1. Parameters Changed in New MEIC Design
Old
Circumference
2.5
1.416 km
Rev Frequency
0.120
0.212
MHz
Harmonic Number
6251
3535
Dipole Bending Radius (e)
110
57.94 m
Dipole Bending Radius (p)
130
Dipole Bend Angle (e)
2.8125
1.98
degree
Dipole Bend Angle (p)
2.64
Crossing Angle 90 60
Angle Factor
1.500
1.333
Arc Length
879.38
445.34
Momentum Compaction (e)
2.366E-04
7.60E-04
Momentum Compaction (p)
3.1E-03
5.76E-03
Total SR Power Limit (e) 10 5 MW

2. At High Energy End, e Current is limited by SR Power, Total or Linear
NEW
OLD
Linear
Total: 10 MW
Linear
Total: 5 MW
GeV
GeV
𝑃 𝑙𝑖𝑛𝑒𝑎𝑟 = 𝐶 𝑆𝑅 𝐸 4 𝐼 2𝜋 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒 2
𝑃 𝑡𝑜𝑡𝑎𝑙 = 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝐼 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒

3. e Current at Low Energy End
OLD
NEW

4. Cavity Number
We want less cavities for impedance and cost budget reason;
We need enough cavities to average out the maximum gradient and coupler feed forward power;
OLD
NEW
500 kW / cavity
12.5 MV / m

5. Longitudinal Impedance Threshold at 5 GeV
𝑍 || 𝑡ℎ𝑟𝑒𝑠ℎ = 2𝐸 𝜐 𝑠 𝑁 𝑐𝑎𝑣 𝑓 HOM 𝐼 𝑏 𝛼 𝜏 𝑠
𝑍 || 𝑡ℎ𝑟𝑒𝑠ℎ = 2 𝑓 𝑅𝐸𝑉 𝜐 𝑠 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝑁 𝑐𝑎𝑣 𝑓 HOM 𝐼 𝑏 𝛼 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒
𝜏 𝑠 ≈ 𝐸 Δ𝐸 𝑓 rev
𝑍 || 𝑡ℎ𝑟𝑒𝑠ℎ ∝ 𝜐 𝑠 𝐹 𝜑 𝑓 rev 𝑁 𝑐𝑎𝑣 𝛼 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒 =𝐾
∆𝐸 𝑙𝑜𝑠𝑠 𝑝𝑒𝑟 𝑡𝑢𝑟𝑛 = 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒
Parameters
New
Old
Syn Tune
0.007
0.013
Angle Factor
1.5
1.333
Rev Freq (MHz)
0.12
0.212
N cavity 5 8
Momentum Comp
2.366e-4
7.5e-4
Dipole Bending R (m)
110
57.94 K
0.968e4
1.057e-4

6. Impedance Threshold for Single Cavity at 3 A, 5 GeV,
21 Cavities in Total

7. Transverse Impedance Threshold
𝑍 𝑥, 𝑦 𝑡ℎ𝑟𝑒𝑠ℎ = 2𝐸 𝑁 𝑐𝑎𝑣 𝑓 rev 𝐼 𝑏 𝛽 𝑥,𝑦 𝜏 𝑥,𝑦
𝜏 𝑠 ≈ 𝐸 Δ𝐸 𝑓 rev
𝑍 𝑥, 𝑦 𝑡ℎ𝑟𝑒𝑠ℎ = 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝑁 𝑐𝑎𝑣 𝐼 𝑏 𝛽 𝑥,𝑦 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒
∆𝐸 𝑙𝑜𝑠𝑠 𝑝𝑒𝑟 𝑡𝑢𝑟𝑛 = 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒
NEW
OLD

8. Stage Operation of e Ring
12 GeV operation requires 21 RF cavities for SR energy compensation.
Lower energy operations need less cavities.
If all 21 cavities are installed, the total cavities impedance will be unnecessarily high for low energy operation, which will significantly lower the maximum allowable e current.
Or, if we can move unneeded cavities out of beam line to lower the total cavity impedance, we can run with higher e current at low energy. But, is this measure practical in operation?
𝑍 || 𝑡ℎ𝑟𝑒𝑠ℎ = 2𝐸 𝜐 𝑠 𝑁 𝑐𝑎𝑣 𝑓 HOM 𝐼 𝑏 𝛼 𝜏 𝑠

9. With 21 cavities for All Energies  235 mA @ 3 GeV
Impedance with 5 GeV is used as the reference, e current needs to be decreased for energy lower than 5 GeV.

