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

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 frequenciesConsidering the moderate damping Q~500*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.

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 / and 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

Overview of present WDS structure*Lowest dipole band: f ~ 1GHz Q~ 10Ref: A. Grudiev, W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

StructureCLIC_GFrequency (GHz)12Avg. Iris radius/wavelength /0.11Input / Output iris radii (mm)3.15, 2.35Input / Output iris thickness (mm)1.67, 1.0Group velocity (% c)1.66, 0.83No. of cells per cavity24Bunch separation (rf cycles)6No. of bunches in a train312

A 3.3 GHz structureBlack: UncoupledRed: coupledSolid curves: First dipoleDashed curves: second dipoleRed: UncoupledBlue: CoupledRed: UncoupledBlue: CoupledWt(0)=110 V/pc/mm/mWt1~ 2 V/pc/mm/m

Comparison between uncoupled and coupled calculations: 8 fold structure3.3 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/mWhy not 3.3 GHz structure?

Cell parameters of a modified CLIC_G structure: Gaussian distributionUncoupled values:/=0.11f = 0.82 GHzf = 3 i.e.(=0.27 GHz)f/favg= 4.5 %*

Cella (mm)b (mm)t (mm)Vg/c (%)f1 (GHz)13.159.91.671.6317.4572.979.861.51.4217.64132.759.791.341.217.89192.549.751.181.018.1242.359.711.00.8618.27

Modified CLIC_G structureUncoupledUncoupledCoupledCoupledQ = 500Q = 500UndampedUndamped*Envelope Wake-fieldAmplitude Wake-field

Cell parameters of seven cells of CLIC_ZC structure having Gaussian distribution Uncoupled values:/=0.102f = 0.83 GHzf = 3f/favg= 4.56%a1=160m and a24= 220m. 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%.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 #a (mm)b (mm)t (mm)Vg/c (%)f1 (GHz)12.999.881.61.4917.5742.849.831.41.3817.7282.729.801.31.2917.85122.619.781.21.1817.96162.519.751.11.0618.07202.379.730.960.9818.2242.139.680.70.8318.4

CLIC_ZC structureCoupledUncoupledUndampedQ = 500Q = 500*Envelope Wake-fieldAmplitude Wake-field

A typical geometry : cell # 1r2hr1h1brcaa+a1a1a2L

E-field in a CLIC_DDS single cell with quarter symmetryManifoldCoupling slotCell modeManifold mode phase/2 = 17.41 GHz0 phase/2 = 14.37 GHz

Uncoupled (designed) distribution of Kdn/df for a four fold interleaved structureIn 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.

Spectral functionAs 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 structureModal QsMean Q

Non-interleaved structureNon-interleaved structureInterleaved structureInterleaved structureEnvelope wakefield of the present CLIC_DDS structure: Q~500Envelope wakefield with an artificially imposed Q = 300

Cell # 1Iris radius = 4.0 mmIris thickness = 4.0 mm , ellipticity = 1Q = 4771R/Q = 1,1640 /mvg/c = 2.13 %cCell # 24Iris radius = 2.3 mmIris thickness = 0.7 mm, ellipticity = 2Q = 6355R/Q = 20,090 /mvg/c = 0.9 %cA 2.3 GHz Damped-detuned structuref = 3.6 = 2.3 GHzf/fc =13.75 %/=0.126

Cell # 1Solid (dashed)curves coupled (uncoupled) modes

Cell # 13

Cell # 24

Spectral function96 cells4-fold interleaving192 cells8-fold interleaving24 cellsNo interleaving48cells2-fold interleaving

96 cells4-fold interleaving192 cells8-fold interleaving24 cellsNo interleaving48cells2-fold interleavingfmin = 65 MHztmax =15.38 nss = 4.61 mfmin = 32.5 MHztmax =30.76 nss = 9.22 mfmin = 16.25 MHztmax = 61.52 nss = 18.46 mfmin = 8.12 MHztmax =123 nss = 36.92 m

Efficiency calculationsFor CLIC_G structure /=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) /=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.

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

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

ParametersCLIC_G (Optimised) [1,2]CLIC_DDS(Non-optimised)Bunch space (rf cycles/ns)6/0.58/0.67Limit on wake (V/pC/mm/m)7.15.6Number of bunches312312Bunch population (109)3.724.5Pulse length (ns)240.8271Fill time (ns)62.940Pin (MW)63.874.5Esur max. (MV/m)245249Pulse temperature rise (K)5353

Rf-beam-eff.27.724.3

192 cellFirst 12 Qs