1. Injector Optimization for Simultaneous Operation with Different Bunch Charges Yauhen Kot BD Meeting 23.04.2012

2. 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

3. 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…

4. Typical beta development over the laser spot size. (seen at the end of the ACC1) 100% transmission from the cathode Emittance minimum Beta minimum  Small beta for transmission under 100%  Local maximum at the point of 100% transmission  Shortly after the 100% transmission emittance minimum  And much later the beta function minimum For higher charges the whole curve shifts to the right

5. 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 possible If we “catch” the beta for higher charge on the falling arm and the other one on the rising arm 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. …and hope that alfas also coincide

6. 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

7. Working points for 20pC. Emittance Point of View Match possible MaxB(1)XYrms  Opt. sensitivity  0.2216670.07851.110 2D Scan for XFEL Injector. 20pC Best Emittance Comfortable Optics Conditions  100% transmission beginning at XY=40  m  Stable optics solutions with the emittance > 0,10 mm mrad possible  Operation reasonable with XYrms between 50-125  m  and MaxB(1) range of 0.2200-0.2245T Mismatch after the change of solenoid field by 0.0005T

8. 2D Scan for XFEL Injector. 100pC Stable optics match is possible Possible to match with the current configuration Emittance minimum  Working Point with respect to the emittance minimum at 0.2230 T x 125 mm  Best emittance: 0,1716 mm mrad  Stable optics solutions with the emittance > 0,24 possible  100% transmission beginning at XY=75mm  Operation reasonable with XYrms between 120-290  m  and MaxB(1) range of 0.2205-0.2245T MaxB(1)XYrms  0.22301250.17161.310

9. 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 Charge100% Transmission at XYrms,  m XY operation window MaxB1 operation window Working Point for best  _min, mm mrad Xyrms,  m MaxB1, T 204050-1250.2200-0.2245670.22160.0785 10075125-2750.2205-0.22451250.22300.1716 250170175-4000.2210-0.22552000.22350.2835 500225250-4750.2225-0.22603000.22350.4302 1000365365-6000.2230-0.22654500.22400.745

10. 2D Scan for XFEL Injector. 250pC  Working Point with respect to the emittance minimum at 0.2235 T x 200 mm  Best emittance: 0,2832 mm mrad  Stable optics solutions with the emittance > 0,32 possible  Operation reasonable with XYrms above 170mm  and MaxB(1) range of 0.2210-0.2255T Transmission below 100% MaxB(1)XYrms  0.22352000.28321.3899

11. Simultaneous Operation with 100pC and 250pC Playable range for both charges Operation with both charges simultaneously is imaginable for MaxB(1)=0.2230 and 0.2235

12. Simultaneous Operation with 100pC and 250pC. MaxB(1)=0.2230 and 0.2235 Both twiss functions coincide for both bunch charges at almost the same settings of the laser. Combined working point at MaxB(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

13. SettingsEmittanceOptics Sensitivity MaxB(1), T XYrms,  m  _250  _100    0.22302000.28390.29391.33651.03071,57 0.22302250.2950.40881.31781.00341,385 0.22302500.30880.55691.28241.00101,106 0.22302750.34020.71511.2081.00721,012 MaxB(1)XY  _250  _100    0.22352000.28320.3471.38991.01031.195 0.22352250.29660.4711.31451.00041.055 0.22352500.32750.61761.23191.00411.078 0.22352750.38590.76831.13951.01211.369 WP for Simultaneous Operation with 100pC and 250pC

14. 2D Scan for XFEL Injector. 500pC Emittance minimum  Working Point with respect to the emittance minimum at 0.2235 T x 300  m  Best emittance: 0,4302 mm mrad  Stable optics solutions with the emittance > 0,60 mm mrad possible  Operation reasonable with XYrms between 250  m and 475  m  and MaxB(1) range of 0.2225-0.2260T 500pC Emittance Match possible, stable optics solution No match possible MaxB(1)XYrms  0.22353000.43021.4363

15. Simultaneous Operation with 250pC and 500pC Playable range for both charges Imaginable for MaxB(1)=0.2240 and 0.2235

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

17. MaxB(1)XY  _500  _250    0.22402750.4390.3861.3911.0701.220 0.22403000.4300.4821.3791.0291.228 0.22403250.4450.6191.3271.0081.221 0.22403500.4700.8011.2571.0011.160 0.22403750.5161.0171.1781.0011.082 WP for Simultaneous Operation with 250pC and 500pC SettingsEmittanceOptics Sensitivity MaxB(1), T XYrms,  m  _500  _250    0.22352750.4720.4681.3911.0701.236 0.22353000.4510.5841.3791.0291.035 0.22353250.4700.7381.3271.0081.001 0.22353500.5170.9311.2571.0011.014 0.22353750.5921.1551.1781.0011.056

