Injector Optimization for Simultaneous Operation with Different

Bunch Charges

Yauhen KotBD Meeting 23.04.2012

Contents• How it theoretically can work, technical constraints• WP for 20pC• WP for 100pC• Operation 20-100pC• WP for 250pC• Operation 100-250pC• WP for 500pC• Operation 250-500pC• WP for 1000pC• Operation 500-1000pC• Conclusions: operation with single bunch charge• Conclusions: simultaneous operation with two bunch charges• Simultaneous operation with two laser systems and single solenoid• Simultaneous operation with two laser systems and two solenoids

Operation with two different bunch charges within the same system.How can it theoretically work?

- The problem of the operation with two different bunch charges at the same time is a question whether it is possible to achieve the same optics functions at the first quadrupole for both charges- Generally bunch charge affects the optics functions similar optics for different charges at the same settings of the solenoid and laser can occur only in the exceptional cases.

Remarks…

Typical beta development over the laser spot size.(seen at the end of the ACC1)

0 20 40 60 80 100 120 140 160 180 2000

50

100

150

200

250

300

Beta for 20pC at MaxB(1)=0.2220 vs. XYrms

20pC 0.2220

100% transmission from the cathode

0 20 40 60 80 100 120 140 160 180 2000

0.050.1

0.150.2

0.250.3

0.350.4

0.450.5

Emittance for 20pC at MaxB(1)=0.2220 vs XYrms 20pC 0.2220

Emittance minimum

Beta minimum

Small beta for transmission under 100%Local maximum at the point of 100% transmissionShortly after the 100% transmission emittance minimumAnd much later the beta function minimum

For higher charges the whole curve shifts to the right

Operation with two different bunch charges within the same system.How can it theoreticaly work?

Operation within the same system but with two different charges is only possibleIf we “catch” the beta for higher charge on the falling arm and the other one on the rising arm

0 100 200 300 400 500 6000

20

40

60

80

100

120

20pC 0.2220 100pC 0.2220 250pC 0.2220500pC 0.2220 1nC 0.2220

The problem of the operation with two different bunch charges at the same time is a question whether it is possible to achievethe same optics functions at the first quadrupole for both chargesGenerally bunch charge affects the optics functions similar optics for different charges at the same settings of the solenoid and laser can occur only in the exceptional cases.

…and hope that alfas also coincide

Technical and Theoretical Constraints

- Max K1 of the quadrupoles in the injector < 10.0- Generally it is not guaranteed that a theoretical match is possible for any initial betas

Working points for 20pC.

Emittance Point of View

25 50 65 75 85 92 100 110 125 150

0,22

0,2205

0,221

0,2215

0,222

0,2225

0,223

0,2235

0,224

0,2245

2D Scan for 20pC. Emittance at I1.Q.A1.10,22 0,2205 0,221 0,2215 0,222 0,2225 0,2230,2235 0,224 0,2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

Tran

smiss

ion

belo

w 1

00%

25 50 65 75 85 92 100 110 125 150

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

2D Scan for 20pC. Matching Ability

Laser Beam Size rms, mm

Match possible

25 50 65 75 85 92 100 110 125 150

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

2D Scan for 20pC. Optics Stability0.2200 0.2205 0.2210 0.22150.2220 0.2225 0.2230 0.2235

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

MaxB(1) XYrms e Opt. sensitivity X

0.2216 67 0.0785 1.110

2D Scan for XFEL Injector. 20pC

Best Emittance

Comfortable Optics Conditions

100% transmission beginning at XY=40mmStable optics solutions with the emittance > 0,10 mm mrad

possibleOperation reasonable with XYrms between 50-125mmand MaxB(1) range of 0.2200-0.2245T Mismatch after the change of solenoid field by 0.0005T

2D Scan for XFEL Injector. 100pC

100 125 150 175 200 225 250 275 300

0,22

0,2205

0,221

0,2215

0,222

0,2225

0,223

0,2235

0,224

0,2245

Emittance at I1.Q.A1.10,22 0,2205 0,221 0,2215 0,222 0,22250,223 0,2235 0,224 0,2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

100 125 150 175 200 225 250 275 300

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

Optics Mismatch after Change of the Solenoid Field by 0.0005T

0.2200 0.2205 0.2210 0.2215 0.22200.2225 0.2230 0.2235 0.2240 0.2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

