10 The Largest Accelerators and Colliders of Their Time
623
Then if there is no reason to differentiate ξ y and β ∗
y in the two rings,
γ + I + = γ − I −
(10.5)
is resulted. As the ratio of beam energies gets larger, the boost at the collision
becomes larger, but the low energy ring must store higher beam current. Thus
the energy ratio was a compromise between the physics merit and the accelerator
difficulty. PEP–II chose 3.1 GeV and 9 GeV for positrons and electrons, while
KEKB chose 3.5 GeV and 8 GeV. A larger ratio was more favored at PEP–II as
it needs a magnetic separation of two beams at the IP as described later. The flavor
of beams, the LER for positrons, was uniquely chosen at KEKB, where the positron
acceleration for the HER was very difficult.
The actual operation of these machines, the condition (10.5) was not kept strictly,
as shown in Table 10.12. One reason was that the natural size of each beam was not
equal, for instance, the LER positron beam was relatively easy to be blown up due
to the electron clouds at high current. Then there was a certain limit on the positron
beam current and the HER current was increased beyond Eq. (10.5). This tendency
was stronger in KEKB than PEP–II, as the former had stronger electron cloud effects
than the latter as described later.
10.4.4 Crossing Angle
One of the design choices is the beam separation scheme near the IP. A crossing
angle is a natural and easy solution of the separation, but the question was the
experience at DORIS [125]. KEKB applied a horizontal crossing angle 2θ x = 22
mrad, relying on simulation of the beam-beam effect. The corresponding Piwinski
angle (≡ θ x σ z /σ ∗
x ) was 0.86. Their conclusion at the design stage was that the effect
of the crossing angle on the beam-beam interaction would not be harmful up to their
design beam-beam parameter 0.05, if the operating betatron tunes were carefully
chosen. Their choice was right and verified the vertical beam-beam parameter of
0.06 in their luminosity marching. Crossing angles were also applied at CESR and
DANE colliders successfully in parallel with the KEKB operation. KEKB even
prepared a crab-crossing scheme [126, 127] for the backup of the crossing angle.
The ratio of the geometric reduction factors R L /R y in Eq. (10.1) does not drastically
decrease for a large crossing angle as shown in [122].
PEP–II was much more nervous on the crossing angle, then they installed a
magnetic separation scheme near the IP with permanent dipole magnets [128]. This
scheme also worked, but their design around the IP had to be more complicated
than with a crossing angle, and gave some limitations on the performance such as
the detector background due to radiative Bhabha events [129], which was much
less significant in Belle. As the space at the IP was limited, they could not install a
compensation system for the detector solenoid field, which might have degraded the
623
Then if there is no reason to differentiate ξ y and β ∗
y in the two rings,
γ + I + = γ − I −
(10.5)
is resulted. As the ratio of beam energies gets larger, the boost at the collision
becomes larger, but the low energy ring must store higher beam current. Thus
the energy ratio was a compromise between the physics merit and the accelerator
difficulty. PEP–II chose 3.1 GeV and 9 GeV for positrons and electrons, while
KEKB chose 3.5 GeV and 8 GeV. A larger ratio was more favored at PEP–II as
it needs a magnetic separation of two beams at the IP as described later. The flavor
of beams, the LER for positrons, was uniquely chosen at KEKB, where the positron
acceleration for the HER was very difficult.
The actual operation of these machines, the condition (10.5) was not kept strictly,
as shown in Table 10.12. One reason was that the natural size of each beam was not
equal, for instance, the LER positron beam was relatively easy to be blown up due
to the electron clouds at high current. Then there was a certain limit on the positron
beam current and the HER current was increased beyond Eq. (10.5). This tendency
was stronger in KEKB than PEP–II, as the former had stronger electron cloud effects
than the latter as described later.
10.4.4 Crossing Angle
One of the design choices is the beam separation scheme near the IP. A crossing
angle is a natural and easy solution of the separation, but the question was the
experience at DORIS [125]. KEKB applied a horizontal crossing angle 2θ x = 22
mrad, relying on simulation of the beam-beam effect. The corresponding Piwinski
angle (≡ θ x σ z /σ ∗
x ) was 0.86. Their conclusion at the design stage was that the effect
of the crossing angle on the beam-beam interaction would not be harmful up to their
design beam-beam parameter 0.05, if the operating betatron tunes were carefully
chosen. Their choice was right and verified the vertical beam-beam parameter of
0.06 in their luminosity marching. Crossing angles were also applied at CESR and
DANE colliders successfully in parallel with the KEKB operation. KEKB even
prepared a crab-crossing scheme [126, 127] for the backup of the crossing angle.
The ratio of the geometric reduction factors R L /R y in Eq. (10.1) does not drastically
decrease for a large crossing angle as shown in [122].
PEP–II was much more nervous on the crossing angle, then they installed a
magnetic separation scheme near the IP with permanent dipole magnets [128]. This
scheme also worked, but their design around the IP had to be more complicated
than with a crossing angle, and gave some limitations on the performance such as
the detector background due to radiative Bhabha events [129], which was much
less significant in Belle. As the space at the IP was limited, they could not install a
compensation system for the detector solenoid field, which might have degraded the