Beam Dynamics Overview Chenghui Yu for CEPC team

Beam Dynamics Overview Chenghui Yu for CEPC team June 28, 2018

Outline • Geometry design • Beam performance Collider ring Booster Linac • Summary

Geometry design • CEPC which aims at researching Higgs boson is a double ring scheme optimized at the beam energy of 120 Ge. V. • Super proton-proton collider (SPPC) will be the next project after the operation of CEPC in the future. • The circumference of CEPC is 100 km which is determined by the requirements of SPPC. • The arc regions of the SPPC collider ring, the CEPC collider ring and the CEPC booster ring are in the same tunnel. • The booster ring of CEPC is located above collider ring with the distance of 2. 4 m

Geometry design • Double ring collider with 2 IPs • Compatible with the geometry of SPPC

Geometry design Interaction region L*=2. 2 m, c=33 mrad, βx*=0. 36 m, βy*=1. 5 mm, Detector solenoid=3. 0 T – Lower strength requirements of anti-solenoids (Bz~7. 2 T) – Enough space for the SC quadrupole coils in two-in-one type (Peak field 3. 8 T & 136 T/m) with room temperature vacuum chamber. – The control of SR power from the superconducting quadrupoles.

Geometry design of the project RF region – Common cavities for Higgs mode, bunches filled in half ring for e+ and e-. – Independent cavities for W & Z mode, bunches filled in full ring. – The outer diameter of RF cavity is 1. 5 m. Distance of two ring is 1. 0 m. • During the operation of Higgs mode all the RF cavities are shared by both e+ and ebeams with the application of the combined magnets nearby the RF cavities. • For the W and Z modes the surveys of e+ and e- rings in the RF region are designed independently by turning off the combined magnets so that all bunches can be filled along the whole rings.

Beam performance Main parameters of CEPC collider ring Higgs Number of IPs Beam energy (Ge. V) Circumference (km) Synchrotron radiation loss/turn (Ge. V) Crossing angle at IP (mrad) Piwinski angle Number of particles/bunch Ne (1010) Bunch number (bunch spacing) Beam current (m. A) Synchrotron radiation power /beam (MW) Bending radius (km) Momentum compact (10 -5) function at IP x* / y* (m) Emittance ex/ey (nm) Beam size at IP x / y ( m) Beam-beam parameters x/ y RF voltage VRF (GV) RF frequency f RF (MHz) (harmonic) Natural bunch length z (mm) Bunch length z (mm) HOM power/cavity (2 cell) (kw) Natural energy spread (%) Energy acceptance requirement (%) Energy acceptance by RF (%) Photon number due to beamstrahlung Lifetime _simulation (min) Lifetime (hour) F (hour glass) Luminosity/IP L (1034 cm-2 s-1) Z（3 T） W Z（2 T） 2 120 80 45. 5 100 1. 73 0. 34 0. 036 16. 5× 2 2. 58 15. 0 242 (0. 68 s) 17. 4 7. 0 12. 0 1524 (0. 21 s) 87. 9 30 30 23. 8 8. 0 12000 (25 ns+10%gap) 461. 0 16. 5 10. 7 1. 11 0. 36/0. 0015 1. 21/0. 0031 20. 9/0. 068 0. 031/0. 109 2. 17 2. 72 3. 26 0. 54 0. 1 1. 35 2. 06 0. 107 100 0. 67 0. 89 2. 93 0. 36/0. 0015 0. 2/0. 0015 0. 54/0. 0016 0. 18/0. 004 13. 9/0. 049 6. 0/0. 078 0. 013/0. 106 0. 0041/0. 056 0. 47 650 (216816) 2. 98 5. 9 0. 75 0. 066 0. 4 1. 47 0. 050 1. 4 0. 94 10. 1 0. 2/0. 001 0. 18/0. 0016 6. 0/0. 04 0. 0041/0. 072 0. 10 2. 42 8. 5 1. 94 0. 038 0. 23 1. 7 0. 023 4. 0 2. 1 0. 99 16. 6 32. 1

Beam performance The studies on key beam dynamic issues have been finished. • • • Design of interaction region Compensation of detector solenoid Control of detector background Lattice design On-axis injection scheme Optimization of dynamic aperture Beam acceleration in the Linac and booster ring Impedance and instabilities Beambeam effect

The design of interaction region *10 -4 – Lower strength requirements of anti-solenoids (~7. 2 T) – two-in-one type (Peak field 3. 8 T & 136 T/m) with room temperature vacuum chamber. Single aperture of QD 0 (Peak field 3. 2 T) 44 turns in each pole with different length to optimize the harmonics.

The compensation of detector solenoid 3 T & 3. 8 m Specification of Anti-Solenoid Anti-solenoid Central field（T） Magnetic length（m） Conductor (Nb. Ti-Cu, mm) Coil layers Excitation current（k. A） Inductance（H） Peak field in coil (T) Number of sections Solenoid coil inner diameter (mm) Solenoid coil outer diameter (mm) Total Lorentz force F z (k. N) Cryostat diameter (mm) Before QD 0 7. 2 1. 1 16 7. 7 4 -75 Within QD 0 2. 8 2. 0 2. 5× 1. 5 8 1. 0 1. 2 3. 0 11 120 390 -13 500 After QD 0 1. 8 1. 98 4/2 1. 9 7 88 22 anti-Solenoid sections with different inner coil diameters Bzds within 0~2. 12 m. Bz < 300 Gauss away from 2. 12 m with local cancellation structure The skew quadrupole coils are designed to make fine tuning of Bz over the QF&QD region instead of the mechanical rotation.

