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 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.

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

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

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

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

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

Coherent synchrotron radiation (cont'd) Wakefield catch up bunch ? Shielding effect A L=rq ~ c B g B' Short range in a bunch ! A' g 3 mm half of chamber height : h C If chamber height >> h, reflected light reaches after bunch passes through. A L 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.

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

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

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