Optimisation of single bunch linacs for possible FEL upgrades

Alexej Grudiev, CERN6/02/2014

CLIC14 workshop

GdA_CLIC Workshop_January 28 - February 1, 2013 2

C8 C9

K1 K4K3K2 K6K5 K7 K8 K9 K10 K11 K12 K13

C1 C2 C3 C4 C5 C6 C7 S1S0BS0AG S2 S3 S4 S5 S6 S7

Kx

X-band

Linac layout and energy ugrading

Present machine layout• Ebeam up to 1.5 GeV• FEL-1 at 80-20 nm and FEL-2 at 20-4 nm• Seeded schemes• Long e-beam pulse (up to 700 fs), with “fresh

bunch technique”

~50 m available

40 m (80%)available for acceleration

Energy upgrade• Space available for acceleration 40 m• Accelerating gradient @12 GHz 60 MV/m• X-band linac energy gain 2.4 GeV • Injection energy .75 GeV• Linac output energy 3.15 GeV

FEL-1 & FEL-2beamlines

New FELbeamline l < 1 nm

Beam input energy≥ 750 MeV

For short bunch (< 100 fs)and low charge (< 100pC)

operation

Motivatio

n

from

Gerardo D’Auria

CLIC13

Aperture scaling and BBUGrowth rate of the BBU due to wakefield kick from head to tail:

04

0

0

40

0

''

40

'

**

114

0'

*

0

'2

ln

;)(

4)()(

4)(

114)(

1~;)(4)(

1

1

EE

GaeNcZ

eGzEzE

acZ

dssdW

W

eacZ

dssdW

esss

acZsW

kdzzEksWNe

Lz

zz

s

z

ss

ss

Lt

Present Upgrade Scaling factor γ’/γ

Lt [m] 40 40

<β> [m] ~10 ~10

E0 [GeV] 0.75 0.75

EL [GeV] 1.5 3.15 1/2

σz [fs] 700 100 1/7

eN [pC] 500 100 1/5

↓

a [mm] 5 5*0.35=1.75 ← 1/(2*7*5)

γ 0.02 0.02 Keep const

* Alex Chao, “Physics of collective beam instabilities in high energy accelerators”, 1993** Karl Bane, “Short-range Dipole Wakefields in Accelerating structures for the NLC”, SLAC-PUB-9663, 2003

Transient in a cavity -> pulse compression

e

el

leresp

inin

respinrad

inradrefradout

in

outinout

QQQQQ

Qt

QC

ttVV

CVV

VVVVV

VVtPP

0

0

0

2

2exp1

)exp()0(

)(

)0(

W

V

Pin

P0

Pout

IinVin

IrefVref

Vrad

Irad

·

Pin

Pout

Short-CircuitBoundaryCondition:

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

-1

-0.5

0

0.5

1

1.5

2

2.5

3

rev/2

V/V

in;

/2

Vin

Vout

Vrad

Vout

tptk

);;;;()( 00

0

epk

t

tttin

out QQttftVV k

pk

Analytical expression for the pulse shape

Effective shunt impedance of Acc. Structure + Pulse Compressor

s

tottot

sin

as

sg

ss

L

pfa

in

outin

gout

g

sf

z

g

RGV

PmLPVR

LQv

LtttzGdzV

tVVP

QR

vtP

QR

vtG

tttLtzvdzz

zgztGtzG

s

];/[ :impedanceshunt Effective

2);','('

)'()'()'(

');(;)'(

')(

);()]('[)',( :gradientdependent -Time

2

0

000

00

0

* i.e. A. Lunin, V. Yakovlev, A. Grudiev, PRST-AB 14, 052001, (2011) ** R. B. Neal, Journal of Applied Physics, V.29, pp. 1019-1024, (1958)

Effective shunt impedance of

TWAS **+

Acceleration in TWAS for transient pulse shape from PC *

=Effective shunt impedance of TWAS+PC **

Effective Shunt impedance in Const Impedance (CI) AS

0 0.5 1 1.5 2 2.5 3 3.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

s

G/G

0; <R

>/R

G/G0

<R>/RRs0/R

τs0

Rs/R

Rs/R

For Q = 8128; Q0 = 180000; Qe = 20000τs0 = 0.6078 => Rs0 /R = 3.3538 But in general it is function all 3 Qs: Q, Q0, Qe

