Beam Loading Effect in CEPC APDR ILC 20170117

Beam Loading Effect in CEPC APDR ILC组 宫殿君 20170117

Outline 1. CEPC Single Ring &APDR(8 DR) RF Parameter 2. Phase shift in APDR 3. Conclusion of Phase shift in CEPC APDR 4. Longitudinal Dynamics 5. Steady state of beam loading in CEPC Single Ring 6. Transient beam loading in APDR

Parameter for CEPC single ring&partial double ring （wangdou 20160918） Number of IPs Energy (Ge. V) Circumference (km) SR loss/turn (Ge. V) Half crossing angle (mrad) New-61 km H-high lumi. H-low power W Z 2 120 61 3. 0 2 120 61 2. 96 2 80 61 0. 58 2 45. 5 61 0. 061 15 15 3. 91 54 16. 6 50 6. 1 3. 25 0. 43/0. 00105 6. 28/0. 04 51. 7/0. 2 0. 118 0. 074 6. 99 650 2. 19 2. 47 3. 9 0. 13 2. 1 6 0. 31 1. 88 2. 0 107 16. 9 50 6. 2 1. 48 0. 272/0. 0013 2. 05/0. 0062 23. 7/0. 09 0. 041 0. 11 3. 48 650 2. 7 2. 95 0. 74 0. 13 2 2. 3 0. 35 1. 84 1. 98 70 11. 0 32. 5 6. 2 1. 48 0. 275 /0. 0013 2. 05 /0. 0062 23. 7/0. 09 0. 042 0. 11 3. 51 650 2. 7 2. 9 0. 48 0. 13 2 2. 4 0. 34 5. 2 1. 16 400 36. 5 21. 3 6. 2 1. 44 0. 1/0. 001 0. 93/0. 0078 9. 7/0. 088 0. 013 0. 073 0. 74 650 2. 95 3. 35 0. 88 0. 087 6. 4 0. 78 1100 67. 6 4. 1 6. 2 2. 9 0. 1/0. 001 0. 88/0. 008 9. 4/0. 089 0. 01 0. 072 0. 11 650 3. 78 4. 0 0. 99 0. 05 1. 7 0. 49 1. 2 0. 34 34 37 37 0. 66 2. 02 0. 82 3. 1 0. 82 2. 01 0. 92 4. 3 0. 93 4. 48 Piwinski angle Ne/bunch (1011) Bunch number Beam current (m. A) SR power /beam (MW) Bending radius (km) Momentum compaction (10 -5) IP x/y (m) Emittance x/y (nm) Transverse IP (um) x/IP y/IP VRF (GV) f RF (MHz) Nature z (mm) Total z (mm) HOM power/cavity (kw) Energy spread (%) Energy acceptance by RF (%) n Life time due to beamstrahlung_cal (minute) F (hour glass) Lmax/IP (1034 cm-2 s-1)

Time Structure in APDR(4+4 DR) Train spacing Bunch spacing：

1. CEPC Single Ring &APDR(8 DR) RF Parameter Main Ring Type Number of IPs Luminosity/IP Energy (Ge. V) SR loss/turn (Ge. V) Circumference (km) Ne/bunch (1011) train number pulse length（us） revolution time(us) revolution frequency(k. Hz) pulse frequency（k. Hz） bunch number train spacing（us） pulse length（us） bunch spacing (ns) bunch charge (n. C) beam current（m. A） pulse current(m. A) SR power(2 Beams)(MW) pulse power loss (MW) RF frequency(MHz) Cavity Cell number Rf voltage (GV) Synchrotron Phase（deg） H-Single single ring 2 2. 0 120 3. 0 54. 8 3. 91 / 0 182. 7 5. 47 273. 5 54 / / / 62. 56 16. 63 / 99. 78 / 650 5 -cell 6. 99 154. 6 H-low power 8 double rings 2 2. 0 120 2. 96 61 2. 0 4 3. 33 203. 3 4. 92 19. 68 18*4 22. 1 3. 33 185 32 11. 02 172. 97 65. 24 512. 00 650 2 -cell 3. 51 122. 5 H-high lumi 8 double rings 2 3. 1 120 2. 96 61 2 4 3. 33 203. 3 4. 92 19. 68 27*4 22. 1 3. 33 123. 3 32 17. 00 259. 53 100. 66 768. 21 650 2 -cell 3. 48 121. 7 W Z 8 double rings 2 2 4. 3 4. 5 80 45. 5 0. 58 0. 061 61 61 1. 16 0. 78 4 4 3. 33 203. 3 4. 92 19. 68 100*4 275*4 22. 1 3. 33 33. 3 12. 1 18. 56 12. 48 36. 53 67. 54 557. 36 1031. 40 42. 37 8. 24 323. 27 62. 92 650 2 -cell 0. 75 0. 11 128. 4 146. 3

