Hybrid designs - directions and potential

1. Hybrid designs - directions and potential Alessandro D’Elia, R. M. Jones and V. Khan

2. Outline • Conventional DDS limitations • A Hybrid Design as a possible CLIC_DDS_B • Single cell studies • Full structure designs and related wakefield damping • CLIC_G + Rect. Manifold studies • Conclusions

3. CLIC_DDS_A: regular cell optimization The choice of the cell geometry is crucial to meet at the same time: Wakefield suppression Surface fields in the specs DDS1_C DDS2_E CLIC_DDS_A-Single CLIC_DDS_A- 8 Fold Interleaving Cell shape optimization for fields

4. A new approach: a Hybrid Structure for CLIC_DDS_B Hybrid Structure WGD_Structure DDS_Structure + =

5. First steps on the Hybrid Structure Very high coupling of first dipolar band from cell to manifold via slot as in WGDS + Erf distribution of the dipolar frequencies as in DDS First three dipole bands are shown in the picture above; encircled is the avoided crossing region which is related to the coupling: here is ~1GHz in DDS_A was <200MHz The Erf distribution of the dipolar modes prevent to these modes to add in phase and this will result in a rapid decay of the wakefield in the short time scale; a high coupling will help when the mode will start to recohere in a longer time scale

6. Some preliminary calculation The following calculations refer to Str#3 (see Slide#39) No interleaving Damped (Q=270) Undamped (Q=6500) 2-Fold interleaving Damped (Q=600) Undamped (Q=6500) V/[pc mm m] V/[pc mm m] 2-Fold interleaving s (m) Damped (Q=270) Undamped (Q=6500) s (m) V/[pc mm m] s (m)

7. Summary table for new CLIC structure prototypes

8. Basic Cell Parameters g=L-t t/2 b eps*t/2=elip First Cell Last Cell L

9. Cell 1 with manifold

10. Proposed 1st Cell WGW WGH SlotH SlotW Htot

11. Last Cell with Manifold

12. Proposed 1st and Last cells WGW WGH SlotH SlotW Htot

13. Procedure adopted to build the full structure • Build 1st, Mid and Last Cells • Distribute the frequencies in Erf fashion • Optimize Erf sigma minimizing the wake on the first trailing bunch • Use this sigma to distribute iris radii and thicknesses • Tune the correct monopole frequency using cavity radius

14. First, Last and Mid cell parameters (Big Band) WGW WGH SlotH SlotW Htot * This is used only to optimize the Erf

15. From 3 cells to the full structure From First, Mid and Last cell fsyn’s and kicks, we enforce a Gaussian distribution of Kdn/dfas a function of f (for the details, please refer to Vasim’s PhD thesis or Roger Jones papers). The wake is  Kdn/df . Fsyn Distribution Kick Distribution 2 Kdn/df Wake envelope

16. Best n Best n=3.64 =0.8587

17. Geometrical parameters of the cells from Erf a26=2.0648 t26=1.0409 b will be used to tune the cell and SlotH will change accordingly to have Htot constant SlotW26=1.5769

18. Wakefield Str#1 (Large Band) “Uncoupled” Wake Damped (Q=1350) Undamped (Q=6500) V/[pc mm m] s (m) NB: Reconstructed wake  Only 1st Dipole band

19. Impedance Full Transverse Impedance (all dipoles) Peak Number Transverse Impedance (First two dipole bands) Peak Number

20. First, Last and Mid cell parameters (Big Av. Cross.) WGW WGH SlotH SlotW Htot * This is used only to optimize the Erf

21. Wakefield Str#2 (Large Av. Crossing) GdfidL Reconstructed wake (only 1st Dipole Band) Damped (Q=156) Undamped (Q=6500) “Uncoupled” Wake V/[pc mm m] s (m)

22. Impedance Full Impedance Peak Number First Dipole Impedance Peak Number

23. What’s wrong? Str#1 Str#2 Non Erf distribution ~ Erf distribution Peak Number Samples Peak Number Design strategy is not correct to ensure Erf distribution on dipoles!!!

24. New strategy • Fix First, Mid and last cell • Optimize  • Vary “a” and “t” accordingly to Erf with previous  • Find out 7 fiducial values (4 + the 3 already found for 1st, Mid and Last cell) in order to get fsynvs “a/t/b” • Get the distribution of fsyn corrected by ksyn • Then optimize again  of the distribution of fsyn • Known fsyn evaluated from Mathematica in the previous point, go back to fsynvs “a/t/b” to find the geometrical parameters of the full structure

25. Detailed Procedure Re-optimize Sigma in

26. First, Last and Mid cell parameters (Str#3) WGW WGH SlotH SlotW Htot * This is used only to optimize the Erf

27. Optimized theoretical FsynvsFsyn HFSS simulations for regular cells Max F=5MHz <F>=1MHz

28. Wakefield: Comparison Str#2 and Str#3 Str3 Str2

29. Wakefield GdfidL Reconstructed wake (only 1st Dipole band)

30. Impedance Full Impedance Peak Number First Dipole Impedance Peak Number

31. Comparison: Str3 coupled and uncoupled Coupled (reconstructed wake from GdfidL) It seems that the coupling changes the nature of the wake in the early meters Uncoupled

32. Is Q distribution playing a role? Coupled Coupled Uncoupled Q distribution plays a marginal role

33. Let’s go back to Kdn/df (1) From Fsyn distribution we get dn/df, then we multiply by the kicks and we would expect to get a Gaussian-like distribution Uncoupled-DDS_A Coupled-DDS_A

34. Let’s go back to Kdn/df (2) Uncoupled-Str3 Coupled-Str3 First Dipole Impedance

35. What is the problem? Uncoupled First Dipole Impedance Uncoupled with all 27 Fsyn’s Uncoupled with only 16 Fsyn’s

36. CLIC_G + Rect. manifold • Linear tapering • Cell parameters: CLIC_G • Tapering: CLIC_G i.e. linear

37. WW WW=7.5 WH =6.5 Wpos=14.5 WH Wpos

40. HFSS single cell simulations Hybrid DDS E-H Boundary condition H-H Boundary condition H-H Boundary condition Hybrid “CLIC_G” E-H Boundary condition

41. Conclusions • We have shown that an average Q<200 can be achieved with this structure with a bandwidth ranging from 2.4-3GHz • However strong coupling results in a change of the nature of dipole distribution • The next step is to analyze the structure for a moderate damping (as in NLC, Q~400-500) in order to preserve the nature of Erf distribution • We have shown that with a Q<600, with 2-fold interleaving a good damping can be anyway achieved • Further studies are needed but the structure looks promising

42. Additional slides