Wakefield suppression in the CLIC main accelerating structures

1. Wakefield suppression in the CLIC main accelerating structures Vasim Khan & Roger Jones

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 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 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. Constraints RF 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 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

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 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

5. A detuned structure In order to keep the beam current same as that of CLIC_G structure and in turn the efficiency ,we assume bunch spacing of 6 cycles (appr. 0.5 ns) . For a moderate Q it naturally requires a structure of large bandwidth to suppress the wakefield sufficiently. It is observed that for a Gaussian distribution of cell parameters and a bandwidth of 3.3 GHz wakefield is sufficiently suppressed. Input required: Synchronous frequencies of end cells (fi) Width of Gaussian distribution(σ) Kick factor (K) 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

6. Dispersion curves for 3 cells Mid cell a =3.95 mm First cell a =4.95 mm TE TE TM TM Last cell a= 2.15 mm TE TM 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

7. Comparison between uncoupled and coupled calculations 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 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. 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 constraints. In this case: 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 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 % 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. Modified CLIC_G structure Coupled Uncoupled Coupled Uncoupled Undamped Undamped Amplitude Wake-field Envelope Wake-field Q = 500 Q = 500 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

11. 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 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 (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%. 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

12. CLIC_ZC structure Coupled Uncoupled Coupled Uncoupled Undamped Undamped Q = 500 Q = 500 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

13. Interleaved cells & SRMS SRMS= 33 V/pC/mm/m SRMS= 7 V/pC/mm/m Q = 500 24 cells Q = 500 192 cells SRMS>1 BBU is likely to occur 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

14. Beam dynamics simulation: 8 fold interleaved structure Q=500 PLACET Beam is injected with realistic offsets from the electrical centre of the cavity. An injection offset of a σy results in ~ 70% emittance dilution at the nominal bunch spacing. Injection offset Red: σy Black: 3σy/4 Blue: σy/2 Green: σy/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

15. CLIC_ZC structure 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

16. Fundamental mode properties: CLIC_ZC Bsur max (A/mX10^3) Esur max (MV/m) Eacc (MV/m) Pin (MW) ∆T (K) Dashed curves: Unloaded conditions Solid curves: Beam loaded conditions 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

17. Summary • With a Gaussian detuning of cell parameters and Q=500, wake-field envelope is damped but it is not sufficiently damped hence we look in to the actual wake felt by the bunch i.e. wake amplitude. • Varying the elasticity of the cells surface fields can be minimise to satisfy RF constraints: (Esur max in particular). • Next ? • We are looking in to realistic tolerances to satisfy the zero crossing • condition for a Q~500. • Introduce damping wave-guide (manifold) to the present • structure. • A bandwidth of ~2GHz with a damping Q of ~ 200, in this case we expect • wake-field to suppress sufficiently for a bunch spacing of 6 to 8 cycles to • satisfy beam dynamics constraint but surface fields will be an issue to take • care of. 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

18. Acknowledgements Thank you We have benefited from valuable discussions with W. Wuenschand A. Grudievregarding the recent structures and with D. Schulte, B. DalenaandA. Latina on the beam dynamics code PLACET. 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