SRF Operation Issues for CEPC with Bunch Trains

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SRF Operation Issues for CEPC with Bunch Trains Jiyuan Zhai IHEP CEPC-Spp. C Study

SRF Operation Issues for CEPC with Bunch Trains Jiyuan Zhai IHEP CEPC-Spp. C Study Group Meeting Sept. 11, 2015, IHEP, Beijing

Content SRF cavity beam loading, HOM power and instability issues for different CEPC lattice

Content SRF cavity beam loading, HOM power and instability issues for different CEPC lattice scheme and operation energy: Pretzel (PZ) Scheme • Higgs (pre-CDR) • Super Z (with wiggler, H. P. Geng) • Super Z (bunch trains, U. Wienands) Local Double Ring (LDR or bunch train) Scheme • Higgs (J. Gao, M. Xiao) • Super Z (J. Gao, M. Xiao)

CEPC Pre-CDR Parameters (1) Unit Main Ring Booster Injection Booster Extraction Beam energy Ge.

CEPC Pre-CDR Parameters (1) Unit Main Ring Booster Injection Booster Extraction Beam energy Ge. V 120 6 120 Circumference km 54. 752 Luminosity / IP cm-2 s-1 2. 04 E+34 - - Energy loss / turn Ge. V 3. 11 17. 6 ke. V 2. 81 SR power MW 103. 42 16. 2 W 2. 46 s 1. 83 E-04 Revolution frequency k. Hz 5. 4755 Bunch charge n. C 60. 56 3. 35 3. 2 Bunch number - 100 50 50 Beam current (total) m. A 33. 2 0. 92 0. 87 Bunch spacing μs 1. 825 3. 65 MHz 0. 55 0. 274 Parameter Revolution period Beam spectrum spacing

CEPC Pre-CDR Parameters (2) Unit Main Ring Booster Injection Booster Extraction Momentum compaction -

CEPC Pre-CDR Parameters (2) Unit Main Ring Booster Injection Booster Extraction Momentum compaction - 3. 36 E-05 7. 69 E-05 Energy spread % 0. 1629 0. 1 (linac) 0. 127 Bunch length mm 2. 65 1. 5 (linac) 2. 66 RF voltage GV 6. 87 0. 213867 5. 12 RF frequency GHz 0. 65 1. 3 Harmonic number - 118800 237423 Synchrotron tune - 0. 180 0. 32076 Energy acceptance (RF) % 5. 99 17. 307 2. 091 Transverse damping time turns 77. 05 682122 (125 s) 85. 2 (15. 56 ms) Longitudinal damping time turns 38. 52 341219 (62 s) 42. 7 (7. 789 ms) Lifetime Bhabha min 51. 77 - - Lifetime BS (sim. ) min 47 - - Parameter

CEPC Pre-CDR Cavity Parameters Parameter Unit Main Ring Cavity frequency MHz 650 Number of

CEPC Pre-CDR Cavity Parameters Parameter Unit Main Ring Cavity frequency MHz 650 Number of cells - 5 Cavity effective length m 1. 154 Cavity iris diameter mm 156 Beam tube diameter mm 170 Cell-to-cell coupling - 3 % R/Q Ω 514 Geometry factor Ω 268 Epeak/Eacc - 2. 4 Bpeak/Eacc m. T/(MV/m) 4. 23 V/p. C 1. 8 V/p. C/m 2. 4 MV/m 20 - 4 E 10 Cavity longitudinal loss factor* k∥ HOM Cavity transverse loss factor* k⊥ Acceptance gradient Acceptance Q 0 at acceptance gradient * bunch length 2. 65 mm (assume same for Higgs and Z energy)

Pretzel Scheme • • 48 bunches / beam, 96 parasitic collision points (~ 500

Pretzel Scheme • • 48 bunches / beam, 96 parasitic collision points (~ 500 m spacing) Horizontal separation, no off-center orbit in RF section One pair of electrostatic separators for each arc (green) One pair of electrostatic separators for P 2, P 3, P 4, P 6, P 7, P 8 H. P. Geng