0 0.5 1 1.5 2 2.5 3 3.5-0.5

0

0.5

1

1.5

2

2.5

3

3.5

s

G/G

0; <R

>/R

G/G0

G/G0

G/G0

G/G0

<R>/R Rs/R

Rs/R

τs0 = 1.2564 => Rs0 /R = 0.8145

No pulse compression With pulse compression

Const Gradient (CG) AS

If the last cell ohmic and diffraction losses are equal => minimum vg.For 12 GHz, Q=8000, lc = 10mm: τs0 = 0.96; min(vg/c) = 0.032 - very low vg at the end BUT CGAS can reach higher Rs/R than CIAS

Lowest group velocity limits the CGAS performance

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

s

G/G

0; <R

>/R

; vg(

0,L s)/v

g

G/G0

<R>/Rvg(0)/vgvg(Ls)/vg

R s

Rs/R

R s/R

No pulse compression

Q = 8128; Q0 = 180000; Qe = 20000τs0 = 0.5366 => Rs0 /R = 3.328 – function Q-factorsRoughly the same as for CIAS with pulse compression

vg_max = vg(1+0.5366); vg_min = vg(1-0.5366)Optimum vg variation is about factor 3.3

0 0.2 0.4 0.6 0.8 1 1.20

0.5

1

1.5

2

2.5

3

3.5

s

G/G

0; <R

>/R

; vg(

0,L s)/v

g

G/G0

G/G0

G/G0

G/G0

<R>/Rvg(0)/vgvg(Ls)/vg

Rs/R

R s/R

With pulse compression

Undamped cell parameters for dphi=150o

70007200

7400

7600

7800

8000

8200

8400

Q0

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.5 1

1.5 2

2.5

33.

54

vg/c [%]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

9101112

1314

R/Q [k /m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

1.8 2

2.22.42.62.83

Esmax/Ea

a/l

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

2.83

3.23.4

3.6

3.8

Hsmax/Ea [mA/V]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

300

400

500

600

700

800

Scmax/Ea

2 [A/V]

a/l

dphi = 150 deg

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.450.50.5

0.50.55

0.55

0.55

0.6

0.6

0.60.65

0.65

0.65

0.65

0.7

0.7

0.7

0.75

s0

Qe

Q6000 6500 7000 7500 8000 85001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3x 10

4

CIAS pulse compression optimumQ0 = 180000 – Q-factor of the pulse compressor cavity(s)tk = 1500 ns – klystron pulse length

Optimum attenuation: τs0 Averaged Shunt Impedance Rs0/R

Optimum value of Qe ~ const: ranges from 20000 for Q=6000 up to 21000 for Q=8000

Point from slide above

Point from slide above

2.82.93

33.1

3.1

3.2

3.2

3.2

3.3

3.3

3.3

3.3

3.3

3.4

3.4

3.4

3.4

3.4

3.5

3.5

3.5

3.5

3.6

3.6

3.6

3.7

3.7

<R>(s0)/R

Qe

Q6000 6500 7000 7500 8000 85001

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3x 10

4 Rs0/R

CIAS Effective Shunt Impedance: w/o and with pulse compression

5560

65

6570

70

7580

8590

95

<R>CImax [M /m]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4 230235 240

245250255260265270275

280

tpCImax [ns]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

240260280

300320340360380

<R>PCCImax [M /m]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4122 124

126128130132134

136

tpPCCImax [ns]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.420500 20600

207002080020900210002110021200

21300

21400

QePCCIopt

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

No pulse compression

With pulse compression

• As expected ~ 4 times higher effective shunt impedance with pulse compression• Optimum pulse length is ~ two times longer no pulse compression is used, still it

is much shorter than the klystron total pulse length

Rs0

Rs0

CIAS linac 40 m long, <G>=60MV/m : w/o and with PC

Total klystron power

Optimum structure length

Klystron power per structure

~# of structures per 0.8x50 MW klystron

2 -> 1/5

~20 -> ~2

16001800

2000

22002400

2600

PtCImin [MW]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.5

1

11.

52

2.5

33.

54

LsCIopt [m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

20

40 60 80 100

120

140

160

180

200

PinCIopt [MW/struct]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

400450

500

550600

PtPCCImin [MW]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.2 0.

4

0.6

0.8

11.

21.

41.

