INVESITGATION OF AN ALTERNATE MEANS OF WAKEFIELD SUPPRESSION IN CLIC MAIN LINACS

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

2. Wakefield suppression in CLIC main linacs 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. 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

3. Constraints RF breakdown constraint 1) 2) Pulsed surface heating 3) Cost factor • Beam dynamics constraints • For a given structure, no. of particles per bunch N is decided by the <a>/λ and Δa/<a> • 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 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 Red: Uncoupled Blue: Coupled Black: Uncoupled Red: coupled Solid curves: First dipole Dashed curves: second dipole Red: Uncoupled Blue: Coupled Wt(0)=110 V/pc/mm/m Wt1~ 2 V/pc/mm/m

6. Comparison between uncoupled and coupled calculations: 8 fold structure 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? 3.3 GHz structure does satisfies beam dynamics constraints but does not satisfies RF breakdown constraints.

7. Cell parameters of a modified CLIC_G structure: Gaussian distribution Uncoupled values: <a>/λ=0.11 ∆f = 0.82 GHz ∆f = 3σ i.e.(σ=0.27 GHz) ∆f/favg= 4.5 %

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

9. 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). Cell parameters of seven cells of CLIC_ZC structure having Gaussian distribution Uncoupled values: <a>/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 (Wmax=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%.

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

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

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

13. Uncoupled (designed) distribution of Kdn/dffor a four fold interleaved structure An erf distribution of the cell frequencies (lowest dipole) with cell number is employed. Kdn/df 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. dn/df Mode separation

14. Spectral function Non- interleaved structure 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. Interleaved structure Modal Qs The modal Qs are calculated using Lorentzian fits to the spectral function. Mean Q

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

16. Cell # 1 A 2.3 GHz Damped-detuned structure Cell # 24 • 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 • 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 ∆f = 3.6 σ = 2.3 GHz ∆f/fc =13.75 % <a>/λ=0.126

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

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

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

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

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

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

23. Efficiency calculations For CLIC_G structure <a>/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) <a>/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. Unloaded Unloaded Allowed limit = 260 MV/m Allowed limit = 56 K Corrected formula for effective pulse length [1] [1] A. Grudiev, CLIC-ACE, JAN 08

25. [1] A. Grudiev, CLIC-ACE, JAN 08 [2] CLIC Note 764

26. 192 cell First 12 Q’s