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 dielectric 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 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. A 3.3 GHz structure 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 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) 13.159.91.671.6317.45 72.979.861.51.4217.64 132.759.791.341.217.89 192.549.751.181.018.1 242.359.711.00.8618.27 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

8. Modified CLIC_G structure Uncoupled Coupled Q = 500 Undampe d 8 Envelope Wake-field Amplitude Wake- field

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 ∆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).

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

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

12. 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

13. 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.

14. 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

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

16. 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 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 A 2.3 GHz Damped-detuned structure ∆f = 3.6 σ = 2.3 GHz ∆f/fc =13.75 % /λ=0.126

17. Cell # 1 Solid (dashed)curves coupled (uncoupled) modes Avoided crossing Uncoupled 2 nd mode Uncoupled 1 st mode Uncoupled manifold mode Coupled 3 rd mode Light line

18. Cell # 13 Avoided crossing Uncoupled 2 nd mode Uncoupled 1 st mode Uncoupled manifold mode Coupled 3 rd mode Light line

19. Cell # 24 Avoided crossing Uncoupled 2 nd mode Uncoupled 1 st mode Uncoupled manifold mode Coupled 3 rd mode Light line

20. f0 fx fpi fsyn Red=f0 Blue=fpi Red dashed=fsyn Black= fx

21. Spectral function 96 cells 4-fold interleaving 192 cells 8-fold interleaving 24 cells No interleaving 48cells 2-fold interleaving

22. 96 cells 4-fold interleaving 192 cells 8-fold interleaving 24 cells No interleaving 48cells 2-fold interleaving ∆fmin = 65 MHz ∆tmax =15.38 ns ∆s = 4.61 m ∆fmin = 32.5 MHz ∆tmax =30.76 ns ∆s = 9.22 m ∆fmin = 16.25 MHz ∆tmax = 61.52 ns ∆s = 18.46 m ∆fmin = 8.12 MHz ∆tmax =123 ns ∆s = 36.92 m

23. Efficiency calculations For CLIC_G structure /λ=0.11, considering the beam dynamics constraint bunch population is 3.72 x 10^9 particles per bunch and the heavy damping can allow an inter bunch spacing as compact as ~0.5 ns. This leads to about 1 A beam current and rf –to- beam efficiency of ~28%. For CLIC_DDS structure (2.3 GHz) /λ=0.126, and has an advantage of populating bunches up to 4.5x10^9 particles but a moderate Q~500 will require an inter bunch spacing of 8 cycles (~ 0.67 ns). Though the bunch spacing is increased in CLIC_DDS, the beam current is compensated by increasing the bunch population and hence the rf-to-beam efficiency of the structure is not affected alarmingly.

24. Corrected formula for effective pulse length [1] Unloaded [1] A. Grudiev, CLIC-ACE, JAN 08 Allowed limit = 260 MV/m Allowed limit = 56 K

25. ParametersCLIC_G (Optimised) [1,2] CLIC_DDS (Non- optimised) Bunch space (rf cycles/ns)6/0.58/0.67 Limit on wake (V/pC/mm/m)7.15.6 Number of bunches312 Bunch population (10 9 )3.724.5 Pulse length (ns)240.8271 Fill time (ns)62.940 Pin (MW)63.874.5 Esur max. (MV/m)245249 Pulse temperature rise (K)53 Rf-beam-eff.27.724.3 [1] A. Grudiev, CLIC-ACE, JAN 08 [2] CLIC Note 764

26. 192 cell First 12 Q’s