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IntraBeam Scattering Calculation

This document provides calculations and procedures for evaluating equilibrium emittances, radiation damping times, and IBS growth rates for low bunch charge. It includes formulas, approximations, and results for the ILC damping ring and SuperB parameters.

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IntraBeam Scattering Calculation

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

  2. Calculations procedure • Evaluate equilibrium emittances ei and radiation damping times ti at low bunch charge • Evaluate the IBS growth rates 1/Ti(ei) for the given emittances, averaged around the lattice, using K. Bane approximation (EPAC02) • 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) • 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 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.pdf

  6. Results for ILC damping ring configuration options A. Wolski

  7. Results for ILC damping ring configuration options A. Wolski

  8. SuperB parameters

  9. IBS momentum spread vs. number of particles/bunch p/p0= 1.05, @ N=5.5•1010 p/p0= 1.05, @ N=5.5•1010

  10. IBS horizontal emittance vs.number of particles/bunch h/h0=1.14, @ N=5.52•1010 h/h0=1.11, @ N=5.52•1010

  11. IBS vertical emittance vs. number of particles/bunch for r = 0, 0.5, 1

  12. LER lattice - IBS emittance growth @ N=5.5e10 with and without wigglers 12 wigglers wig = 0.4m Lwig = 2.45m Nominal values

  13. LER lattice - IBS emittance growth for different wiggler fields N=5.5e10

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

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

  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

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