Stable optics match is possible

100 125 150 175 200 225 250 275 300

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

Matching Ability0.2200 0.2205 0.22100.2215 0.2220 0.2225

Laser Beam Size rms, mm

Possible to match with the current configuration

Emittance minimum

Working Point with respect to the emittance minimum at 0.2230 T x 125 mmBest emittance: 0,1716 mm mradStable optics solutions with the emittance > 0,24 possible100% transmission beginning at XY=75mmOperation reasonable with XYrms between 120-290mm and MaxB(1) range of 0.2205-0.2245T

MaxB(1) XYrms e X

0.2230 125 0.1716 1.310

Simultaneous Operation with 20pC and 100pC

Obviously no common areas simultaneous operation of the bunch of 20pC with the bunch charge over 100pC is not possible.The situation cannot be cured by means of the additional solenoid only. Another laser system is needed.

Match possible

Match possible

Charge 100% Transmission at XYrms, mm

XY operation window

MaxB1 operation window

Working Point for best e e_min, mm mrad

Xyrms, mm MaxB1, T

20 40 50-125 0.2200-0.2245 67 0.2216 0.0785

100 75 125-275 0.2205-0.2245 125 0.2230 0.1716

250 170 175-400 0.2210-0.2255 200 0.2235 0.2835

500 225 250-475 0.2225-0.2260 300 0.2235 0.4302

1000 365 365-600 0.2230-0.2265 450 0.2240 0.745

25 50 65 75 85 92 100 110 125 150

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

2D Scan for 20pC. Matching Ability

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

100 125 150 175 200 225 250 275 300

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

2D Scan for 100pC. Matching Ability

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

2D Scan for XFEL Injector. 250pC

150 175 200 225 250 275 300 325 350 375

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

Emittance at I1.Q.A1.10.2200 0.2205 0.2210 0.2215 0.22200.2225 0.2230 0.2235 0.2240 0.2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

150 175 200 225 250 275 300 325 350 375

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

Optics Stability0.2205 0.2210 0.2215 0.2220 0.2225 0.22300.2235 0.2240 0.2245 0.2250 0.2255

Laser beam size rms, mm

Sole

noid

fiel

d st

reng

th M

axB(

1), T

150 175 200 225 250 275 300 325 350 375

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

Matching Ability0.2200 0.2205 0.2210

Laser Beam Size rms, mm

Working Point with respect to the emittance minimum at 0.2235 T x 200 mmBest emittance: 0,2832 mm mradStable optics solutions with the emittance > 0,32 possibleOperation reasonable with XYrms above 170mmand MaxB(1) range of 0.2210-0.2255T

Transmission below 100%

MaxB(1) XYrms e X

0.2235 200 0.2832 1.3899

Simultaneous Operation with 100pC and 250pC

150 175 200 225 250 275 300 325 350 375

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

250pC. Matching Ability0.2200 0.2205 0.2210 0.22150.2220 0.2225 0.2230 0.22350.2240 0.2245 0.2250 0.2255

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

100 125 150 175 200 225 250 275 300

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

100pC. Matching Ability

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

150 175 200 225 250 275 300

0,222

0,2225

0,223

0,2235

0,224

0,2245

Optics mismatch by change of the bunch charge from 150 to 250pC

0,222 0,2225 0,223 0,2235 0,2240,2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth,

T

Playable range for both charges

Playable range for both charges

Operation with both charges simultaneously is imaginablefor MaxB(1)=0.2230 and 0.2235

Simultaneous Operation with 100pC and 250pC. MaxB(1)=0.2230 and 0.2235

100 150 200 250 300 350 4000

0.10.20.30.40.50.60.70.80.9

1em. 100pC em. 250pC

100 150 200 250 300 350 4000

102030405060708090

100beta 100pC beta 250pC

100 150 200 250 300 350 400

-5-4.5

-4-3.5

-3-2.5

-2-1.5

-1-0.5

0alfa 100pC alfa 250pC

100 150 200 250 300 350 4000

0.2

0.4

0.6

0.8

1

1.2em. 100pC em. 250pC

100 150 200 250 300 350 4000

20

40

60

80

100

120beta 100pC beta 250pC

100 150 200 250 300 350 400

-6

-5

-4

-3

-2

-1

0

alfa 100pC alfa 250pC

Both twiss functions coincide for both bunch charges at almost the same settings of the laser.

