1. RF Parameters for New 2.2 km MEIC Design
Shaoheng Wang
11/06/2014
CASA

2. RF Cavities in e Ring Limiting Factors Tasks SRF Cavities
Compensate SR Energy loss,
As high as 25 MeV/turn
Maintain the Short Bunch Length: 1.2 mm
Maintain Stable Beam Longitudinal Motion:
Robinson, Multibunch
Gradient < 10 MV/m
Forward Power per Cavity
< 500 kW
HOM Impedance Small Enough to Avoid Multi-bunch Instability
Cyro Operation
Limited Space in Ring
Cost
SRF Cavities

3. Electron Ring Parameters
Input Parameters
Electron Ring Parameters
Circumference m
Rev Frequency
0.139
MHz
RF frequency
Harmonic Number
5379
Radius of Dipole
Dipole Bend Angle
2.801
degree
Crossing Angle
81.700
Angle Factor
1.454
Beta Function at RF Cav
5.000
Momentum Compaction
2.142E-03
Bunch Length 12 mm
Linear SR Power Limit 10
kW/m
Total SR Power Limit MW
CavityActiveLength
0.20
Cavity Insertion Length
1.91
temperature
4.2 K
BCS Resistance
215.32 nΩ
Residual Resistance
3.89
Surface Resistance
219.2
Geometric Factor
192.4
R/Q
105.7
Qzero
8.78E+08
Shunt Impedance
9.27E+04 MΩ
Ring Design
Cavity
Design

4. Total RF Voltage and Syn Phase
𝜎= 𝑐 𝜂 𝜔 𝑠 𝛿𝐸 𝐸 = 2𝜋 𝑐 𝜔 𝐸 𝐻𝑒 𝑉 𝑝𝑒𝑎𝑘 𝜂 cos 𝜓 𝑠 𝛿𝐸 𝐸
𝑉 𝑝𝑒𝑎𝑘 sin 𝜑 𝑠 = 𝑉 𝑒𝑓𝑓
Maintain the Short
Bunch Length: 1.2 mm

5. Current, Beam Power, Cavity Number, Impedance
Gradient limit
Forward power limit
Cavity Number
Beam
Power
Impedance
Multi-bunch
Instability
Current
SR energy loss
Luminosity

6. Staged Operation

7. 3A @ 5GeV, Impedance Spectrum, Feedback (Factor of 3)

8. Saw-tooth Beam Current Profile

9. Operation Point, Robinson Instability, Pfwd Limit, Efficiency

10. Output Parameters Energy 3 5 12 GeV gamma 5871.8 9785.7 23484.4
GeV
gamma
5871.8
9785.7
Current
1.18
3.00
0.41 A
Energy Spread
3.40E-04
5.60E-04
1.35E-03
Phase Slip Factor
2.1E-03
SR power per ring
0.11
2.19
10.00 MW
Energy Loss per Turn
0.09
0.73
24.18
MeV
SR power per unit length
0.110
2.167
10.000
kW/m
Veff MV
Vpeak
0.71
3.29
50.80
Syn. Phase
7.59
12.82
28.42
degree
Vgap
0.66
1.95
Gradient
3.6
3.3
9.8
MV/m
Syn. Tune
0.021
0.034
0.083
Power fed to beam per Cavity
111.5
437.2
384.6 kW
Forward Power
200.6
477.5
397.0
Cavity Power Loss
5.5
4.7
41.2 W
Reflected Power
89.2
40.2
12.4
Coupling Beta
1.01E+05
1.71E+05
1.33E+04 δf
-64.7
-176.1
-7.4
kHz
Qext
8.67E+03
5.14E+03
6.57E+04
Qloaded
Long. SR Damping Time
228.28
49.31
3.57 mS
Tran. SR Damping Time
456.57
98.62
7.13
Active Cavity Number 1 26
Temperature
4.2 K

11. SRF Cavities in ion Collider Ring
Limiting Factors
Tasks
Gradient < 10 MV/m
Forward Power per Cavity
< 500 kW
HOM Impedance Small Enough to Avoid Multi-bunch Instability
Cyro Operation
Limited Space in Ring
Cost
Maintain the Short Bunch Length: 1.2 mm
Maintain Stable Beam Longitudinal Motion:
Robinson, Multibunch
SRF Cavities

12. Preliminary Parameters
Particle
Proton
Energy
100
GeV
gamma
107.6
Current
0.50 A
Energy Spread
2.00E-04
Phase Slip Factor
9.5E-03
Vpeak
36.29 MV
Syn. Phase
0.00
degree
Vgap
1.65
Gradient
8.238
MV/m
Syn. Tune
0.054
Forward Power
146.73 kW
Cavity Power Loss
2.93E+01
Reflected Power
146.7
Coupling Beta
2.00E+04 δf
-12.0
kHz
Qext
4.39E+04
Qloaded
Active Cavity Number 22
Circumference m
Rev Frequency
0.139
MHz
RF frequency
Harmonic Number
5379
Radius of Dipole
Dipole Bend Angle
4.090
degree
Crossing Angle
81.700
Angle Factor
1.454
Arc Length
Momentum Compaction
9.6E-03
Bunch Length 12 mm
CavityActiveLength
Cavity Insertion Length
1.91
temperature
4.2 K
BCS Resistance nΩ
Residual Resistance
Surface Resistance
219.2
Geometric Factor
R/Q
Qzero
8.78E+08
Shunt Impedance
9.27E+04 MΩ

13. Low Frequency RF Cavities in Booster and Ion Collider Ring
To be presented soon.