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Machine parameters of SuperKEKB

SuperKEKB Mini Workshop November 28, 2003. Machine parameters of SuperKEKB. Y. Ohnishi / KEK. Luminosity. Luminosity formula: Alternative luminosity formula: Beam-beam parameter: Transparency condition:. N : number of particles/bunch f : collision frequency. s y * / s x * = 1%-6%

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Machine parameters of SuperKEKB

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  1. SuperKEKB Mini Workshop November 28, 2003 Machine parameters of SuperKEKB Y. Ohnishi / KEK

  2. Luminosity • Luminosity formula: • Alternative luminosity formula: • Beam-beam parameter: • Transparency condition: N : number of particles/bunch f : collision frequency sy*/sx* = 1%-6% RL/Rxy= ~0.8 w/o dynamical effect due to beam-beam Assumed that no beam size blowup due to electron cloud.

  3. ex/ey=18/0.18 nm ex/ey=30/1.8 nm Luminosity reductions • Luminosity reduction • Beam-beam reduction K0 : Bessel function qx : crossing angle (in the boosted frame) Montague's factor longitudinal beam distribution

  4. List of machine parameters Luminosity 1035 is optimized by by*=3 mm, xy=0.05, I=9.4/4.1 A.

  5. includes beam size ratio and ratio of reduction factors. Beam-beam parameters • Luminosity is given by overlap integral: (cm-2s-1) (Ohmi, beam-beam simulations) ~1 ~0.8

  6. Coherent synchrotron radiation • SR is emitted independently when wave length is shorter than bunch length. • Intensity ∝ N (E ∝ N1/2;statistical) • SR of longer wave length is emitted coherently. (E ∝ N;same phase) • Intensity ∝ N2 ←Coherent Synchrotron Radiation (CSR) • CSR spectrum region is enlarged as bunch length decreases. Refs. : Yokoya, Oho2003, Juhao Wu, G. Stupakov, et al., SLAC-PUB-9629, G. Stupakov and S. Heifets, PR-ST vol.5 054402

  7. L=rq A ~ c B g B' A' g +z Coherent synchrotron radiation (cont'd) Emitted energy per unit orbit length : • Head of bunch is accelerated, tail of bunch is decelerated. Energy gain is expressed by : F(z/sz) z Head of bunch Tail of bunch

  8. Coherent synchrotron radiation (cont'd) • Wakefield catch up bunch ? • Shielding effect L=rq A ~ c B g B' Short range in a bunch ! A' 3 mm g half of chamber height : h C If chamber height >> h, reflected light reaches after bunch passes through. L A B shielding cut-off wave length : lc ~ 4 mm (r=23/2/p1/2) in LER SR at longer wave length is shielded. Coefficient r has less accuracy.

  9. On ReZ and ImZ plane W→+i0 n0 : number of particles/unit length CSR in wiggler • Dispersion relation: • Impedance of wiggler (low frequency) Particles : Gaussian distribution Bw : peak magnetic field of the wiggler (0.773 T) lw : period in meter (1.6 m)

  10. Lw = 120 m (half of KEKB LER) sz = 6 mm sz = 5 mm sz = 4 mm sz = 3 mm CSR in wiggler (cont'd) • Threshold wave length vs bunch current

  11. Integrated luminosity Hazumi 5x1035 major upgrade more RF crab cavities more RF

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