Combined working point atMaxB(1)=0.2235 XYrms=225

Combined working point is almost the same as the working point for 250pC

Generally: the emittance of the smaller bunch charge could be more effective reduced by means of the laser beam size. On the other hand it grows even faster for larger laser beam sizes

Operation of the both bunch charges (150 and 250pC) at the same settings of the laser and the solenoid field is possible.

In that case we get the best possible emittance and somehow unstable optics for 250pC on the one hand and very stable optics solution but blowed up emittance for 100pC.

MaxB(1)=0.2230 MaxB(1)=0.2235

Settings Emittance Optics SensitivityMaxB(1), T XYrms, mm e_250 e_100 X_250 X_100 X_250100

0.2230 200 0.2839 0.2939 1.3365 1.0307 1,57

0.2230 225 0.295 0.4088 1.3178 1.0034 1,385

0.2230 250 0.3088 0.5569 1.2824 1.0010 1,106

0.2230 275 0.3402 0.7151 1.208 1.0072 1,012

MaxB(1) XY e_250 e_100 X_250 X_100 X_250100

0.2235 200 0.2832 0.347 1.3899 1.0103 1.195

0.2235 225 0.2966 0.471 1.3145 1.0004 1.055

0.2235 250 0.3275 0.6176 1.2319 1.0041 1.078

0.2235 275 0.3859 0.7683 1.1395 1.0121 1.369

WP for Simultaneous Operation with 100pC and 250pC

200 210 220 230 240 250 260 270 2800

50

100

150

200

250

300

350

Emittance increase with respect to minimum 0.2230, 100 0.2230, 250

XYrms, mm

Emitt

ance

incr

ease

, %

200 210 220 230 240 250 260 270 2800

50

100

150

200

250

300

350

Emittance increase with respect to minimum0,2235, 100 0,2235, 250

XYrms, mm

Emitt

ance

incr

ease

, %

2D Scan for XFEL Injector. 500pC

250 275 300 325 350 375 400 425 450 475 500

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

0.2260

500pC. Emittance at I1.Q.A1.1 0.2220 0.2225 0.2230 0.22350.2240 0.2245 0.2250 0.2255

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

treng

th M

axB(

1), T

250 275 300 325 350 375 400 425 450 475 500

0,222

0,2225

0,223

0,2235

0,224

0,2245

0,225

0,2255

0,226

500pC. Optics Stability0,222 0,2225 0,223 0,2235 0,224 0,22450,225 0,2255 0,226

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

treng

th M

axB(

1), T

250 275 300 325 350 375 400 425 450 475 500

0,222

0,2225

0,223

0,2235

0,224

0,2245

0,225

0,2255

0,226

500pC. Matching Ability0,222 0,2225 0,2230,2235 0,224 0,2245

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

treng

th M

axB(

1), T

Emittance minimum

Working Point with respect to the emittance minimum at 0.2235 T x 300 mmBest emittance: 0,4302 mm mradStable optics solutions with the emittance > 0,60 mm mrad possibleOperation reasonable with XYrms between 250mm and 475mmand MaxB(1) range of 0.2225-0.2260T

500pC Emittance

Match possible, stable optics solution

No match possible

MaxB(1) XYrms e X

0.2235 300 0.4302 1.4363

Simultaneous Operation with 250pC and 500pC

150 175 200 225 250 275 300 325 350 375

0.2200

0.2205

0.2210

0.2215

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

250pC. Emittance at I1.Q.A1.10.2200 0.2205 0.2210 0.2215 0.2220 0.2225 0.22300.2235 0.2240 0.2245 0.2250 0.2255

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

tren

gth

Max

B(1)

, T

Playable range for both charges

250 275 300 325 350 375 400 425 450 475 500

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

0.2260

500pC. Emittance at I1.Q.A1.1 0.2220 0.2225 0.2230 0.2235 0.22400.2245 0.2250 0.2255 0.2260

