1. IntraBeam Scattering Calculation
T. Demma, S. Guiducci
27 January 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, (2005)

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

4. ILC Damping Ring OCS Parameters
Energy (GeV) 5
Circumference (m)
6114
N particles/bunch
2x10-10
Damping time x (ms) 22
Emittance gex (nm)
5500
Emittance gey (nm) 20
Momentum compaction
1.6 x10-4
Energy spread
1.3x10-3
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

5. Results for ILC damping ring configuration options
OCS conf. options
OCS this calculation
N/bunch
2 1010
xibs/x0
1.2
1.23
yibs/y0
@ r=0.5
1.1
1.12
pibs/p0
1.01
libs/l0
A. Wolski

6. SuperB parameters h[nm] v [pm] s [mm] p/p h/ s [ms] E[Gev] HER 7
1.6 4 5
5.8e-4
40/20
LER
2.8
8e-4

7. IBS Horizontal emittance growth vs
IBS Horizontal emittance growth vs. number of particles/bunch for r = 0, 0.5, 1

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

9. IBS relative momentum spread growth vs
IBS relative momentum spread growth vs. number of particles/bunch for r = 0, 0.5, 1

10. Conclusions Next steps:
Retune the arc cells to get the nominal emittance with the IBS
Add some wigglers to get the nominal emittance with the IBS
In any case only minor modifications are needed since the emittance growth is quite small
Both HER and LER have ~ the same emittance growth: an optimum parameter choice