Injection design of CEPC Cui Xiaohao And CEPC Group 2018/11/12

1. Introduction: A Linac accelerate electrons and positrons to 10 GeV. A booster with the same circumference with the collider. For high luminosity, top-up injection is needed. For the simplicity and robustness of the injection system, a conventional off-axis injection is chosen as our baseline design. For Higgs mode, an swap-out on axis injection is chosen as another choice, in case of small DA in the collider.

Some key parameters of the collider ring   Higgs W Z Energy (GeV) 120 80 45.5 Bunch number 242 1524 12000 Bunch Charge (nC) 24 19.2 12.8 Bunch Current (mA) 17.4 87.9 461 Revolution Period (ms) 0.3336 Emittance x/y (nm) 1.21/0.0031 0.54/0.0016 0.17/0.004 Life time (Hour) 0.67 1.4 4

The geometry of the injection system

2. Off-Axis Injection: Injection from Linac to booster Booster ramping to Extraction Energy Inject from booster to collider Booster ramping to 10 GeV repeat

Injection time structure: Different injection time Structure for different mode

This injection system fulfills the 3% top-up injection and full injection. Mode Higgs W Z Injection Mode Top-up Full Bunch number 242 1220 6000 Bunch Charge (nC) 0.72 1 0.384 0.55 Beam Current (mA) 0.5227 0.726 2.63 3.67 6.91 10 Current threshold 1 mA 4 mA 10 mA Number of Cycles 2 Current decay 3% Ramping Cycle (sec) (Up + Down） 6.6 3.8 Filling time (sec) （e+，e-) 25.84 39.6 275.2 Injection period (sec) 47 131 438 Full Injection time 10 min 15 min 2.2 Hour (collide from 230mA

Acceptance >4sxc + 6sxi + S For Higgs: e_x = 1.21 nm.rad; e_inject = 3.1 nm.rad sx = 0.47 mm, s_inject = 0.45 mm Septum = 2 mm Acceptance > 13 s X’ X Bumped Stored beam Septum 2mm Injected beam For W: e_x = 1.21 nm.rad; e_inject = 1.59 nm.rad sx = 0.47 mm, s_inject = 0.45 mm Septum = 2 mm Acceptance > 14 s For Z: e_x = 0.17 nm.rad; e_inject = 0.51 nm.rad sx = 0.18 mm, s_inject = 0.16 mm Septum = 2 mm Acceptance > 16 s Bump Height Acceptance >4sxc + 6sxi + S

Current evolution in collider-Higgs Top up  one injection (26s/35s) every 47s Full injection from empty  10 min Collider lifetime (non-collision) 924 hours: dominated Toucheck lifetime Top up Full injection

Current evolution in collider-W Top up  one injection (46s) every 153s Full injection from empty  15 min Collider lifetime (non-collision) 105 hours: dominated Toucheck lifetime Top up Full injection

Current evolution in collider-Z Top up  one injection (4.6min) every 7.3min Full injection from empty  2.2 hours (bootstrapping start from half of the design current) Collider lifetime (non-collision) 53 hours: dominated Toucheck lifetime Top up Full injection

Kickers and Septums for booster injection and extraction: Component Length (m) Waveform Deflection angle (mrad) Field (T) Beam-Stay-clear H(mm) V(mm) Septum 2 DC 9.1 0.152 63 Kicker 0.5 Half_sin 0.034 Booster Extraction Component Length (m) Waveform Deflection angle (mrad) Field (T) Beam-Stay-clear H(mm) V(mm) Septum 10 DC 10.4 0.41 20 Kicker 2 Half_sin 0.2 0.04

Kickers and Septums for collider injection: Component Length (m) Waveform Deflection angle (mrad) Field (T) Beam-Stay-clear H(mm) V(mm) Septum 8.75 DC 14 0.64 20 7 0.32 3.5 0.16 1.75 0.08 Kicker 2 Half_sin 0.1 0.02

3. On-Axis Injection: 1. Inject 242 small bunches into the booster. Linac booster collider 2. Ramp the booster to high energy and inject several (7 for example) bunches from the collider into the booster. Ramp up booster collider 3. Large bunches stay in the booster for 4 damping time(200ms), so that the injected bunches merge with booster bunches. booster collider Repeat 4. Inject the merged large bunches back to the same empty buckets left by the last step. 5. Repeat the last steps. booster collider

Merge bunches in the booster 1. The booster is used as an accumulator ring. 2. Inject the large bunch in the collider into the booster, not the other way around. 3. off-axis injection and bunch mergence are performed in the booster, whose dynamic aperture is large enough. 4. With this on-axis injection, the required dynamic aperture in the collider is only 8 sx. 5. For W, Z mode, the dynamic aperture in the collider is large enough, and we don’t need this on-axis injection.

DA requirement: Off-axis 13sx X 15 sy On-axis 8sx X 15 sy The required horizontal DA in the booster reduce from 13sx to 8sx. The required vertical DA also decrease a little. X Y On-axis 8sx X 15 sy X

Time structure of the booster: Exchange bunches between the booster and collider 26 times. 2.4 s 5.2 s 5 s Linac to booster Ramp up Ramp down Injection cycles Positron injection Electron injection 3% current decay in the collider The small bunch charge in booster is 3% of the charge of the colliding bunch in the collider. With a 3% current decay, the injection period of CEPC should be less than 47s. Current limit in the booster The bunch charge in the collider is 24nC, which is less than the booster's single bunch charge limit of 100 nC. At the beginning, only 7 bunches are injected into the booster, so that the current in the booster does not exceed the 1mA threshold limited by the RF power. 35.2 s

Injection from the collider to booster Bunch after injection Bunch before injection Septum A vertical off-axis injection Transfer beam from the collider to booster vertically. 4-kicker bump in the booster. Septum kicker Phase space of the first 100 turns

Injection from booster to the collider Bunch after injection Bunch before injection A vertical on-axis injection Septum Transfer beam back to the collider vertically. Septum quad kicker Phase space of the first 100 turns

Longitudinal phase shift We need to inject the bunch back into the same bucket after damping in the booster. The booster and collider has the same circumference, which makes this easier. Due to the different paths traveled by the injection beam and the circulating beam, a longitudinal deviation is introduced. Booster 261.2 m 2.4 m collider 261.189 m Longitudinal phase shift The length of the transport line is 261.2 meters, and the path difference between the injected beam and the circulating beam is only 0.011 meters, or 0.037 ns in time. This is equivalent to a 17 degree phase shift in the booster, and is in the stable region. This phase shift can be damped by synchrotron radiation. Or move the RF phase of the booster Did experiment at BEPC II, we found that 200 ms is enough to move a 17 degree.

Beam loading effect is weak Transient beam loading in the booster by the injection of large bunch and larger total beam current With 7 large bunches (0.07mA) evenly distributed among the other small bunches. Max cavity voltage drop is 0.48 %. Max phase shift is 0.63 deg. For 13 large bunches. Assume they are in a very short bunch train. Max cavity voltage drop is 5.8% . The maximum phase shift is 7.7 deg.

flip-flop instability We considered bunch instability due to the absence of several bunches in the collider. A beam-beam simulation shows that there is no flip-flop instability. Simulation result of Zhang Yuan

4. Summary An baseline injection design from Linac to the collider is discussed, which can work for Higgs, W, Z mode. An on-axis injection is designed to reduce the required dynamic aperture for Higgs energy injection. Future work will be more focused on the optimization of the injection design, and considering the hardware.

Thank you For your attention!