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

treng

th M

axB(

1), T

Playable range for both charges

0.223 0.2235 0.224 0.2245 0.225 0.2255

250

275

300

325

350

375

250 275 300 325 350 375

Imaginable for MaxB(1)=0.2240 and 0.2235

Simultaneous Operation with 250pC and 500pC. MaxB(1)=0.2235 and 0.2240

100 150 200 250 300 350 400 450 5000

0.2

0.4

0.6

0.8

1

1.2

1.4

em. 250pC em. 500pC

100 150 200 250 300 350 400 450 50005

1015202530354045

beta 250pC beta 500pC

100 150 200 250 300 350 400 450 500

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0alfa 250pC alfa 500pC

100 150 200 250 300 350 400 450 5000

0.5

1

1.5

2

2.5

em. 250pC em. 500pC

100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

beta 250pC beta 500pC

100 150 200 250 300 350 400 450 500

-8

-7

-6

-5

-4

-3

-2

-1

0alfa 250pC alfa 500pC

MaxB(1)=0.2235

MaxB(1)=0.2240

Operation at MaxB(1)=0.2235 gives similar but not equal opticsOperation at MaxB(1)=0.2240 provides a long range of laser beam size (275 to 375mm) with almost equal optics for 250pC and 500pC.

MaxB(1) XY e_500 e_250 X_500 X_250 X_500250

0.2240 275 0.439 0.386 1.391 1.070 1.220

0.2240 300 0.430 0.482 1.379 1.029 1.228

0.2240 325 0.445 0.619 1.327 1.008 1.221

0.2240 350 0.470 0.801 1.257 1.001 1.160

0.2240 375 0.516 1.017 1.178 1.001 1.082

WP for Simultaneous Operation with 250pC and 500pC

Settings Emittance Optics Sensitivity

MaxB(1), T XYrms, mm e_500 e_250 X_500 X_250 X_500250

0.2235 275 0.472 0.468 1.391 1.070 1.236

0.2235 300 0.451 0.584 1.379 1.029 1.035

0.2235 325 0.470 0.738 1.327 1.008 1.001

0.2235 350 0.517 0.931 1.257 1.001 1.014

0.2235 375 0.592 1.155 1.178 1.001 1.056

250 270 290 310 330 350 370 3900

50

100

150

200

250

300

350

Emittance Change w.r. to minimum in %0.2235, 250 0.2235, 500

XYrms, mm

emitt

ance

chan

ge, %

250 270 290 310 330 350 370 3900

50

100

150

200

250

300

Emittance Change w.r. to minimum in %

0.2240, 250 0.2240, 500

XYrms, mm

emitt

ance

cha

nge,

%

2D Scan for XFEL Injector. 1000pC

350 375 400 425 450 475 500 525 550 575 600

0,223

0,2235

0,224

0,2245

0,225

0,2255

0,226

0,2265

0,227

Emittance at I1.Q.A1.10,223 0,2235 0,224 0,2245 0,2250,2255 0,226 0,2265 0,227

Laser Beam Size rms XY, mm

Sole

noid

Stre

ngth

Max

B(1)

, T

350 375 400 425 450 475 500 525 550 575 600

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

0.2260

0.2265

0.2270

Optics Stability0.2230 0.2235 0.2240 0.2245 0.22500.2255 0.2260 0.2265 0.2270

Laser Beam Size rms XY, mm

Sole

noid

Str

engt

h M

axB(

1), T

350 375 400 425 450 475 500 525 550 575 600

0,223

0,2235

0,224

0,2245

0,225

0,2255

0,226

0,2265

0,227

Matching Ability0,223 0,2235 0,2240,2245 0,225 0,2255

Laser Beam Size rms XY, mm

Sole

noid

Stre

ngth

Max

B(1)

, T

Emittance minimum

Emittance minimum is feasible but may have an unstable optics

Working point for the emittance minimum:

MaxB(1) XYrms e X

0.2240 450 0.745 1.452

100% transmission beginning at XY=365mmStable optics solutions with the emittance > 1,00 mm mrad

possibleOperation reasonable with XYrms between 365mm and 600mmand MaxB(1) range of 0.2230-0.2265T

Match possible, stable optics solution

No match possible

Simultaneous Operation with 500pC and 1000pC

0.223 0.2235 0.224 0.2245 0.225 0.2255 0.226

350

375

400

425

450

475

500

Optics Difference between 1nC and 500pC350 375 400 425 450 475 500

Solenoid Field Strength MaxB1, T

Lase

r Bea

m Si

ze rm

s, m

m

250 275 300 325 350 375 400 425 450 475 500

0.2220

0.2225

0.2230

0.2235

0.2240

0.2245

0.2250

0.2255

0.2260

500pC. Emittance at I1.Q.A1.1 0.2220 0.2225 0.2230 0.22350.2240 0.2245 0.2250 0.2255

