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

At High Energy End, e Current is limited by SR Power, Total or Linear NEW OLD Linear Total: 10 MW Linear Total: 5 MW 0.4 A @ 12 GeV 0.1 A @ 12 GeV 𝑃 𝑙𝑖𝑛𝑒𝑎𝑟 = 𝐶 𝑆𝑅 𝐸 4 𝐼 2𝜋 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒 2 𝑃 𝑡𝑜𝑡𝑎𝑙 = 𝐹 𝜑 𝐶 𝑆𝑅 𝐸 4 𝐼 𝑅 𝑑𝑖𝑝𝑜𝑙𝑒

e Current at Low Energy End OLD NEW

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

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

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

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

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

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

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

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

RF Cavity Parameters in e Ring Energy 3 5 12   GeV gamma 5871.8 9785.7 23484.4 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 2503.678 m Rev Frequency 0.120 MHz RF frequency 748.500 Harmonic Number 6251 Radius of Dipole 110.000 Dipole Bend Angle 2.813 degree Crossing Angle 90.000 Angle Factor 1.500 Arc Length 879.380 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

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

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 2503.501 m Rev Frequency 0.120 MHz RF frequency 748.500 Harmonic Number 6251 Radius of Dipole 130.000 Dipole Bend Angle 2.640 degree Crossing Angle 90.000 Angle Factor 1.500 Arc Length 875.000 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

Robinson Stability Ibeam Ibeam Itotal Itotal Igenerator Igenerator

Longitudinal Impedance Threshold for 78 GeV Proton

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) 15.5~78 Frequency Range (MHz) 0.956~0.958 Ramping Time (sec) 10 Vgap (kV) 5.2 Beam Absorbed Power (kW) 26.1 Total Power Lossave (kW) 118

THE END

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