6

LsPCCIopt [m]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

2

4 6 8 10 12 14 1618

2022

24

PinPCCIopt [MW/struct]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

0

1

2

3

4

5

6

7

8

rev/2

P/P

in

Pin

Pout

CIAS high gradient related parameters: w/o and with PC

20

40 60 80 100

120

140

160

180

200

PinASCI [MW]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

180 200

220240260280300320

EsCImax [MV/m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

4

4

5

5

6

78910

ScCImax [W/m2]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

20

40 60 80 100

120

140

160

PinASPCCI [MW]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

160

180 200

220240260280300

EsPCCImax [MV/m]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

3

4

4

5

5

6789

ScPCCImax [W/m2]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

Typical Pulse lengthAS Pin(t=0) AS Esurf(z=0,t=0) AS Sc(z=0,t=0)

Flat pulse: 230-290 nsAbove the HG limits for larger apertures

Peaked pulse:122-136 ns60-70 ns

Assamption:Effective pulse length for breakdowns is ~ half of the compressed pulseÞ Breakdown limits are very close for large a/λ and thin irisesA dedicated BDR measurements are needed for compressed pulse shape

CIAS with PC: max. Lstruct < 1m20

40 60 80 100

120

140

160

180

200

PinASCI [MW]

d/h

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

180 200

220

240

260280

300320

EsCImax [MV/m]

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

4

4

5

5

6

78910

ScCImax [W/m2]

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

20

30 40 50 60 70 80 90 100

110

PinASPCCI [MW]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

160

170

180190

200210220230240250260

EsPCCImax [MV/m]

a/l0.12 0.14 0.16 0.18

0.1

0.15

0.2

0.25

0.3

0.35

0.4

33.

5 4

4

4.5 4.5

5

5

5.56

ScPCCImax [W/m2]

a/l0.12 0.14 0.16 0.18

0.1

0.15

0.2

0.25

0.3

0.35

0.4

5560

65

6570

70

7580

8590

95

<R>CImax [M /m]

d/h

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4 230235 240

245250255260265

270

275280

tpCImax [ns]

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

240

260

280

300320

340360

380

<R>PCCImax [M /m]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.15

0.2

0.25

0.3

0.35

0.4

8090

10011

0120

130

tpPCCImax [ns]

a/l0.12 0.14 0.16 0.18

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1800

018

500

1900

019

500

2000

020

500

20500

21000

QePCCIopt

a/l0.12 0.14 0.16 0.18

0.1

0.15

0.2

0.25

0.3

0.35

0.4

For high vg cornerShorter tpLower Qe

More PtotalLess Pin/klyst.

Lower field and power quantities

2000

2500

3000

3500

PtCImin [MW]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1

LsCIopt [m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

20

30 4050 60

70 80

90

PinCIopt [MW/struct]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

400450

500 550

600

PtPCCImin [MW]

a/l

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

LsPCCIopt [m]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

2

4 6 8 10 12 14

16

PinPCCIopt [MW/struct]

a/l0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

Rs0

CIAS and CGAS with PC, different RF phase advance, no constraints

0.12 0.14 0.16 0.180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

d/h,

Pt[G

W],

Ls[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCIAS

0.12 0.14 0.16 0.180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

d/h,

Pt[G

W],

Ls[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCGAS

d/h, 120o

Pt, 120o

Ls, 120o

Sc, 120o

d/h, 135o

Pt, 135o

Ls, 135o

Sc, 135o

d/h, 150o

Pt, 150o

Ls, 150o

Sc, 150o

CLIC_G_undamped: τs=0.31 < τs0=0.54; Ls=0.25m; Qe=15700; Pt = 400MWH75 : τs=0.50 ~ τs0=0.54; Ls=0.75m; Qe=20200; Pt = 613MW

CIAS and CGAS with PC, different RF phase advance, Ls < 1m

0.12 0.14 0.16 0.180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

d/h,

Pt[G

W],

Ls[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCIAS

0.12 0.14 0.16 0.180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

d/h,

Pt[G

W],

Ls[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCGAS

d/h, 120o

Pt, 120o

Ls, 120o

Sc, 120o

d/h, 135o

Pt, 135o

Ls, 135o

Sc, 135o

d/h, 150o

Pt, 150o

Ls, 150o

Sc, 150o

Small aperture linac, 2.4 GeV, 40mRF phase advance 2π/3a/lambda 0.118d/h 0.1Pt 322 MWLs 0.833 m# klystrons 8# structures 8 x 6 = 48a 2.95 mmd 0.833 mmvg/c 2.22 %tp 125 nsQe 20700