Laser Beam Size rms, mm

Sole

noid

Fie

ld S

treng

th M

axB(

1), T

Playable range for both charges

350 375 400 425 450 475 500 525 550 575 600

0,223

0,2235

0,224

0,2245

0,225

0,2255

0,226

0,2265

0,227

1000pC. Emittance at I1.Q.A1.10,223 0,2235 0,224 0,2245 0,2250,2255 0,226 0,2265 0,227

Laser Beam Size rms XY, mm

Sole

noid

Stre

ngth

Max

B(1)

, T

Playable range for both charges

Imaginable for MaxB(1)=0.2240 and 0.2245T

Simultaneous Operation with 500pC and 1000pC. MaxB(1)=0.2240 and 0.2245

200 250 300 350 400 450 500 550 6000

0.20.40.60.8

11.21.41.61.8

2em. 500pC em. 1000pC

200 250 300 350 400 450 500 550 6000

5

10

15

20

25

30

35beta 500pC beta 1000pC

200 250 300 350 400 450 500 550 600

-5-4.5

-4-3.5

-3-2.5

-2-1.5

-1-0.5

0

alfa 500pC alfa 1000pC

MaxB(1)=0.2240

MaxB(1)=0.2245

200 250 300 350 400 450 500 550 6000

0.20.40.60.8

11.21.41.61.8

2em. 500pC em. 1000pC

200 250 300 350 400 450 500 550 60005

1015202530354045

beta 500pC beta 1000pC

200 250 300 350 400 450 500 550 600

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

alfa 500pC alfa 1000pC

Operation at MaxB(1)=0.2240 T: same optics and same emittance for XY=400. Only different chargesOperation at MaxB(1)=0.2245 T: equal optics for XY=500mm. At this point is 500pC bunch significantly larger than the one with 1000pC!

Settings Emittance Optics SensitivityMaxB(1), T XYrms, mm e_1000 e_500 X_1000 X_500 X_10005000.2240 375 0.9825 0.5921 1,2792 1,178 1.400

0.2240 400 0.8284 0.703 1,3712 1,1085 1.118

0.2240 425 0.7645 0.852 1,425 1,0586 1.118

0.2240 450 0.7453 1.041 1,4518 1,0276 1.104

0.2240 475 0.7528 1.269 1,4382 1,0099 1.130

MaxB(1) XY e_1000 e_500 X_1000 X_500 X_10005000.2245 375 0.9761 0.7265 1.2095 1.0933 1.599

0.2245 400 0.8645 0.8612 1.2951 1.0513 1.232

0.2245 425 0.8125 1.032 1.3300 1.0240 1.064

0.2245 450 0.8073 1.239 1.3294 1.0087 1.026

0.2245 475 0.8397 1.485 1.3011 1.0023 1.045

WP for Simultaneous Operation with 500pC and 1000pC

350 370 390 410 430 450 470 4900

50

100

150

200

250

Emittance Change w. r. to Minimum in %

0.2240, 500 0.2240 1000

XYrms, mm

Emitt

ance

Cha

nge,

%

350 370 390 410 430 450 470 4900

50

100

150

200

250

300

Emittance Change w. r. to Minimum in %0.2245, 500 0.2245, 1000

XYrms, mm

Emitt

ance

Cha

nge,

%

Conclusions – I. Working Points for the Operation with Different Bunch Charges

Charge 100% Transmission at XYrms, mm

XY operation window

MaxB1 operation window

Working Point for best e e_min, mm mrad

Xyrms, mm MaxB1, T

20 40 50-125 0.2200-0.2245 67 0.2216 0.0785

100 75 125-275 0.2205-0.2245 125 0.2230 0.1716

250 170 175-400 0.2210-0.2255 200 0.2235 0.2835

500 225 250-475 0.2225-0.2260 300 0.2235 0.4302

1000 365 365-600 0.2230-0.2265 450 0.2240 0.745

Charge 100% Transmission at XYrms, mm

XY operation window

MaxB1 operation window

Working Point for best e e_min, mm mrad

Sensitivity of the optics solution XXYrms, mm MaxB1, T

20 40 50-125 0.2200-0.2245 67 0.2216 0.0785 1.110

100 75 125-275 0.2205-0.2245 125 0.2230 0.1716 1.310

250 170 175-400 0.2210-0.2255 200 0.2235 0.2835 1.390

500 225 250-475 0.2225-0.2260 300 0.2235 0.4302 1.436

1000 365 365-600 0.2230-0.2265 450 0.2240 0.745 1.452

Relaxed optics for the bunch charge of 20pC Tough optics conditions for the bunch charge over 100pC