The control of detector background For the upstream of IP, The critical energy of photons from the DIPOLE is controlled less than 45 ke. V within 150 m. For the downstream of IP, the critical energy of photons is less than 97 ke. V within 100 m. The total SR power generated by the QD 0 is 639 W in horizontal and 165 W in vertical. The critical energy of photons is about 1. 3 Me. V in horizontal and 397 ke. V in vertical. The total SR power generated by the QF 1 is 1567 W in horizontal and 42 W in vertical. The critical energy of photons is about 1. 6 Me. V in horizontal and 225 ke. V in vertical. No SR hits directly on the beryllium pipe. SR power contributed within 10 x will go through the IP. 3 mask tips are added to shadow the beam pipe wall from 0. 7 m to 3. 93 m reduces the number of photons that hit the Be pipe from 2 104 to about 200 (100 times lower).

The lattice design – – Distance of two ring is 0. 35 m to adopt twin-aperture Q & B magnets. FODO cell, 90 /90 , non-interleaved sextupole scheme. Sextupoles are independent type for the flexibility of optics. Crab-waist scheme with local chromaticity correction.

The on-axis injection Only for Higgs mode On-axis injection For Higgs, W and Z modes Off-axis injection

The on-axis injection Several circulating bunches of collider ring are extracted to the booster ring. The circulating bunches of booster will be merged with the injected bunches. Then the merged bunches in the booster ring are injected into collider ring by vertical on-axis injection scheme. The procedure will be repeated several times so that all the circulating bunches of booster can be accumulated in the collider ring. The beamloading effect of booster RF system is weak. The maximum cavity voltage drop is 0. 48% and the maximum phase shift is 0. 63 degree. The peak HOM power per RF cavity is 62 W.

Dynamic aperture optimization Higgs mode W mode Z mode

Crab waist=100% • • • Dynamic aperture optimization Higgs mode with errors SAD is used 145 turns tracked 100 samples IR sextupoles + 32 arc sextupoles (Max. free various=254) Damping at each element RF ON Radiation fluctuation ON Sawtooth On with tapering The requirements Component x (mm) y (mm) z (mm) Dipole Quadrupole 0. 05 0. 03 0. 15 x (mrad) 0. 2 y (mrad) 0. 2 z (mrad) 0. 1 Field error 0. 01% 0. 02% Errors setting of misalignment and field for the collider ring. The special magnets in the interaction region are 1/10 of normal magnets. After close orbit and optics correction, the RMS close orbits in the arcs are smaller than 30 µm horizontally and 50 um vertically. The beta beatings are less than 1% and the coupling can be controlled under 0. 26%.

Beam acceleration in the booster ring • The diameter of the inner aperture of vacuum chamber is selected as 55 mm for the consideration of impedance to improve threshold of bunch current. • Standard FODO cells are chosen for the booster lattice with 90 degrees phase advance of each cell in the horizontal and vertical planes.

Beam acceleration in the booster ring Main parameters of CEPC booster at injection energy Main parameters of CEPC booster at extraction energy

Beam acceleration in the Linac 1200 m 1. 1 Ge. V Parameter • The total beam transfer efficiency from transfer line to the injection point of collider ring is higher than 90%. • The transfer efficiency can be much higher with the application of damping ring which the beam energy is 1. 1 Ge. V. e- /e+ beam energy Repetition rate e- /e+ bunch population Symbol Unit Designed Ee-/Ee+ Ge. V 10 frep Hz 100 Ne-/Ne+ > 9. 4× 109 / >9. 4× 109 n. C > 1. 5 Energy spread (e- /e+ ) σe < 2× 10 -3 / < 2× 10 -3 Emittance (e- /e+ ) εr nm rad < 120 Bunch length (e- /e+ ) σl mm 1/1 e- beam energy on Target Ge. V 4 e- bunch charge on Target n. C 10

The impedance and instabilities Components Number Z||/n, mΩ kloss, V/p. C ky, k. V/p. C/m Resistive wall - 6. 2 363. 7 11. 3 RF cavities 240 -1. 0 225. 2 0. 3 Flanges 20000 2. 8 19. 8 2. 8 BPMs 1450 0. 12 13. 1 0. 3 Bellows 12000 2. 2 65. 8 2. 9 Pumping ports 5000 0. 02 0. 4 0. 6 IP chambers 2 0. 02 6. 7 1. 3 Electro-separators 22 0. 2 41. 2 0. 2 Taper transitions 164 0. 8 50. 9 0. 5 11. 4 786. 8 20. 2 Total At the design bunch intensity, the bunch length will increase 22% and 113% for H and Z respectively. Bunch spacing >25 ns will be needed to eliminate the electron cloud instability.

The Beambeam effect • Dynamic aperture requirements • Beam lifetime • Optimized parameters for luminosity Beam tail distribution with crab-waist collision. Lifetime with real lattice and with beam-beam interaction at Higgs

Summary • The design of accelerator physics can meet the luminosity requirements at Higgs, W and Z. • The studies on key beam dynamic issues have been finished. The beam parameters and the specifications of special magnets have been finalized. The hardware devices are all reasonable. • A preliminary procedure for the IP elements assembly has been studied. • Low magnetic field problem, eddy current effect, simulation with errors , mechanical optimization of IR, etc. are still under studying. • The optimization to reduce machine cost and improve the beam performance will continue.