Constant Impedance Accelerating Structure with input power coupler only

P CRF load

Klystron

Pulse compressor

Hybrid

Middle aperture linac, 2.4 GeV, 40m

RF phase advance

2π/3 3π/4

a/lambda 0.145 0.145d/h 0.1313 0.1Pt 401 MW 401 MWLs 1 m 1 m# klystrons 10 10# structures 10 x 4 = 40 10 x 4 = 40a 3.62 mm 3.62 mmd 1.09 mm 0.937 mmvg/c 3.75 % 3.29%tp 90 ns 102 nsQe 18000 19000

Constant Impedance Accelerating Structure with input power coupler only

P CRF load

Klystron

Pulse compressor

Hybrid

Large aperture linac, 2.4 GeV, 40mRF phase advance 5π/6a/lambda 0.195d/h 0.183Pt 602 MWLs 1.333 m# klystrons 15# structures 15 x 2 = 30a 4.87 mmd 1.90mmvg/c 4.425 %tp 101 nsQe 18500

Constant Impedance Accelerating Structure with input power coupler only

P CRF load

Klystron

Pulse compressor

Hybrid

FERMI energy upgrade• An analytical expression for effective shunt impedance of

the CI and CG AS without and with pulse compression have been derived.

• Maximizing effective shunt impedance for a given average aperture gives the optimum AS+PC design of a single bunch linac

• Different constraints have been applied to find practical solutions for a FERMI energy upgrade based on the X-band 2.4 GeV, 60 MV/m linac

• Closer look together with beam dynamics experts is necessary to chose the right structure

Motivations from PSI

X-band Energy Vernier for ATHOSParameters specs:Required energy gain: dE = +-0.4 GeVTotal length available for acceleration: Lt = 16 mIf: the aim to introduce the same amount of Longitudinal Wake (W_L) as in C-band Linac3: W_L3Then: Since W_L~L/a^2: <a_X> = <a_C>/sqrt(L3_C/Lt)=6.44mm/sqrt(104m/16m)=2.53mm => <a_X>/λ=0.101 Total power from the klystrons at 1.5us: Ptot is significantly less then on can get from one XL5 and we are far from breakdown limit. => higher dE is possible even with one XL5. For example, for 0.5 m long CIAS: 40MW => 0.53GeV or 2x40MW => 0.76GeV

0.09 0.1 0.11 0.12 0.13 0.14 0.150

0.05

0.1

0.15

0.2

0.25

0.3

0.35

d/h,

Pt[G

W]*

10, L

s0[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCIAS: 12GHz, 0.4GeV, 16m

0.09 0.1 0.11 0.12 0.13 0.14 0.150

0.05

0.1

0.15

0.2

0.25

0.3

0.35

d/h,

Pt[G

W]*

10, L

s0[m

]/10,

Sc[

W/

m2 ]/1

0

a/l

PCCGAS: 12GHz, 0.4GeV, 16m

d/h, 120o

Pt, 120o

Ls0, 120o

Sc, 120o

d/h, 135o

Pt, 135o

Ls0, 135o

Sc, 135o

d/h, 150o

Pt, 150o

Ls0, 150o

Sc, 150o

a/λ=0.10298% of W_L3L_s = 0.5m 32 CI Acc. Str.Ptot = 22MW+ WG loss + op. margin

a/λ=0.12961% of W_L3L_s = 1m 16 CI Acc. Str.Ptot = 24MW+ WG loss + op. margin

Const Gradient (CG) AS require the same power

Const Impedance (CI) AS have a bit higher EM fields and Sc at the input cell

More motivations from PSI

ARAMIS energy upgrade.• It is probably unreasonable to take 0.5 m CIAS from the previous slide since it is too

short and aperture is too small (there is already enough W_L in ARAMIS line)• Taking 1m long CIAS from the previous slide: 24m long X-linac with 3 XL5s (3x40MW)

can provide energy increase: dE = 1.1GeV. In this case, we may come close to the BDR limit of 4MW/mm^2 (BDR~1e-7) so we may start to see some breakdowns at this levels !

• The above 1m long CIAS is rather close to a potential Fermi linac energy upgrade structure (middle aperture). It probably can be the same structure for both projects.

• A different structure (i.e. larger aperture) is maybe a better choice. More refined specs are needed to make optimized design.