1. Initial Calculations of Intrabeam Scattering life times in ELIC lattices by Betacool code Chaivat Tengsirivattana CASA, Jefferson Lab University of Virginia The 4 th Electron-Ion Collider Workshop Hampton University, VA May 20,2008

2. 3-9 GeV electrons 3-9 GeV positrons 12 GeV CEBAF Upgrade Pre-booster Ion ring 30-225 GeV protons 15-100 GeV/u ions ELIC Conceptual Design

3. Figure-8 Ring with 80 deg. Crossing (2100 m circumference) Courtesy of Dr. Alex Bogacz 330 m 150 m 80 deg

4. 30 full cells 8 empty cells 3 transition cells Figure-8 Ion Ring (half) - Lattice at 225 GeV Courtesy of Dr. Alex Bogacz Arc dipoles: : $Lb=170 cm $B=73.4 kG $rho =102 m Arc quadrupoles: $Lb=100 cm $G= 10.4 kG/cm

5. ELIC design parameters of ion ring Courtesy of Dr. Yuhong Zhang ParameterUnitIon Ring Beam energyGeV22515010030 e/A ring circumferencekm2.1 Bunch collision frequencyGHz1.5 Number of particles/bunch10 0.420.4 0.12 Beam currentA1110.3 Energy spread, rms10 -4 3 Bunch length, rmsmm5 Beta*mm5 Horizontal emittance, norm mm 1.2510.70.2 Vertical emittance, norm mm 0.050.040.060.2 Beam-beam tune shift (vertical) per IP 0.0060.01 0.009 Peak luminosity per IP, 10 34 cm -2 s -1 7.47.75.50.8 Number of IPs4

6. Touschek Effect and Intrabeam Scattering 1.Touschek Effect -Large angle -transformation of a small transverse momentum into a large longitudinal momentum, due to relativistic effect -Both particles are lost immediately 2.Intrabeam Scattering -Small angle -Multiple scattering -Diffusion in all three dimension, change the beam dimensions

7. BETACOOL code – LEPTA lab, JINR, Russia Courtesy of Dr. Anatoly Sidorin Lattice structure -ELIC lattice Beam parameters -Set values Ring parameters -Set values

8. ParameterUnit Beam EnergyGeV30 Ring circumferencem2,100 Number of bunches10,509 Horizontal rms emittanceµm0.006026 Vertical rms emittanceµm0.006026 Number of Particles1.2 × 10 9 RF VoltageMV100 Case I: Beam Energy 30 GeV

11. Coulomb logarithm Definition :

12. ModelHorizontalVerticalLongitudinal Martini – Numerical3.4 min2.6 hr82.3 hr Martini – Analytical3.4 min2.6 hr82.3 hr Martini – Coulomb Log3.4 min2.6 hr82.3 hr Bjorken – Mtingwa26.2 sec 8.2 min Case I: Beam Energy 30 GeV

13. ParameterUnit Beam EnergyGeV100 Ring circumferencem2,100 Number of bunches10,509 Horizontal rms emittanceµm0.006511 Vertical rms emittanceµm0.0005581 Number of Particles4 × 10 9 RF VoltageMV350 Case II: Beam Energy 100 GeV

16. ModelHorizontalVerticalLongitudinal Martini – Numerical5.97 min51.5 min3.98 hr Martini – Analytical5.97 min51.5 min3.98 hr Martini – Coulomb Log5.97 min51.5 min3.98 hr Bjorken – Mtingwa5.39 min27.7 sec93.6 min Case II: Beam Energy 100 GeV

17. ParameterUnit Beam EnergyGeV150 Ring circumferencem2,100 Number of bunches10,509 Horizontal rms emittanceµm0.006220 Vertical rms emittanceµm0.0002488 Number of Particles4 × 10 9 RF VoltageMV520 Case III: Beam Energy 150 GeV

20. ModelHorizontalVerticalLongitudinal Martini – Numerical10.4 min78.7 min5.68 hr Martini – Analytical10.4 min78.7 min5.68 hr Martini – Coulomb Log10.4 min78.7 min5.68 hr Bjorken – Mtingwa16.2 min38.8 sec4.90 hr Case III: Beam Energy 150 GeV

21. ParameterUnit Beam EnergyGeV225 Ring circumferencem2,100 Number of bunches10,509 Horizontal rms emittanceµm0.005194 Vertical rms emittanceµm0.0002078 Number of Particles4.2 × 10 9 RF VoltageMV100 Case IV: Beam Energy 225 GeV

23. ModelHorizontalVerticalLongitudinal Martini – Numerical20.6 min6.2 hr10.2 hr Martini – Analytical20.6 min6.2 hr10.2 hr Martini – Coulomb Log20.6 min6.2 hr10.2 hr Bjorken – Mtingwa32.9 min80.0 sec11.93 hr Case IV: Beam Energy 225 GeV

26. Cooling rates E-Cooling30 GeV150 GeV Initial Cooling rate-1.1 x 10 -3 -1.7 x 10 -3 Cooling rate at Equilibrium-5.6 x 10 -2 -1.7 x 10 -2 Growth rates HorizontalVerticalLongitudinal 30 GeV Martini4.8 x 10 -3 1.0 x 10 -4 3.4 x 10 -6 Bjorken – Mtingwa 3.8 x 10 -2 2.0 x 10 -3 225 GeV Martini8.1 x 10 -4 4.5 x 10 -5 2.7 x 10 -5 Bjorken – Mtingwa5.1 x 10 -4 1.3 x 10 -2 2.3 x 10 -5 Electron Cooling Rates

27. Summary - Growth rates of new ring, 2100m, has been calculated. - Horizontal and Longitudinal life times are agreed between different models. - Discrepancy of life times in vertical (small) direction between models, trying to understand. - Beam could be cooled by electron cooling for longer life times