RF Section for Pretzel Scheme P 1 (IP 1) & P 5 (IP 3)

RF Section for Pretzel Scheme P 1 (IP 1) & P 5 (IP 3) Main Ring module (10 m) Four 650 MHz 5 -cell cavities inside Half RF Section (6 modules, 70 m), 3 module pairs (klystrons, valve boxes) DIS SEP IP \ Half FODO cell (23. 6 m) One FODO cell (47. 2 m) FFS (350 m) Pn (n = 2, 3, 4, 6, 7, 8) DIS SEP Pn \ Two FODO cells (95 m)

Local Double Ring Scheme • One bunch train per beam RF • No pretzel

Local Double Ring Scheme • One bunch train per beam RF • No pretzel e+ e- • Crab waist possible ~3 km (10 μs) macro-bunch • Cost less than whole double-ring • More bunches for high luminosity Z, W Parameters Value Unit 54374 m 47. 2 m 118800 One bucket length in the ring 0. 46 m Bucket number in double beam pipe 6156 Circumference Length of one FODO cell Harmonic number • Local double section 10% of the whole ring • 120 FODO cells length • 1. 416 km on each side of IP J. Gao, M. Xiao, M. Koratzinos

LDR Time Structure Parameters Z W H Beam energy [Ge. V] 45 80 120

LDR Time Structure Parameters Z W H Beam energy [Ge. V] 45 80 120 Synchrotron radiation power per beam [MW] 50 50 50 SR loss/turn U 0 [Ge. V] 0. 062 0. 6 3. 01 Beam current I [m. A] 796. 8 84. 03 16. 62 Bunch population Ne [1011] 3. 09 3. 65 3. 61 Bunch number 2688 240 48 2 25 128 Distance between bunches [m] 0. 92 11. 5 58. 88 Bunch space time [ns] 3. 1 38. 3 196. 3 Bucket interval per bunch J. Gao, M. Xiao

Cavity Configuration One RF section D ~ 65 m d ~ 700 m (IP

Cavity Configuration One RF section D ~ 65 m d ~ 700 m (IP PZ) ~ 190 m (Pn PZ) ~ 3000 m (IP LDR) D ~ 65 m e- e+ RF length of one module = 29 λ/2 = 6. 7 m 5λ/2 3λ/2 [(2 n+1)λ/2, 2 cav. with one klystron] λ = 0. 461 m • For counter-rotating beams, all 5 -cell cavity centers must be at nλ/2 from Pn. • Beam time structure various in cavities, modules, RF sections of diff. schemes. • Define the max. arrival time difference of e+ and e- in one cavity Ta : 2. 7 μs (end cavity) for IP PZ, 170 μs (nearest RF section to IP) for LDR

Parasitic Loss and Beam Loading • Tb : bunch spacing Td = 2 QL/ωn

Parasitic Loss and Beam Loading • Tb : bunch spacing Td = 2 QL/ωn cavity filling time Assume incoherent HOM excitation, average Fr = ½, same as single pass excitation. P. B. Wilson, SLAC-PUB-6062 Equally-spaced bunches will have steady beam loading for fundamental mode. Cavity detuning for compensation.

Beam Loading of Bunch Trains • Consider one bunch train of the LDR scheme.

Beam Loading of Bunch Trains • Consider one bunch train of the LDR scheme. • Beam loading is different for different bunches. • Cavity voltage amplitude, synchrotron phase and tune will be modulated periodically. • Accurate analytical calculation difficult P. B. Wilson, SLAC-PUB-6062 because of syn. phase oscillation in the ring. Simulation (KEKB, SLC-DR). Phasor for injection, gap left to cure instability, bunch trains … • LLRF feedback compensation.

