1. IntraBeam Scattering Calculation T. Demma, S. Guiducci SuperB Workshop LAL, 17 February 09

2. Calculations procedure 1.Evaluate equilibrium emittances  i and radiation damping times  i at low bunch charge 2.Evaluate the IBS growth rates 1/T i (  i ) for the given emittances, averaged around the lattice, using K. Bane approximation (EPAC02) 3.Calculate the "new equilibrium" emittance from: For the vertical emittance use* : where r  varies from 0 (  y generated from dispersion) to 1 (  y generated from betatron coupling) 4.Iterate from step 2 * K. Kubo, S.K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams," Phys. Rev. ST Accel. Beams 8, 081001 (2005)

3. Bane's approximation K. Bane, “A Simplified Model of Intrabeam Scattering,” Proceedings of EPAC 2002, Paris, France (2002)

4. Completely-Integrated Modified Piwinski formulae K. Kubo, S.K. Mtingwa, A. Wolski, "Intrabeam Scattering Formulas for High Energy Beams," Phys. Rev. ST Accel. Beams 8, 081001 (2005).

5. ILC Damping Ring OCS Parameters Energy (GeV)5 Circumference (m)6114 N particles/bunch2x10 -10 Damping time  x (ms) 22 Emittance  x (nm) 5500 Emittance  y (nm) 20 Momentum compaction1.6 x10 -4 Energy spread1.3x10 -3 Bunch length (mm)6.0 To check the code the IBS effect calculated for the ILC damping ring OCS lattice has been compared with the results for the configuration options A. Wolski, J. Gao, S. Guiducci eds., “Configuration Studies and Recommendations for the ILC Damping Rings”, LBNL–59449, February 2006 https://wiki.lepp.cornell.edu/ilc/pub/Public/DampingRings/ConfigStudy/DRConfigRecommend.pdfhttps://wiki.lepp.cornell.edu/ilc/pub/Public/DampingRings/ConfigStudy/DRConfigRecommend.pdf

6. Results for ILC damping ring configuration options A. Wolski OCS conf. options OCS this calculation N/bunch2 10 10  x ibs /  x 0 1.21.23  y ibs /  y 0 @ r  =0.5 1.11.12  p ibs /  p 0 1.01  l ibs /  l 0 1.01

7. Results for ILC damping ring configuration options A. Wolski N0.1e101.0e102.0e10  x /  x0 1.011.121.23  y /  y0 1.011.061.12  p /  p0 1.001.0031.006  x (nm) 0.560.620.68  y (pm) 2.012.122.23 pp 0.0013  l (mm) 6.0 6.1

8. SuperB parameters E[Gev]  h [nm]  v [pm]  s [mm]  p /p  h /  s [ms] HER71.6455.8e-440/20 LER42.8758e-440/20

9. IBS momentum spread vs. number of particles/bunch  p /  p0 = 1.05, @ N=5.510 10

10. IBS horizontal emittance vs.number of particles/bunch  h /  h0 =1.14, @ N=5.5210 10  h /  h0 =1.11, @ N=5.5210 10

11. IBS vertical emittance vs. number of particles/bunch for r  = 0, 0.5, 1 N=5.5210 10  v /  v0 rr 1.100 1.110.5 1.151 N=5.5210 10  v /  v0 rr 1.080 1.100.5 1.131

12. LER lattice - IBS emittance growth @ N=5.5e10 with and without wigglers No IBSWith IBS B wig (T)0.0.850.0.85 V RF (MV)5.46.35.46.3  x,y (ms) 39.032.439.032.4  p (ms) 19.516.219.516.2  x /  x0 1.151.18  y /  y0 1.101.12  p /  p0 1.06 xx 2.7e-92.3e-93.1e-92.7e-9 yy 7.0e-126.3e-127.7e-127.0e-12 ll 5.04.75.35.0 pp 8.1e-48.2e-48.6e-48.7e-4 12 wigglers wig = 0.4m L wig = 2.45m Nominal values

13. LER lattice - IBS emittance growth for different wiggler fields B wig (T)0.1.01.31.6 V RF (MV)5.46.67.38.7  x,y (ms) 39.030.526.522.8  p (ms) 19.515.313.311.4  x /  x0 1.151.18  y /  y0 1.101.121.11  p /  p0 1.06 1.041.03  x0 2.7e-92.1e-91.9e-91.7e-9  y0 7.0e-126.3e-12  p0 8.1e-48.4e-49.0e-49.9e-4  l0 5.04.74.8 xx 3.1e-92.5e-92.3e-92.0e-9 yy 7.7e-127.0e-12 pp 8.6e-48.9e-49.4e-41.0e-3 ll 5.35.0 N=5.5e10

14. Insertion of Wigglers Damping time  x,y and RF voltage V RF vs. wiggler field B w B w (T) Relative energy spread  p and emittance  x vs. wiggler field B w N = 5.5e-10,  l = 5mm,  y = 7pm

15. Emittance and sigmap vs. wiggler field with ( ) and without (---) IBS Nominal value xx pp

16. Conclusions The effect of IBS on the transverse emittance is reasonably small for both rings It can be compensated by adding 12 low field wigglers to get the nominal transverse emittance at the expenses of an increased energy spread and RF voltage Another possibility to get the nominal emittance is to increase the phase advance in the arc cells An interesting study: develop a MonteCarlo code to study the beam size distribution in the presence of IBS