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

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 1/12/20082 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. 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

Constraints RF 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). 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 Ref: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

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 1/12/ th 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

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. 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December Input required: Synchronous frequencies of end cells (fi) Width of Gaussian distribution(σ) Kick factor (K)

Dispersion curves for 3 cells First cell a =4.95 mm Mid cell a =3.95 mm Last cell a= 2.15 mm TE TM TE TM TE 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Comparison between uncoupled and coupled calculations 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 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

Comparison between uncoupled and coupled calculations: 8 fold structure 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December GHz structure does satisfies beam dynamics constraints but does not satisfies RF constraints. In this case: 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?

Cella (mm)b (mm)t (mm)Vg/c (%)f1 (GHz) 1st Ref Ref Ref th 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 % 91/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Modified CLIC_G structure Uncoupled Coupled Q = 500 Undamped 10 Envelope Wake-field Amplitude Wake-field 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Cell #a (mm)b (mm)t (mm)Vg/c (%)f1 (GHz) 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). 111/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

CLIC_ZC structure Coupled Uncoupled Undamped Q = Envelope Wake-field Amplitude Wake-field 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Interleaved cells & S RMS Q = cells Q = cells 13 1/12/ th 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

Beam dynamics simulation: 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 PLACET Beam is injected with realistic offsets from the electrical centre of the cavity. An injection offset of a σ y results in ~ 70% emittance dilution at the nominal bunch spacing. Injection offset Red: σ y Black: 3σ y /4 Blue: σ y /2 Green: σ y /4 8 fold interleaved structure Q=500

CLIC_ZC structure #ParametersZC1ZC2(initial)Unit 1 /λ IP/OP iris thickness1.6 / 0.7 mm 3IP / OP iris radii2.99 / /2.13mm 4IP / OP group velocity1.49 / /.83mm 5First / Last cell Q06366 / / First / Last cell Shunt impedance107 / /138MΏ /m 7Filling time ns 8IP Power (peak)4847MW 9RF-to-beam efficiency2928.8% 10Bunch population3.0X X Esur (max)275221MV/m 12Eacc (avg)100 MV/m 13∆T max1514.0K MW(ns)^1/3/mm 15Luminosity (in1%)9.6X X10 33 m -2 16FOM9.28.8a.u. (% /10 9 ) 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008

Fundamental mode properties: CLIC_ZC 1/12/ 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

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). 171/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 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.

Thank you 1/12/ th ICFA Workshop under the sponsorship of the ICFA BD panel, X-Band RF structure and beam dynamics workshop, Cockcroft Institute, 1st – 4th December 2008 We have benefited from valuable discussions with W. Wuensch and A. Grudiev regarding the recent structures and with D. Schulte, B. Dalenaand A. Latina on the beam dynamics code PLACET. Acknowledgements