1. INVESITGATION OF AN ALTERNATE MEANS OF WAKEFIELD SUPPRESSION IN CLIC MAIN LINACS CLIC_DDS

2. Wakefield suppression in CLIC main linacs We are looking into an alternative scheme in order to suppress the wake-field in the main accelerating structures: Detuning the first dipole band by forcing the cell parameters to have Gaussian spread in the frequencies Considering the moderate damping Q~500 2 The present main accelerating structure (WDS)for the CLIC relies on linear tapering of cell parameters and heavy damping with a Q of ~10. The wake-field suppression in this case entails locating the damping materials in relatively close proximity to the location of the accelerating cells.

3. Constraints RF breakdown constraint 1) 2) Pulsed surface heating 3) Cost factor Beam dynamics constraints 1)For a given structure, no. of particles per bunch N is decided by the /λ and Δa/ 2)Maximum allowed wake on the first trailing bunch Rest of the bunches should see a wake less than this wake(i.e. No recoherence). Ref: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

4. Overview of present WDS structure StructureCLIC_G Frequency (GHz)12 Avg. Iris radius/wavelength /λ0.11 Input / Output iris radii (mm)3.15, 2.35 Input / Output iris thickness (mm)1.67, 1.0 Group velocity (% c)1.66, 0.83 No. of cells per cavity24 Bunch separation (rf cycles)6 No. of bunches in a train312 4 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 Lowest dipole band: ∆f ~ 1GHz Q~ 10 Ref: A. Grudiev, W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

5. Comparison between uncoupled and coupled calculations Black: Uncoupled Red: coupled Solid curves: First dipole Dashed curves: second dipole Red: Uncoupled Blue: Coupled Red: Uncoupled Blue: Coupled W t (0)=110 V/pc/mm/m W t1 ~ 2 V/pc/mm/m

6. Comparison between uncoupled and coupled calculations: 8 fold structure 6 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 3.3 GHz structure does satisfies beam dynamics constraints but does not satisfies RF breakdown constraints. Finite no of modes leads to a recoherance at ~ 85 ns. But for a damping Q of ~1000 the amplitude wake is still below 1V/pc/mm/m Why not 3.3 GHz structure?

7. Cella (mm)b (mm)t (mm)Vg/c (%)f1 (GHz) 1st3.159.91.671.6317.45 Ref 12.979.861.51.4217.64 Ref 22.759.791.341.217.89 Ref 32.549.751.181.018.1 24th2.359.711.00.8618.27 Cell parameters of a modified CLIC_G structure: Gaussian distribution Uncoupled values: /λ=0.11 ∆f = 0.82 GHz ∆f = 3σ i.e.(σ=0.27 GHz) ∆f/favg= 4.5 % 7 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

8. Modified CLIC_G structure Uncoupled Coupled Q = 500 Undampe d 8 Envelope Wake-field Amplitude Wake- field 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

9. Cell #a (mm)b (mm)t (mm)Vg/c (%)f1 (GHz) 12.999.881.61.4917.57 42.849.831.41.3817.72 82.729.801.31.2917.85 122.619.781.21.1817.96 162.519.751.11.0618.07 202.379.730.960.9818.2 242.139.680.70.8318.4 Cell parameters of seven cells of CLIC_ZC structure having Gaussian distribution Uncoupled values: /λ=0.102 ∆f = 0.83 GHz ∆f = 3σ i.e.(σ=0.27 GHz) ∆f/favg= 4.56% ∆a1=160µm and ∆a24= 220µm. The first trailing bunch is at 73% of the peak value (W max =180 V/pC/mm/m). ∆f=110 MHz. There is a considerable difference in the actual wake-field experienced by the bunch, which is 1.7 % of peak value which was otherwise 27%. Zero crossing of wake-field We adjust the mode frequencies to force the bunches to be located at the zero crossing in the wake-field. We adjust the zero crossing by systematically shifting the cell parameters (aperture and cavity radius). 9 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

