamber?

34. 2006/9/25-26 ILCDR06, Cornell University 34 Clearing Electrode Model for clearing electrode –Electrode: 1mm  1mm  1000 mm rod –Support: 2mm  2 mm  2* One support:Al 2 O 3 + thin conductive layer –10 mm from wall L.Wang et al., EPAC2006 [MAFIA] (*Note: Several additional ceramics supports will be required)

35. 2006/9/25-26 ILCDR06, Cornell University 35 Clearing Electrode Z //  =10  -1 m -1 ~150 MHz (~ /2 resonance) Metal Ceramics R S <~1  Q ~ 2/0.06~30 @2GHz

36. 2006/9/25-26 ILCDR06, Cornell University 36 Clearing Electrode Z T R T <~3000  Q ~ 2/0.06~30 @2GHz  =10  -1 m -1 Metal Ceramics

37. 2006/9/25-26 ILCDR06, Cornell University 37 Clearing Electrode Loss Factor  [  -1 m -1 ] k [V C -1 ] 0 (ceramics)3.85x10 8 18.31x10 8 101.59x10 9 Metal3.88x10 9 (~TiN?) (~Ti)

38. 2006/9/25-26 ILCDR06, Cornell University 38 Clearing Electrode Ref: DA  NE type Loss Factor –~6x10 10 V C -1 (  z = 8 mm) R S ~ 40  Q ~ 30 Electrode: 50mm x 50mm x t 1mm Support: 10mm x10mm x10mm+Coating (t = 0.8 mm,  =1  -1 m -1 )

39. 2006/9/25-26 ILCDR06, Cornell University 39 Clearing Electrode What should be considered next? –Instabilities (CBI, Microwave Instability?) –Heating –Structure (More realistic one) –Experiments at KEKB (in B, Wiggler)? –etc.

40. 2006/9/25-26 ILCDR06, Cornell University 40 end

41. 2006/9/25-26 ILCDR06, Cornell University 41 Simulation Calculation of Q, R S and R T by MWS –Q: Frequency spectrum of S １１ between two antennae –R S : Longitudinal –R T : Transverse [][] [  /m]

42. 2006/9/25-26 ILCDR06, Cornell University 42 Simulation W s (  ): FFT of Wake Potential (at x = 0, y = 0)  (  ): FFT of bunch profile Z s (  ): Longitudinal impedance –R S and Q are calculated fitting to [][] [][] Calculation of Q, R S by MAFIA –From wake potential

43. 2006/9/25-26 ILCDR06, Cornell University 43 Simulation Example of Z S at  z = 8 mm,  = 1  10 3  -1 m -1 Real Part Imaginary Part Mode-1 Mode-2 Longitudinal Impedance [MAFIA]

44. 2006/9/25-26 ILCDR06, Cornell University 44 Wake Wake(z) at  =1  10 7 、 1  10 3 Little damping Little difference for 32m calculation –Calculation error increased for longer calculation length: Limit of MAFIA Damped withiin 32m →OK for  /t > 1  = 1  10 7  = 1  10 3

45. 2006/9/25-26 ILCDR06, Cornell University 45 Heating of head Surface current density at 10A, 5000 bunches –q = 2  10 -8 C → B x ~6  10 -5 T → H x = 48 A/m Surface resitance, R (f r = 1.5 GHz)  –Cu:  = 5.8  10 7 1/  m Joule loss at surface, P –P = I 2 R = (48  8  10 -3 ) 2  (1.0  10 -2  90  10 -3 /8  10 -3 )  4 = 0.066W –Too small ・・ Main input was from wall current –No frequency component of Mode-1

46. 2006/9/25-26 ILCDR06, Cornell University 46 Heating of head Refernce

47. 2006/9/25-26 ILCDR06, Cornell University 47 Heating of Head Estimation of temperature Only radiation Generally, radiation power, P 12, from an object with an area of A 1, Emissivity of  1, temperature of T 1 to another one with an area of A 2, Emissivity of  2, temperature of T 2 s b ： Stefan-Boltzmann constant = 5.67  10 -8 W/m 2 K 4 A1A1 A2A2

48. 2006/9/25-26 ILCDR06, Cornell University 48 Heating of Head A 1 =2.8  10 -3 m 2 、 A 2 = 1.55  10 -1 m 2 (500mm long pipe) 、 T 2 = 293 K 、  1 = 0.2 - 0.8(copper) 、  2 = 0.5 (Rough SS) for 50Winput, ~600 ℃ at  1 ~0.5, ~850 ℃  1 ~0.2. Blazing is possible? A1A1 A2A2  1 =0.2  1 =0.8  1 =0.5

49. 2006/9/25-26 ILCDR06, Cornell University 49 Simulation –R T and Q are calculated fitting to Calculation of Q, R T by MAFIA –From wake potential W T (  )=W T [y=y 1 ](  )-W T [y=-y 1 ](  ), y 1 →0: Z T (  ): Transverse (y) impedance [  m -1 ]

50. 2006/9/25-26 ILCDR06, Cornell University 50 Simulation Example at  z = 8 mm,  = 1  10 3  -1 m -1 Real Part Imaginary Part Mode 1 Mode 2 Transverse Impedance

51. 2006/9/25-26 ILCDR06, Cornell University 51 Cold Model Dependence of Q (Mode-1) on  / t Two SiC bars (Case-3) Tendency is in good agreement with calculation Measured Q was 1/10~1/20 of calculation.