Conclusions – II. Operation with Two Different Bunch Charges

Bunch Pair MaxB(1) XY De_higher charge, %

De_smaller charge, %

X_higher charge

X_smaller charge

X_Charge1Charge2

100-250pC 0.2235 200 0 102 1.3899 1.0103 1.195

250-500pC 0.2240 275 2.0 36.3 1.391 1.070 1.220

500-1000pC 0.2240 400 11.2 63.4 1.3712 1.1085 1.118

WP is to be chosen at the smallest laser beam size which still provides the 100% transmission of the bunch with the higher charge. WP could be mostly found in the near of the emittance optimum for the higher charge Lower bunch charge will necessarily suffer a big emittance increase Relaxed optics for the lower bunch at the combined WP

Operation with Two Laser Systems and Single Solenoid

That means: Fixed solenoid field for each WP But variable laser beam sizes for each bunch charge

Scan over all possible laser beam sizes for each solenoid fieldand look for

minexpexp21

min2

2

min1

1 X

bunchbunche

eee

05.121X bunchbunch

Operation with Two Laser Systems and Single Solenoid

Table: Max Solenoid Field Strength for different operation modes, T

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0.2216 0.2233 0.2238 0.2240 0.2245

100 0.2230 0.2232 0.2237 0.2240

250 0.2235 0.2235 0.2240

500 0.2235 0.2236

1000 0.2235

Table: Laser Beam Size rms for different operation modes, mm

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 67 73 72 75 76

100 143 125 125 145 195

250 200 175 200 210 240

500 275 250 260 300 290

1000 393 375 375 375 365

Operation with Two Laser Systems. Emittance

Table: Emittance for different operational modes, mm mrad

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0.0786 0.1107 0.1203 0.1279 0.1394

100 0.2004 0.1761 0.1864 0.2245 0.3900

250 0.3080 0.2962 0.2832 0.2886 0.3714

500 0.4716 0.5439 0.4783 0.4302 0.4387

1000 0.8980 0.9830 0.9825 0.9997 0.745

Table: Emittance change in % for different operational modes

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0 40.8 53.0 62.7 77.4

100 13.8 0 5.86 27.5 121

250 8.77 4.60 0 1.89 31.1

500 9.62 26.4 11.19 0 1.97

1000 13.8 31.9 31.8 34.1 0

Operation with Two Laser Systems and Two Solenoids

That means: Variable solenoid field for each bunch charge Variable laser beam sizes for each bunch charge

Scan for each WP of bunch 1 the whole area of WPs of bunch 2 and look for

minexpexp21

min2

2

min1

1 X

bunchbunche

eee

025.121X bunchbunch

Operation with two laser systems and additional solenoid

Table: Max Solenoid Field Strength for different operation modes, T

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0.2216 0.2213 0.2215 0.2215 0.2210

100 0.2225 0.2230 0.2228 0.2225 0.2225

250 0.2230 0.2230 0.2235 0.2233 0.2230

500 0.2237 0.2235 0.2235 0.2235 0.2235

1000 0.2238 0.2239 0.2238 0.2239 0.2235

Table: Laser Beam Size rms for different operation modes, mm

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 67 75 75 85 99

100 128 125 128 165 175

250 182 175 200 223 250

500 275 275 275 300 320

1000 375 393 418 425 365

Operation with two laser systems and additional solenoid

Table: Emittance for different operational modes, mm mrad

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0.0786 0.0804 0.0798 0.0867 0.1003

100 0.1812 0.1761 0.1779 0.1899 0.1957

250 0.2852 0.2857 0.2832 0.2947 0.3088

500 0.4486 0.4420 0.4387 0.4302 0.4419

1000 0.9911 0.8777 0.7906 0.7700 0.7453

Table: Emittance change in % for different operational modes

Charge of the Partner Bunch, pC

Bunch Charge, pC 20 100 250 500 1000

20 0 2.29 1.53 10.3 27.7

100 2.90 0 1.02 7.86 11.1

250 0.74 0.88 0 4.06 9.04

500 4.27 2.73 1.98 0 2.72

1000 33.0 17.8 6.08 3.32 0