10. CLIC_ZC structure Coupled Uncoupled Undampe d Q = 500 10 Envelope Wake-field Amplitude Wake- field

11. Interleaved cells & S RMS Q = 500 24 cells Q = 500 192 cells 11 44th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 S RMS = 33 V/pC/mm/m S RMS = 7 V/pC/mm/m S RMS >1 BBU is likely to occur * * Ref: R.M. Jones, et al, 2002, SLAC-PUB-9407, LINAC-02

12. A typical geometry : cell # 1 r2 h r1 h1 b rc a a+a1 a1 a2 L

13. E-field in a CLIC_DDS single cell with quarter symmetry Manifold Coupling slot Cell mode Manifold mode π phase ω/2π = 17.41 GHz 0 phase ω/2π = 14.37 GHz

14. Uncoupled (designed) distribution of Kdn/df for a four fold interleaved structure Kdn/df dn/df Mode separation In order to provide adequate sampling of the uncoupled Kdn/df distribution cell frequencies of the neighbouring structures are interleaved. Thus a four-fold structure (4xN where N = 24) is envisaged. An erf distribution of the cell frequencies (lowest dipole) with cell number is employed.

15. Spectral function As the manifold to cell coupling is relatively strong there is a shift in the coupled mode frequencies compared to uncoupled modes which changes the character of the modes. For this reason we use spectral function method to calculate envelope of wakefield. The modal Qs are calculated using Lorentzian fits to the spectral function. Interleaved structure Non- interleaved structure Modal Qs Mean Q

16. Non-interleaved structure Interleaved structure Envelope wakefield of the present CLIC_DDS structure: Q~500 Envelope wakefield with an artificially imposed Q = 300

17. Uncoupled mode Q = 500 Q = 300

18. Cell # 1 Iris radius = 4.0 mm Iris thickness = 4.0 mm, ellipticity = 1 Q = 4771 R’/Q = 1,1640 Ω /m vg/c = 2.13 %c ~ dipole frequencies (GHz) 0 mode π mode 1 16.63 15.89 2 18.08 24.58 3 19.46 25.84 Cell # 24 Iris radius = 2.3 mm Iris thickness = 0.7 mm, ellipticity = 2 Q = 6355 R’/Q = 20,090 Ω /m vg/c = 0.9 %c ~ dipole frequencies (GHz) 0 mode π mode 1 13.02 18.18 2 18.74 20.19 3 20.43 21.49 A 2.3 GHz Damped-detuned structure Details: delf, sig, etc.

19. 3 disp curve s+avoi. Cross. F0,fpi,fx,fsyn vs # : represent by line

20. Corrected formula for effective pulse length Unloaded 249.352.3 Some explanation about bunch spacing and population. Plot for nb Some more detail on eff. Cal. Compare eff. With clic_g Put allowed surface field values

21. 24 cell structure Spectral function 2 kdn/df : coupled mode 2 kdn/df : uncoupled mode Spectral function 4-fold interleaving 96 cell structure 8-fold interleaving 192 cell structure Replace by new plots Cal. Q’s of first few modes

22. Wake-function : Inverse Fourier Transform of spectral function 4-fold interleaving 96 cell structure 8-fold interleaving 192 cell structure No interleaving 24 cell structure Replace by new plots

23. Next ? Optimisation of the manifold geometry to achieve minimum possible Q (100-200). Optimisation of the dipole bandwidth keeping in mind the constraints on the surface fields. Increasing the bunch spacing to 8 or 10 cycles to satisfy the beam dynamics constraints on the wakefield, in this case efficiency of the overall collider will have to be compromised. Considering all the above optimisation procedure the first trailing bunch is still expected to see a higher envelop-wakefield than allowed. In this case a zero-crossing scheme of the amplitude of wake will be employed. Conclusion The present CLIC_DDS structure has similar structure specifications like that of CLIC_G for lowest dipole bandwidth (~ 1 GHz) and bunch spacing (6 cycles). Interleaving the neighbouring structure frequencies helps in reducing the average envelope wakefield by a factor of appr. 2 for first 4m. The envelope wakefield for the first 3 bunches with four fold interleaving and an enforced Q = 300 is above the acceptable limit.