H-Single H-low power H-high lumi W Z 2. 19 0. 13 / 384 1. 147 4 12 96 18. 20 15. 87 4. E+10 7. 59 E+06 514 268 259. 8 1. 78 3. 70 2. 7 0. 13 8 480 0. 462 6 10 80 7. 31 15. 83 2. E+10 2. 35 E+05 213 284 135. 9 0. 57 0. 41 2. 7 0. 13 8 480 0. 462 6 10 80 7. 25 15. 69 2. E+10 1. 54 E+05 213 284 209. 7 0. 57 0. 62 3. 0 0. 087 8 192 0. 462 6 4 32 3. 91 8. 46 2. E+10 4. 25 E+04 213 284 220. 7 0. 57 0. 77 3. 8 0. 05 8 32 0. 462 2 2 16 3. 75 8. 12 2. E+10 3. 36 E+04 213 284 257. 5 0. 57 0. 92 maximum voltage decrease(1+1) / 12% 18% 72% >100% maximum phase shift(deg) (1+1) / 12. 8 19 64. 3 / maximum voltage decrease(4+4) / 3% 4. 5% 18% 35% maximum phase shift(deg) (4+4) / 3. 2 4. 8 16. 7 24. 6 Energy Spread（%） RF Station Cavity number effective length（m） cavity/module/station total module Cavity Voltage(MV) Quality Factor Q 0 @2 K Loaded Q R/Q （Ω） Geometry Factor G（Ω） Input Power/Cavity(kw) Loss Factor(V/p. C） HOM Power/Cavity(kw) For W and Z, both voltage decrease and phase shift are large. For Z in 1+1 DR, the maximum voltage decrease is more than 100%, when the last bunch in the train passes the cavity. What the bunch sees is a decelerating field.

2. Phase shift in APDR The total cavity voltage associated with bunch n: K. Bane, etc. Compensating the unequal bunch spacing in the NLC damping ring, EPAC 96 The beam induced voltage for bunch n:

Phase shift: Total phase variation For CEPC APDR: CEPC PDR： The total phase variation in a train can be written：

3. Conclusion of Phase shift in CEPC APDR

Phase shift of different cavity in APDR: APDR Higgs Low power Z Z Cavity 5 -cell 2 -cell 1 -cell Bunch charge (n. C) 32 32 12. 5 Bunch number 70 70 1100 Bunch spacing（ns） 185 12. 1 Cavity voltage (MV) 7. 31 3. 75 Input Power/Cavity(kw) 135. 9 257. 5 R/Q 514 213 106 Cavity number 480 32 32 6. 33 15. 83 8. 12 16. 24 Synchrotron phase(deg) (π-arcsin） 123 146 maximum voltage decrease(1+1) 16. 5 11. 5 / 70 % maximum phase shift(deg) (1+1) 30 12 / 49 maximum voltage decrease(4+4) 6. 9% 3. 3% 35 % 22. 6 % maximum phase shift(deg) (4+4) 7. 2 3 24. 6 12. 3

Comparison with other collider: BEPCII-Collider BEPCII-SR light Main Ring Type Number of IPs Luminosity/IP Energy (Ge. V) Circumference (km) Ne/bunch (1011) revolution frequency(k. Hz) pulse frequency（k. Hz） bunch number train spacing（us） pulse length（us） bunch spacing (ns) bunch charge (n. C) beam current（m. A） SR loss/turn (Ge. V) SR power(2 Beams)(MW) Pulse(beam) power loss (MW) RF frequency(MHz) Cavity Cell number Rf voltage (GV) Synchrotron Phase（deg） Cavity number effective length（m） cavity/module/station total module Cavity Voltage(MV) Quality Factor Q 0 @2 K R/Q （Ω（ Input Power/Cavity(kw) Loss Factor(V/p. C） Maximum voltage decrease Maximum phase shift (deg) Double ring 1 0. 038 1. 89 237. 5 m 0. 485 1. 262 5^10*1. 25 93 / / 8 7. 75 910 121 ke. V 220. 22 kw 122 kw 499. 8 1 1. 5 MV 173. 4 1 0. 3 1 / 1 1. 5 Single Ring(outer) / / 2. 5 241. 1 m 0. 135 1. 243 5^10*1. 25 93 / / 8 2. 16 250 336 ke. V 168 kw 96 kw 499. 8 1 1. 5 MV 166. 1 1 0. 3 1 / 1 1. 5 LEP 2 CEPC H-Single CEPC H-low power Single Ring 4 2 E 31 45. 6 26. 66 11. 25 45. 01 4 / / 88. 9μs 26. 56 1. 2 0. 134 0. 65 0. 16 355. 2 5 0. 38 159. 4 128 2. 06 8 8 16 2. 97 Single Ring 4 4 E 31 101. 0 26. 66 2. 78 11. 25 45. 01 4 / / 88. 9μs 44. 8 2 2. 05 8. 23 4. 10 355. 2 4 2. 34 116. 8 288 1. 7 4 18 72 8. 12 single ring 2 2. 0 120 61 3. 91 5. 47 273. 5 54 / / 3765 62. 56 16. 63 3. 0 99. 78 50 650 5 -cell 6. 99 154. 6 384 1. 147 4 12 96 18. 20 8 double rings 2 2. 0 120 61 2. 0 4. 92 19. 68 4*18 22. 1 3. 33 185 32 11. 02 2. 96 65. 24 512. 00 650 2 -cell 3. 51 123 480 0. 462 6 10 80 7. 31 5 1. 00 E+09 95. 3 8 1. 00 E+09 95. 3 1. 4 6 15. 87 15. 83 2 E 4 1300 3. 2 E 9(4. 5 K) 232 . 4 E+10 514 . 2 E+10 213 / / 339 64 23 22. 5 220 0. 075 0. 3% 0. 23 170 0. 075 0. 065% 0. 063 259. 8 5. 07 28. 6 1. 78 0. 158 5 0. 31%(one bunch) 0. 41%（one bunch） 0. 16%(one bunch) 0. 6（one bunch) 0. 93（one bunch） 0. 31(one bunch) 135. 9 0. 58 3% 3. 3

