1. He Zhang, David Douglas, Yuhong Zhang MEIC R&D Meeting, 09/04/2014
Development of ERL-CC cooler parameters: preliminary consideration for the cooler solenoid
He Zhang, David Douglas, Yuhong Zhang
MEIC R&D Meeting, 09/04/2014

2. Summary
Checked parameters of non-magnetized electron beam in the cooling solenoid
Beam transport (matched beam)
Space charge
Electron beam temperature
Cooling rate
Non-magnetized electron beam will NOT work
He Zhang

3. Beam Transport Larmor motion
Electron mass is much less than proton mass. With other parameters the same, the Larmor frequency of electron is much higher (~2000 times) than that of proton.
Constant 𝛽 function for electrons in the solenoid (matched electron beam)
𝐵 0 is the solenoid field
He Zhang

4. Beam Transport No need to match the 𝛽 function for protons
When 0.5∗𝐾𝐿 is small
Space charge dominated or not?
𝐼 – beam peak current, 𝜎 – RMS beam size,
𝜀 𝑛 – normalized emittance, 𝐼 𝐴 – Alfen current
𝐼 𝐴 =31 MA for protons, 𝐼 𝐴 =17 kA for electrons
𝑅 0 >1 space charge dominated
He Zhang

5. At the Injection Energy (Kp=25 GeV)
Protons
𝜀 𝑛 (μm·rad)
𝛽 𝑐𝑒𝑛𝑡𝑒𝑟 (m)
𝛽 𝑒𝑛𝑑 (m)
𝜎 𝑐𝑒𝑛𝑡𝑒𝑟 (mm)
𝜎 𝑒𝑛𝑑 (mm)
𝑙 𝑝 (cm)
𝑇 𝑝 (eV)
0.8 10
32.5
0.5
0.9
coasting
2073
Electrons
𝐵(T)
𝛽 𝑚𝑎𝑡𝑐ℎ (cm)
𝜎 𝑒 (mm)
𝑙 𝑒 (cm)
𝜀 𝑛 (μm·rad)
𝑇 𝑒 (eV)
𝑅 0 2
4.71
1.1
700
2× 10 5
3× 10 −4 1
9.43
300
5× 10 4
1.3× 10 −3
0.03
314
8.79
39.52
0.70
Non-magnetized cooling rate:
Assuming 𝜀 𝑛 =0.8 μm⋅rad, when 𝐵=0.03 T, 𝑅 𝑐 =3× 10 −4 s −1 , 𝑡=3031s.
He Zhang

6. At the Collision Energy (Kp=100 GeV)
Protons
𝜀 𝑛 (μm·rad)
𝛽 𝑐𝑒𝑛𝑡𝑒𝑟 (m)
𝛽 𝑒𝑛𝑑 (m)
𝜎 𝑐𝑒𝑛𝑡𝑒𝑟 (mm)
𝜎 𝑒𝑛𝑑 (mm)
𝑙 𝑝 (cm)
𝑇 𝑝 (eV)
0.3 10
32.5
0.2
0.36 1
3028
Electrons
𝐵(T)
𝛽 𝑚𝑎𝑡𝑐ℎ (cm)
𝜎 𝑒 (mm)
𝑙 𝑒 (cm)
𝜀 𝑛 (μm·rad)
𝑇 𝑒 (eV)
𝑅 0 2
18.34
1.1
700
2× 10 5
8× 10 −5 1
36.68
300
5× 10 4
4× 10 −4
0.12
314
0.5
8.79
153.9
0.05
Non-magnetized cooling rate:
Assuming 𝜀 𝑛 =0.3 μm⋅rad, when 𝐵=0.12 T, 𝑅 𝑐 =1.1× 10 −5 s −1 , 𝑡=9× 10 4 s.
He Zhang

7. Magnetized Cooling Time Estimation
Magnetized cooling time (V. Parkhomchuk)
END
He Zhang