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

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

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

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

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

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

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