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# Machine parameters of SuperKEKB - PowerPoint PPT Presentation

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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November 28, 2003

### Machine parameters of SuperKEKB

Y. Ohnishi / KEK

• 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.

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

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

• 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

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

• 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.

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)

sz = 6 mm

sz = 5 mm

sz = 4 mm

sz = 3 mm

CSR in wiggler (cont'd)

• Threshold wave length vs bunch current

Hazumi

5x1035

major

upgrade

more RF

crab cavities

more RF