4. Longitudinal Dynamics 1). Longitudinal motion equation： Synchronous particles: Non-synchronous particles: The longitudinal oscillation equation: ith particle Hamitonian： The separatrix：

2). RF bucket ： APDR Higgs low power： APDR Higgs high lumi：

APDR W: APDR Z:

BEPCII-Collider : BEPCII-SR light :

CEPC APDR 8 DR（20160918） BEPCII Higgs-LP Higgs-HL W Z Collider SR Light 120 80 45. 5 1. 89 2. 5 3. 51 3. 48 0. 75 0. 11 1. 5 MV 1. 5 MW 122. 5 121. 7 128. 4 146. 3 174. 8 165. 1 Maximum Voltage Decrease(%) 3 4. 5 18 35 0. 3 0. 065 Maximum Phase Shift (deg) 3. 2 4. 8 16. 7 24. 6 0. 23 0. 063 RF bucket (deg) 57. 5 -156. 3 58. 3 -154. 7 51. 6 -169. 1 33. 7 -209. 5 5. 2 -301. 8 14. 9 -261. 8 Bucket area A (Me. Vrad) 0. 27 0. 25 0. 14 0. 07 4. 20 E-03 3. 00 E-03 Bucket area A(e. Vs) 2. 90 2. 69 0. 57 0. 06 7. 44 6. 05 Energy（Ge. V） Integral Area of RF bucket:

3). RF Energy Acceptance Phase shift can make the RF energy acceptance decrease APDR Higgs-lp Higgs-hl W Z 3. 2 4. 8 16. 7 24. 6 2. 4 2. 3 1. 8 1. 1 2. 03 1. 7 0. 6 0. 3

5. Steady state of beam loading in CEPC Single Ring 1). Time variation of voltage P. B. Wilson. Transient beam loading in electron-position storage rings. CERN-ISR-TH/78 -23

Time Variation of Cavity Voltage: Time Variation of Cavity Phase: Before next bunch arrives, the input power has re-filled the stored energy, Both the cavity voltage and phase is recovered, so next bunch can’t feel the voltage and phase variation.

6. Transient beam loading in APDR Because of the presence of gap, there is no steady state in ADPR. 1). Filling power Higgs-low power: Take cavity detuning into consideration Filling power vs. filling time: Difference between on-resonance and optimum-detuning: Choose the flat curve, filling time is 200 us, filling power is 428 k. W.

2). Power needed to compensate the loss energy Optimum detuning frequency: For APDR H-low power:

APDR H-low power H-high lumi W Z Syn phase P. B. Wilson(deg) 32. 5 31. 7 38. 4 56. 3 Vc(V) 7. 31 E+06 7. 25 E+06 3. 91 E+06 3. 75 E+06 Vg 0 filling voltage 7. 32 E+06 7. 26 E+06 3. 91 E+06 3. 75 E+06 Vgi input voltage)V( 2. 20 E+06 2. 23 E+06 1. 10 E+06 7. 08 E+05 Opti detuning frequency(Hz) -8. 80 E+02 -1. 30 E+03 -6. 14 E+03 -1. 58 E+04 detuning angle(rad) 5. 67 E-01 - 5. 53 E-01 - 6. 76 E-01 - 1. 02 E+00 - Pg needed(k. W)/cavity 1. 07 1. 60 1. 68 1. 97 Input power/cavity(k. W) 135. 9 209. 7 220. 7 257. 5 For APDR Higgs-low power: (bunch number 18)

Cavity voltage phasor variation among different bunches: Cavity voltage amplitude variation among different bunches:

Conclusion 1. Because of large pulse current, for W and Z, both voltage decrease and phase shift are large. For Z in 4+4 DR, the phase shift is 24. 6° 2. The R/Q per cell is constant, so for certain cavity number, the phase shift can be reduced with less cavity number. 3. Because of large gap(87% of circumference), the phase shift in CEPC APDR is much larger than the other colliders in the world. 4. In APDR, Z has the smallest RF bucket, W has the largest RF energy acceptance decrease induced by the phase shift. 5. In Single Ring, the input power can re-fill the energy extracted by bunches, there is no phase shift between different bunches. 6. In APDR, the input power needed to compensate the loss energy is 1. 07 MW in bunch spacing for Higgs-low power. That can’t be achieved, so the cavity voltage can’t be recovered.