1. Intra-beam Scattering Study for Low Emittance of BAPS S.K.Tian(IHEP)

2. Outline  Intra-beam scattering theory  BAPS machine parameters(a temporary design lattice )  Recent BAPS IBS calculations

3. Intra-Beam Scattering  Particles in a circular accelerator execute transverse betatron oscillations, the transverse velocities are statistically distributed, these particles can be scattered by collisions so transferring transverse momenta into longitudinal momenta, In general, one should distinguish between:  large-angle single scattering ---TOUSCHEK effect---Lift time  multiple small-angle scattering---intra-beam scattering---Rise time Sketch maps

4. Conventional theory of IBS Conventional IBS theory in Accelerator Physics (Bjorken-Mtingwa) derive T i by the formula: indicates that the integral is to be averaged around the accelerator lattice S6 S1 S5 S4 S3 S2

5. Basic Parameters of BAPS ParameterSymbol, unitValue Beam energyE, GeV5 CircumferenceC, m1364.8 Beam currentI 0, mA100 Bunch numbernbnb 1836 Number of particles per bunchNbNb 1.55  10 9 Natural bunch length  l0, mm 2.9 RF frequencyf rf, MHz500 Harmonic numberh2276 Natural energy spread e0e0 1.5  10  3 Momentum compaction factor pp 4  10  5 Betatron tune x / y 113.4/39.3 Synchrotron tune s 0.004 Damping time (H/V/s)  x /  y /  z, ms 28, 43, 29 Emittance (horz./vert.)  x /  y, pm 10/10 Trans. beam size (horz./vert.)  x /  y,  m 4.4/7.4

6. Lattice functions in the BAPS ring Circumference: 1364.8 m, 2 superperiods, 36 supercells Working point: 111.39, 39.30 Natural chromaticity: -184, -181 Natural emittance: 51 pm.rad Y. Jiao

7. Recent BAPS IBS calculations IBS effect – Scan on Energy Steady-state horizontal emittance VS. energy @coupling=0.01

8. Recent BAPS IBS calculations IBS effect---particle numbers Steady-state horizontal emittance VS. bunch current@coupling=0.01

9. Recent BAPS IBS calculations IBS effect – Scan on coupling factor Steady-state horizontal emittance VS. the coupling factor@I=100mA For simplicity and for the purpose of IBS calculations, we assume that the vertical emittance is primarily generated by the coupling, and the effects of the vertical dispersion can be ignored.

10. Recent BAPS IBS calculations IBS effect – damping wiggler the emittance reduction depends on the wiggler period length, the wiggler peak field, and the total wiggler length. Relative emittance reduction versus wiggler lengthRelative emittance reduction versus wiggler field

11. Recent BAPS IBS calculations Damping Ratio: 0.27618 elegant:ex0 (m) = 1.403855e-011 Emittance_w0: 14.09157 [pm] U0 (MeV) = 1.072198e+000  6.259949e+000

12. Recent BAPS IBS calculations Steady-state horizontal emittance @different current and different emity

13. Recent BAPS IBS calculations Accumulated growth rates in x VS. Hx along the ring

14. Conclusions  Intra-beam scattering is an effect which becomes important in future low emittance ring-base light sources and becomes a limiting factor for reaching ultimate storage ring.  To compensate the IBS emittance growth, we can use one or more strong damping wigglers in dispersion-free regions.  Changing the coupling factor can reduce the IBS effect, how to obtain k=1 in electron storage rings is an interesting topic.

15. Reference ： M. Borland, "elegant: A Flexible SDDS- Compliant Code for Accelerator Simulation,“ Advanced Photon Source LS-287, September 2000. Karl Bane, Kirk Bertsche, Yunhai Cai ， etc A Design Report of the Baseline for PEP-X: an Ultra-Low Emittance Storage Ring