Optimisation of single bunch linac for FERMI upgrade

Optimisation of single bunch linac for FERMI upgrade

Alexej Grudiev, CERN5/06/2013

HG2013, ICTP Trieste, Italy

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

Motiv

ation

from

Gerard

o D’A

uria

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

E

E

Ga

eNcZ

eGzEzE

a

cZ

ds

sdWW

ea

cZ

ds

sdW

es

ss

a

cZsW

kdzzEk

sWNe

Lz

zz

s

z

s

s

s

s

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

QQ

QQQ

Q

t

QC

ttVV

CVV

VVVVV

V

VtPP

0

0

0

2

2exp

1

)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 QQttftV

Vk

pk

Analytical expression for the pulse shape

Pulse compression: example

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

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

Example at 12 GHz:

Q0 = 180000; Qe = 20000tk = 1500 ns klystron pulse lengthtp = 100 ns compressed pulse length

Average power gain == average power in compressed pulse / input power = 5.6 Average power efficiency = = compressed pulse energy/ input pulse energy = 34.7 %

Effective shunt impedance of Acc. Structure + Pulse Compressor

s

tottot

sin

as

sg

ss

L

pfa

in

outin

gout

g

sf

z

g

R

GVPm

LP

VR

LQv

LtttzGdzV

tV

VP

Q

R

vtP

Q

R

vtG

tttLtzv

dzz

zgztGtzG

s

];/[ :**impedanceshunt Effective

2);','('

)'()'()'(

');(;)'(

')(

);()]('[)',( :gradient*dependent -Time

2

0

000

0

0

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 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

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

91011

12

1314

R/Q [k /m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

1.82

2.2

2.42.62.83

Esmax/E

a

a/

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/E

a [mA/V]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

300

400

500

600

700

800

Scmax/E

a2 [A/V]

a/

dphi = 150 deg

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.450.5

0.5

0.50.55

0.55

0.55

0.6

0.6

0.6

0.65

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


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

245250255260265270

275280

tpCImax

[ns]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

24026

0280

300320340360380

<R>PCCImax

[M /m]

a/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4122 124

126128

130

132

134

136

tpPCCImax

[ns]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.420500

2060020700208002090021000

21100

21200

21300

21400

QePCCIopt

a/0.12 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.

5

22.

53

3.5

4

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

550

600

PtPCCImin

[MW]

a/

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/0.12 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/0.12 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

/2P

/Pin

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

220

240

260280300320

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/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

160

180 200

220

240260280300

EsPCCImax

[MV/m]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

3

4

4

5

5

6789

ScPCCImax

[W/m2]

a/0.12 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

260

280300

320

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/

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/0.12 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/0.12 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

245

250

255

260

265

270

275

280

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/

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

012

0

130

tpPCCImax

[ns]

a/0.12 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/0.12 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 55

060

0PtPCCI

min [MW]

a/

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/0.12 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/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

Rs0

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

,Ls)/

vg

G/G0

<R>/R

vg(0)/vg

vg(Ls)/vg

R s

Rs/R

R s/R


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

,Ls)/

vg

G/G

0

G/G0

G/G0

G/G0

<R>/R

vg(0)/vg

vg(Ls)/vg

Rs/R

R s/R


3.23.

3

3.3

3.3

3.4

3.4

3.4

3.5

3.5

3.5

3.6

3.6

3.63.7

3.7

3.7

<R>(s0

)/R

Qe

Q6000 6500 7000 7500 8000 8500

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5x 10

4

0.480.5

0.5

0.52

0.52

0.54

0.54

0.54

0.56

0.56

0.56

0.56

0.58

0.58

0.58

0.6

0.6

0.62

s0

Qe

Q6000 6500 7000 7500 8000 8500

1.5

1.6

1.7

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5x 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 21000 for Q=6000 up to 22000 for Q=8000



Rs0/R

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



• CGAS has higher Rs compared to CIAS if no pulse compression is used and the same Rs with pulse compression

• Optimum pulse length is ~ 4.5 times longer if no pulse compression is used, still it is significantly shorter than the klystron total pulse length

70

80

80

90

100

110

<R>CGmax

[M /m]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

300

350

400

450

450

500

550

600

tpCGmax

[ns]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.0310.0320.0330.0340.0350.0360.037

vgCGmim

/c [%]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

24026

0280

300320

340360380

<R>PCCImax

[M /m]

a/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4124

126

128

130

132

134

136

138

tpPCCImax

[ns]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

0.2

0.4

0.6

0.8

1

11.