10. Use Less Cavities for Lower Energies  1.17 A @ 3 GeV
Current
Total Impedance
RF Input power
Cavity Number

11. RF Gradient at 12 GeV NEW OLD 21 Cavities, 6.9 MV/m3
Coupler power limited
20 Cavities,
12.5 MV/m
Gradient limited

12. RF Cavity Parameters in e Ring
Energy 3 5 12
GeV
gamma
5871.8
9785.7
Current
0.24
3.00
0.41 A
Energy Spread
3.40E-04
5.60E-04
1.35E-03
Phase Slip Factor
2.4E-04
SR power per ring
0.02
2.26
10.37 MW
Energy Loss per Turn
0.10
0.75
25.05
MeV
SR power per unit length
0.022
2.184
10.000
kW/m
Veff MV
Vpeak
0.25
1.30
29.06
Syn. Phase
22.80
35.65
59.51
degree
Vgap
0.26
1.38
Gradient
1.263
1.295
6.920
MV/m
Syn. Tune
0.004
0.007
0.017
Beam Power per Cavity
23.1
452.9
493.7 kW
Forward Power
25.98
465.52
498.92
Cavity Power Loss
2.35E-05
2.48E-05
7.07E-04
Reflected Power
2.9
12.6
5.2
Coupling Beta
1.96E+06
2.29E+07
8.12E+05 δf
-67.7
-593.0
-8.9
kHz
Qext
6.57E+03
5.64E+02
1.59E+04
Qloaded
Long. SR Damping Time
256.09
55.31
4.00 mS
Tran. SR Damping Time
512.17
110.63
8.00
Active Cavity Number 1 21
Circumference m
Rev Frequency
0.120
MHz
RF frequency
Harmonic Number
6251
Radius of Dipole
Dipole Bend Angle
2.813
degree
Crossing Angle
90.000
Angle Factor
1.500
Arc Length
Beta Function at RF Cav
4.000
Momentum Compaction
2.366E-04
Bunch Length
7.5 mm
Linear SR Power Limit 10
kW/m
Total SR Power Limit MW
CavityActiveLength
0.2
Cavity Insertion Length
1.91
temperature
2.1 K
BCS Resistance
7.918 nΩ
Residual Resistance 13
Surface Resistance
20.9
Geometric Factor
270
R/Q
105
Qzero
1.29E+10
Shunt Impedance
1.36E+06 MΩ

13. Robinson Stable Region
Strong beam loading requires direct RF cavity feedback to increase the stable operation margin.

14. Ion Collider Ring Bunching Cavities
Particle
Proton
Lead ion
Energy 78 35
GeV/u
gamma
84.1
38.7
Current
0.50 A
Energy Spread
3.00E-04
Phase Slip Factor
3.0E-03
2.4E-03
Vpeak
33.15
31.03 MV
Syn. Phase
0.00
degree
Vgap
1.95
1.83
Gradient
9.750
9.125
MV/m
Syn. Tune
0.035
0.029
Forward Power
182.24
346.71 kW
Cavity Power Loss
1.40E-03
1.23E-03
Reflected Power
182.2
346.7
Coupling Beta
5.00E+05 δf
-17.3
-5.3
kHz
Qext
2.58E+04
Qloaded
Active Cavity Number 17
Circumference m
Rev Frequency
0.120
MHz
RF frequency
Harmonic Number
6251
Radius of Dipole
Dipole Bend Angle
2.640
degree
Crossing Angle
90.000
Angle Factor
1.500
Arc Length
Momentum Compaction
3.100E-03
Bunch Length 10 mm
CavityActiveLength
0.2
Cavity Insertion Length
1.91
temperature
2.1 K
BCS Resistance
7.918 nΩ
Residual Resistance 13
Surface Resistance
20.9
Geometric Factor
270
R/Q
105
Qzero
1.29E+10
Shunt Impedance
1.36E+06 MΩ

15. Robinson Stability
Ibeam
Ibeam
Itotal
Itotal
Igenerator
Igenerator

16. Longitudinal Impedance Threshold for 78 GeV Proton

17. Low Frequency RF Systems, 15.5 ~ 78 GeV, H = 8
RF cavity type Ferrite loaded RF cavity
Harmonic number 8
Cavity Number 2
Gap number per cavity 2
Cavity length (m) 2.2
Ferrite toroid inner radius (m) 0.25
Ferrite toroid outer radius (m) 0.5
Ferrite stack length (m) 1.0
Maximum Vgap (kV) 10.0
Ion species protons (H+)
Energy (GeV/u) ~78
Frequency Range (MHz) ~0.958
Ramping Time (sec) 10
Vgap (kV) 5.2
Beam Absorbed Power (kW) 26.1
Total Power Lossave (kW) 118

18. THE END

19. Example of Space for RF Cavities
x= x=3m
F. Lin