Beam Loading of Bunch Trains Rough estimation for H-LDR: Tb-train = 0. 2 μs,

Beam Loading of Bunch Trains Rough estimation for H-LDR: Tb-train = 0. 2 μs, Ttrain = 10 μs, Tg = 183 us, Td = 1077 us. Tb-train and Ttrain << Td, the bunch train can be treated as a macro-bunch. Tg << Td, the beam induced voltage is same as the equal-spacing, thus the same average beam loading. Phase difference between the head and tail bunches: 10 deg Voltage difference between the head and tail bunches: 2. 8 MV D. Boussard, CERN SL / 91 -16

HOM Power and Coupled Bunch Instability • HOM power 10 ~ 50 times higher

HOM Power and Coupled Bunch Instability • HOM power 10 ~ 50 times higher for HL-Z than H • CBI threshold ~ 1000 times lower for HL-Z (feedback not easy due to small bunch spacing) than H • Beam instabilities for bunch train • Bunch train beam spectrum and HOM spectrum relation.

HOM of Bunch Train for Higgs Run • HOM damping time limit between the

HOM of Bunch Train for Higgs Run • HOM damping time limit between the nb bunches in a bunch train is ~ 50 times lower than the pretzel scheme (beam instability to be studied). • Average HOM power same with pretzel scheme. • Positive coherent HOM vector superposition could happen rather than simply adding their power. • According to LEP 2 bunch train measurement [CERN SL/94 -95], the HOM power enhancement factor is nb^(1/2) (assume no HOM coherence between two counter-rotating beams, but could happen). HOM coupler power handling capacity should have enough margin.

HOM Impedance for Higgs (Pretzel) Monopole Mode f (GHz) R/Q (Ω) Qlimit σf =

HOM Impedance for Higgs (Pretzel) Monopole Mode f (GHz) R/Q (Ω) Qlimit σf = 0 MHz Qlimit σf = 0. 5 MHz Qlimit σf = 5 MHz TM 011 1. 173 84. 8 5. 1 E+5 2. 9 E 7 5. 8 E 7 TM 020 1. 350 5. 5 6. 8 E+6 3. 7 E 7 7. 5 E 7 Dipole Mode f (GHz) R/Q (Ω/m) Qlimit σf = 0 MHz Qlimit σf = 0. 5 MHz Qlimit σf = 5 MHz TE 111 0. 824 832. 2 2. 3 E+4 1. 2 E 6 2. 4 E 6 TM 110 0. 930 681. 2 2. 8 E+4 1. 5 E 6 3. 0 E 6 TE 112 1. 225 36. 2 5. 2 E+5 1. 9 E 6 3. 7 E 6 TM 111 1. 440 101. 5 1. 9 E+5 1. 0 E 7 2. 0 E 7 cut-off • Large HOM frequency spread from cavity to cavity relaxes the Q requirement • Easy to reach these Q values with HOM couplers on beam tubes for the modes below cut-off frequency • Some modes above cut-off may trap in the cavity and cryomodule

Coherence of Counter-Rotating Beams Generally no coupling of counter-rotating bunches in the ring because

Coherence of Counter-Rotating Beams Generally no coupling of counter-rotating bunches in the ring because of rapid distance change (average to zero). But coherence may happen in the cavity (depends on cavity position and modes symmetry). δ Vb 2 V 2+ Vb 1 V 2 - V 1+ V 1 - δ θ-δ Beam induced voltage is decided by the charge, not moving direction, Therefore, V 1+ = V 2 - , V 2+ = V 1 - , δ = 2π Ta / Tn , θ = 2π Tb / Tn We have therefore, For the case Ta << Tb , K = 1/2 by averaging the first cosine term. Thus, twice the single beam loss.

