622
K. Hübner et al.
Table 10.12 Progress of machine parameters of the PEP–II and KEKB B-factories
PEP–II
KEKB (no crab) KEKB (crab)
8/16/2006
11/15/2006
6/17/2009
Date
LER
HER
LER
HER
LER
HER
Circumference [m]
2200
3016
Beam energy [GeV]
3.1
9.0
3.5
8.0
3.5
8.0
Effective crossing angle [mrad]
0
22
0 (crab)
Beam current [A]
2.90
1.88
1.65
1.33
1.64
1.19
Bunches
1722
1389
1584
Bunch current [mA]
4.02
1.09
1.19
0.96
1.03
0.71
Bunch spacing [m]
1.2
1.8–2.4
1.8
Horizontal emittance ε x [nm]
30
50
18
24
18
24
RF frequency [MHz]
476
509
Bunch length σ z [mm]
10
10
8
6
8
6
β ∗
x [cm]
30
30
59
56
120
120
β ∗
y [cm]
0.9
1.1
0.65
0.59
0.59
0.59
Horizontal size @ IP [μm]
95
158
103
116
147
170
Vertical size @ IP [μm]
4.7
4.7
1.9
1.9
0.94
0.94
Beam-beam ξ x
0.072 0.064 0.115 0.075
0.125 0.100
Beam-beam ξ y
0.064 0.053 0.104 0.058
0.130 0.090
Luminosity [nb −1 s −1 ]
12.1
17.6
21.1
Integrated luminosity/day [pb −1 ]
858
1260
1479
Integrated luminosity/7 days [fb −1 ]
5.41
7.82
8.43
Integrated luminosity/30 days [fb −1 ] 19.8
30.2
23.0
Total integrated luminosity [fb −1 ]
557
1040
The left, center, right correspond to the highest performance of PEP–II, KEKB (no crab) and
KEKB (crab), respectively. The integrated luminosities are the delivered numbers for PEP–II, and
recorded for KEKB. 1 nb −1 = 10 33 cm −2 s −1
and the definition of luminosity
L =
N + N − f
4πσ ∗
x σ ∗
y
R L
(10.3)
where N and f are the number of particles per bunch and the collision frequency
(I = Nef ), respectively, and we have assumed the beam sizes are common in two
beams. The factors R L , x, y are the geometric reduction factors due to the hour-glass
effect and the crossing angle.
While a round-beam scheme may have a merit of a factor of 2 on the luminosity
according to Eq. (10.1), a flat beam scheme has been chosen in most e + e − colliders,
as the round-beam focusing in both planes is more difficult for an extremely small
β ∗ . For a flat beam, σ ∗
x σ ∗
y , the luminosity is written as
L ≈
1
2er e
γ Iξ y
β ∗
y
±
R L
R y
.
(10.4)
K. Hübner et al.
Table 10.12 Progress of machine parameters of the PEP–II and KEKB B-factories
PEP–II
KEKB (no crab) KEKB (crab)
8/16/2006
11/15/2006
6/17/2009
Date
LER
HER
LER
HER
LER
HER
Circumference [m]
2200
3016
Beam energy [GeV]
3.1
9.0
3.5
8.0
3.5
8.0
Effective crossing angle [mrad]
0
22
0 (crab)
Beam current [A]
2.90
1.88
1.65
1.33
1.64
1.19
Bunches
1722
1389
1584
Bunch current [mA]
4.02
1.09
1.19
0.96
1.03
0.71
Bunch spacing [m]
1.2
1.8–2.4
1.8
Horizontal emittance ε x [nm]
30
50
18
24
18
24
RF frequency [MHz]
476
509
Bunch length σ z [mm]
10
10
8
6
8
6
β ∗
x [cm]
30
30
59
56
120
120
β ∗
y [cm]
0.9
1.1
0.65
0.59
0.59
0.59
Horizontal size @ IP [μm]
95
158
103
116
147
170
Vertical size @ IP [μm]
4.7
4.7
1.9
1.9
0.94
0.94
Beam-beam ξ x
0.072 0.064 0.115 0.075
0.125 0.100
Beam-beam ξ y
0.064 0.053 0.104 0.058
0.130 0.090
Luminosity [nb −1 s −1 ]
12.1
17.6
21.1
Integrated luminosity/day [pb −1 ]
858
1260
1479
Integrated luminosity/7 days [fb −1 ]
5.41
7.82
8.43
Integrated luminosity/30 days [fb −1 ] 19.8
30.2
23.0
Total integrated luminosity [fb −1 ]
557
1040
The left, center, right correspond to the highest performance of PEP–II, KEKB (no crab) and
KEKB (crab), respectively. The integrated luminosities are the delivered numbers for PEP–II, and
recorded for KEKB. 1 nb −1 = 10 33 cm −2 s −1
and the definition of luminosity
L =
N + N − f
4πσ ∗
x σ ∗
y
R L
(10.3)
where N and f are the number of particles per bunch and the collision frequency
(I = Nef ), respectively, and we have assumed the beam sizes are common in two
beams. The factors R L , x, y are the geometric reduction factors due to the hour-glass
effect and the crossing angle.
While a round-beam scheme may have a merit of a factor of 2 on the luminosity
according to Eq. (10.1), a flat beam scheme has been chosen in most e + e − colliders,
as the round-beam focusing in both planes is more difficult for an extremely small
β ∗ . For a flat beam, σ ∗
x σ ∗
y , the luminosity is written as
L ≈
1
2er e
γ Iξ y
β ∗
y
±
R L
R y
.
(10.4)