18. 2D Scan for XFEL Injector. 1000pC Emittance minimum Emittance minimum is feasible but may have an unstable optics Working point for the emittance minimum: MaxB(1)XYrms  0.22404500.7451.452  100% transmission beginning at XY=365  m  Stable optics solutions with the emittance > 1,00 mm mrad possible  Operation reasonable with XYrms between 365  m and 600  m  and MaxB(1) range of 0.2230-0.2265T Match possible, stable optics solution No match possible

19. Simultaneous Operation with 500pC and 1000pC Playable range for both charges  Imaginable for MaxB(1)=0.2240 and 0.2245T

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

21. SettingsEmittanceOptics Sensitivity MaxB(1), T XYrms,  m  _1000  _500    0.22403750.98250.59211,27921,1781.400 0.22404000.82840.7031,37121,10851.118 0.22404250.76450.8521,4251,05861.118 0.22404500.74531.0411,45181,02761.104 0.22404750.75281.2691,43821,00991.130 MaxB(1)XY  _1000  _500    0.22453750.97610.72651.20951.09331.599 0.22454000.86450.86121.29511.05131.232 0.22454250.81251.0321.33001.02401.064 0.22454500.80731.2391.32941.00871.026 0.22454750.83971.4851.30111.00231.045 WP for Simultaneous Operation with 500pC and 1000pC

22. Conclusions – I. Working Points for the Operation with Different Bunch Charges Charge100% Transmission at XYrms,  m XY operation window MaxB1 operation window Working Point for best  _min, mm mrad Xyrms,  m MaxB1, T 204050-1250.2200-0.2245670.22160.0785 10075125-2750.2205-0.22451250.22300.1716 250170175-4000.2210-0.22552000.22350.2835 500225250-4750.2225-0.22603000.22350.4302 1000365365-6000.2230-0.22654500.22400.745 Charge100% Transmission at XYrms,  m XY operation window MaxB1 operation window Working Point for best  _min, mm mrad Sensitivity of the optics solution  XYrms,  m MaxB1, T 204050-1250.2200-0.2245670.22160.07851.110 10075125-2750.2205-0.22451250.22300.17161.310 250170175-4000.2210-0.22552000.22350.28351.390 500225250-4750.2225-0.22603000.22350.43021.436 1000365365-6000.2230-0.22654500.22400.7451.452  Relaxed optics for the bunch charge of 20pC  Tough optics conditions for the bunch charge over 100pC

23. Conclusions – II. Operation with Two Different Bunch Charges Bunch PairMaxB(1)XY  _higher charge, %  _smaller charge, %  higher charge  smaller charge  Charge1  Char ge2 100-250pC0.223520001021.38991.01031.195 250-500pC0.22402752.036.31.3911.0701.220 500-1000pC0.224040011.263.41.37121.10851.118  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

24. 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 field and look for

25. 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 201002505001000 200.22160.22330.22380.22400.2245 1000.22300.22320.22370.2240 2500.2235 0.2240 5000.22350.2236 10000.2235 Table: Laser Beam Size rms for different operation modes,  m Charge of the Partner Bunch, pC Bunch Charge, pC 201002505001000 206773 72 75 76 100143125 145195 250200175200210240 500275250260300290 1000393375 365

26. Operation with Two Laser Systems. Emittance Table: Emittance for different operational modes, mm mrad Charge of the Partner Bunch, pC Bunch Charge, pC 201002505001000 200.07860.11070.12030.12790.1394 1000.20040.17610.18640.22450.3900 2500.30800.29620.28320.28860.3714 5000.47160.54390.47830.43020.4387 10000.89800.98300.98250.99970.745 Table: Emittance change in % for different operational modes Charge of the Partner Bunch, pC Bunch Charge, pC 201002505001000 20040.853.062.777.4 10013.805.8627.5121 2508.774.6001.8931.1 5009.6226.411.1901.97 100013.831.931.834.10

27. 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

28. 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 201002505001000 200.22160.22130.2215 0.2210 1000.22250.22300.22280.2225 2500.2230 0.22350.22330.2230 5000.22370.2235 10000.22380.22390.22380.22390.2235 Table: Laser Beam Size rms for different operation modes,  m Charge of the Partner Bunch, pC Bunch Charge, pC 201002505001000 206775 8599 100128125128165175 250182175200223250 500275 300320 1000375393418425365

29. 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 201002505001000 200.07860.08040.07980.08670.1003 1000.18120.17610.17790.18990.1957 2500.28520.28570.28320.29470.3088 5000.44860.44200.43870.43020.4419 10000.99110.87770.79060.77000.7453 Table: Emittance change in % for different operational modes Charge of the Partner Bunch, pC Bunch Charge, pC 201002505001000 2002.291.5310.327.7 1002.9001.027.8611.1 2500.740.8804.069.04 5004.272.731.9802.72 100033.017.86.083.320