CEPC RF Parameters H-PZ H-LDR Beam energy (Ge. V) 120 SR power per beam

CEPC RF Parameters H-PZ H-LDR Beam energy (Ge. V) 120 SR power per beam (MW) 50 Z-PZW Z-PZBT Z-LDR 45 0. 084 13. 4 50 SR loss / turn U 0 (Ge. V) 3. 11 3. 01 0. 06 Luminosity L (cm-2 s-1) 2 E 34 2 E 32 2. 3 E 34 7 E 34? Bunch charge q (n. C) 60 58 5 22. 4 50 2 x 16. 6 2 x 1. 4 2 x 223 2 x 797 No. of bunches per train nb 1 48 1 28 2688 No. of bunch trains nt 48 1 50 64 1 Cavity voltage Vc (MV) 17. 9 6 ? ? RF power per cavity P (k. W) 280 0. 22 70+17. 8+ 260+143+ Bunch space in train Tt (ns) / 196. 3 / 4. 6 3. 1 Bunch (train) space Tb (μs) 3. 8 183 3. 8 2. 9 183 Max. arrival time diff. Ta (μs) 2. 7 170 Fundamental mode (FM) QL 2. 2 E 6 < 3 E 8 < 2. 2 E 6 < 2. 2 E 5 Cavity filling time Td (μs) 1077 >> 1077 < 107 3. 5 0. 025 17. 8 143 2 E 6~8 E 7 5 E 5~2 E 7 3 E 3~1 E 5 1 E 3~3 E 4 Average beam current I (m. A) HOM power per cavity (k. W) HOM CBI Qext limit

High Current Super Z Operation • HOMs power will be a major issue for

High Current Super Z Operation • HOMs power will be a major issue for running at the Z pole. Reduce the cavity frequency, reduce cell number, reduce cavity number in one module, SRF staging (as FCC-ee) • Large detuning (larger than the revolution frequency), longitudinal coupled-bunch mode instability, feedback • Robison instability, direct feed back (like BEPCII) • Many other beam dynamics and hardware issues related to bunch train operation • Z-pole design should be compromised with well-defined boundary conditions (machine layout, luminosity, beam dynamics, SRF)

Summary • CEPC beam loading, HOM power and multi-bunch instabilities are related to beam

Summary • CEPC beam loading, HOM power and multi-bunch instabilities are related to beam time structure & cavity configuration in the ring. • Pre-CDR SRF design is suitable for Higgs run of the Local Double Ring (Bunch Train) scheme. Transient beam loading could be compensated by LLRF feedback. Details to be studied. • Coherence of two counter-rotating beams have (trivial? ) effect on the beam loading and HOMs. • Pre-CDR cavity can’t be used for high luminosity (hyper) Z run. Need inputs from physics requirement.

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FCC-ee Parameters Version 2. 0 (2014 -09 -05) LEP 2 FCC-ee Z FCC-ee W

FCC-ee Parameters Version 2. 0 (2014 -09 -05) LEP 2 FCC-ee Z FCC-ee W FCC-ee H FCC-ee tt Circumference [km] 26. 7 100 Bending radius [km] 3. 1 11 Beam energy [Ge. V] 104 45. 5 80 120 175 Beam current [m. A] 3. 04 1450 152 30 6. 6 4 16700 4490 1360 98 Bunch population [1011] 4. 2 1. 8 0. 7 0. 46 1. 4 Beam size at IP s* [mm] - Horizontal - Vertical 182 3. 2 121 0. 25 41 0. 084 22 0. 044 45 0. 045 Energy loss / turn [Ge. V] 3. 34 0. 03 0. 33 1. 67 7. 55 SR power / beam [MW] 11 Total RF voltage [GV] 3. 5 5. 5 11 RF frequency [MHz] 352 Bunches / beam Luminosity / IP [1034 cm-2 s-1] Luminosity lifetime [min](1) Luminosity lifetime corresponds to 4 IPs. 50 2. 5 4 800 0. 012 28. 0 12. 0 6. 0 1. 8 434 298 73 29 21