21.

41.

61.

82

vgPCCGmim

/c [%]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

Rs0

Rs0

CGAS 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 -> 1/3

~20 -> ~2

Optimum structure length and input power per structure are very similar to the CIAS

1400

1600

1800

1800

20002200

PtCGmin

[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

3

LsCGopt

[m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

20 40 60 8010

012

0

PinCGopt

[MW/struct]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

400450

500

550

600

PtPCCGmin

[MW]

a/

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.

4

LsPCCGopt

[m]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

2

4 6 8 10 12 1416

1820

22

PinPCCGopt

[MW/struct]

a/0.12 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

/2P

/Pin

Pin

Pout

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

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

Flat pulse: 250-650 nsAbove the HG limits for larger apertures

Peaked pulse:122-138 ns60-70 ns

• Due to much shorter compressed pulse the CGAS with PC is safer in terms of high gradient related parameters than w/o PC

• Also due to CG profile it is significantly safer than CIAS with PC

PinASCG [MW]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

EsCGmax

[MV/m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

ScCGmax

[W/m2]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

PinASPCCG [MW]

a/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

EsPCCGmax

[MV/m]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

ScPCCGmax

[W/m2]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

CGAS with PC: max. Lstruct < 1mFor high vg corner

Shorter tpHigher vg_min

More PtotalLess Pin/klyst.

A little bit lower field and power quantities

405060

7080

80

90

100

110

<R>CGmax

[M /m]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

100

150

200

25030

0

300

350

350 40

0

400

450

450

tpCGmax

[ns]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

0.5

11.

52

2.5

3

vgCGmim

/c [%]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

240

26028

0

300320

340360380

<R>PCCImax

[M /m]

a/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

809010

011012

0

130

130

tpPCCImax

[ns]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

0.5

1

11.

52

2.5

3

vgPCCGmim

/c [%]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

10

20 30 40 50 60 7080

90Pin

ASCG [MW]

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

100

110 120

130

140150160170180

EsCGmax

[MV/m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

1.5

2

2.53

ScCGmax

[W/m2]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

20

30 40 50 60 70 80 90 100

110

110

PinASPCCG [MW]

a/

d/h

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

120

13014

0

150

160170180190200210220

EsPCCGmax

[MV/m]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

2

2

2.5

3

3.54

ScPCCGmax

[W/m2]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

1500

2000

2500

3000

PtCGmin

[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

LsCGopt

[m]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

10

20 30 40 50 60 7080

90

PinCGopt

[MW/struct]

0.12 0.14 0.16 0.180.1

0.2

0.3

0.4

400450

500

550

600

PtPCCGmin

[MW]

a/

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

LsPCCGopt

[m]

a/0.12 0.14 0.16 0.18

0.1

0.2

0.3

0.4

2

4 6 8 10 12 14

PinPCCGopt

[MW/struct]

a/0.12 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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

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


P CRF load

Klystron

Pulse compressor

Hybrid

Large aperture linac, 2.4 GeV, 40m

RF 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


P C

RF load

Klystron

Pulse compressor

Hybrid

Single- versus Double-rounded cells

~6%

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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

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[

GW

], L

s[m

]/10

, S

c[W

/m

2 ]/10

a/

PCCGAS

d/h, SingRR

Pt, SingRRLs, SingRR

Sc, SingRR

d/h, DoubRR

Pt, DoubRRLs, DoubRR

Sc, DoubRR

• By doing double rounded cells instead of single rounded cells Q-factor is increased by 6%

• The total linac power is reduced only by 3.7% (not 6%) because optimum is adapted to the Q

• No tuning will be possible

Conclusions

• 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

Documents

Optimisation of single bunch linac for FERMI upgrade