1. Machine parameters of SuperKEKB
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. 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

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

5. 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.

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

7. 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

8. 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.

9. 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)

10. 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

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