INVESITGATION OF AN ALTERNATE INVESITGATION OF AN ALTERNATE MEANS OF WAKEFIELD MEANS OF WAKEFIELD

SUPPRESSION IN CLIC MAIN LINACSSUPPRESSION IN CLIC MAIN LINACS

CLIC_DDSCLIC_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 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.

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 <a>/λ and Δa/<a>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).

mMVEsur /260max

KT 56max

mmnsMWCP inpin33 18

N

XmXmmpCVWt

9

1

104///667.6

Ref: A. Grudiev and W. Wuensch, Design of an x-band accelerating structure for the CLIC main linacs, LINAC08

Overview of present WDS structure

Structure CLIC_G

Frequency (GHz) 12

Avg. Iris radius/wavelength <a>/λ 0.11

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 cavity 24

Bunch separation (rf cycles) 6

No. of bunches in a train 312

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

A 3.3 GHz structure

Black: UncoupledRed: coupled

Solid curves: First dipoleDashed curves: second dipoleRed: UncoupledBlue: Coupled

Red: UncoupledBlue: Coupled

Wt(0)=110 V/pc/mm/mWt1~ 2 V/pc/mm/m

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?

Cell a (mm) b (mm) t (mm) Vg/c (%) f1 (GHz)

1 3.15 9.9 1.67 1.63 17.45

7 2.97 9.86 1.5 1.42 17.64

13 2.75 9.79 1.34 1.2 17.89

19 2.54 9.75 1.18 1.0 18.1

24 2.35 9.71 1.0 0.86 18.27

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 %

7

Modified CLIC_G structure

UncoupledUncoupled

Coupled

Coupled

Q = 500

Q = 500

Undamped Undamped

8

Envelope Wake-fieldAmplitude Wake-field

Cell # a (mm) b (mm) t (mm) Vg/c (%) f1 (GHz)

1 2.99 9.88 1.6 1.49 17.57

4 2.84 9.83 1.4 1.38 17.72

8 2.72 9.80 1.3 1.29 17.85

12 2.61 9.78 1.2 1.18 17.96

16 2.51 9.75 1.1 1.06 18.07

20 2.37 9.73 0.96 0.98 18.2

24 2.13 9.68 0.7 0.83 18.4

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%.

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).

CLIC_ZC structure

Coupled

UncoupledUndamped

Q = 500

Q = 500

10

Envelope Wake-field

Amplitude Wake-field

A typical geometry : cell # 1

r2

h

r1

h1b

rc

a

a+a1

a1

a2

L

E-field in a CLIC_DDS single cell with quarter symmetry

Manifold

Coupling slotCell mode

Manifold mode

π phaseω/2π = 17.41 GHz

0 phaseω/2π = 14.37 GHz

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.

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 structure

Non- interleaved structure

Modal Qs

Mean Q

Non-interleaved structure

Non-interleaved structure

Interleaved structure

Interleaved structure

Envelope wakefield of the present CLIC_DDS structure: Q~500

Envelope wakefield with an artificially imposed Q = 300

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 %<a>/λ=0.126

Cell # 1

Solid (dashed)curves coupled (uncoupled) modes

Avoided crossing

Uncoupled 2nd mode

Uncoupled 1st mode

Uncoupled manifold mode

Coupled 3rd mode

Light line

Cell # 13

Avoided crossing

Uncoupled 2nd mode

Uncoupled 1st mode

Uncoupled manifold mode

Coupled 3rd mode

Light line

Cell # 24

Avoided crossing

Uncoupled 2nd mode

Uncoupled 1st mode

Uncoupled manifold mode

Coupled 3rd mode

Light line

f0

fx

fpi

fsynRed=f0Blue=fpiRed dashed=fsynBlack= fx

Spectral function

96 cells4-fold interleaving

192 cells8-fold interleaving

24 cellsNo interleaving

48cells2-fold interleaving

96 cells4-fold interleaving

192 cells8-fold interleaving

24 cellsNo interleaving

48cells2-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

Efficiency calculations

A 1.19

GHz 11.9942

6101.61072.3

I19-9

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).

A 1.13

GHz 11.9942

8101.6104.75

I19-9

V/pc/mm/m 1.71072.3150

10410010W

9

9limitT

V/pc/mm/m 5.6104.75150

10410010W

9

9limitT

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.

A 31.1I @ 23.4%

tLEaccIη b

CLIC_DDS

fillrbin tttPypulseenerg

beamenergy

p

rfillrfillbp

τT

ns 2462

pp1t

2

pp1ttttτ

0.5637.77

21.12

P

Ppp

.5MW47P

ULout

Lout

in

te)(approxima ns 23t

ns 40t

ns 208.111.9942

3128t

r

fill

b

Corrected formula for effective pulse length [1]

UnloadedUnloaded

1.19AI @ 27.7%ηCLIC_G

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

Allowed limit = 260 MV/m

Allowed limit = 56 K

Parameters CLIC_G (Optimised)

[1,2]

CLIC_DDS(Non-

optimised)

Bunch space (rf cycles/ns) 6/0.5 8/0.67

Limit on wake (V/pC/mm/m) 7.1 5.6

Number of bunches 312 312

Bunch population (109) 3.72 4.5

Pulse length (ns) 240.8 271

Fill time (ns) 62.9 40

Pin (MW) 63.8 74.5

Esur max. (MV/m) 245 249

Pulse temperature rise (K) 53 53

Rf-beam-eff. 27.7 24.3

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

192 cell

First 12 Q’s