156
E. Metral et al.
When we re-write the luminosity as
L =
N 2 kf
4πσ x σ y
=
Nkf
4πσ x
N
σ y
(4.64)
we get an idea of what is happening. In e + e − colliders the horizontal beam size
σ x is usually much larger than the vertical beam size σ y and changes very little.
In order for the luminosity to increase proportionally to the intensity N, the factor
N/σ y must be constant. This implies that with increasing current the vertical beam
size increases in proportion above the beam–beam limit. This has been observed in
all e + e − colliders and since the vertical beam size is usually small, this emittance
growth can be very substantial before the life time of the beam is affected or beam
losses are observed [163].
The dynamics of machines with high synchrotron radiation is dominated by the
damping properties and the beam–beam limit is not a universal constant nor can it
be predicted. Simulation of beams with many particles can provide an idea of the
order of magnitude [164, 165].
4.6.4 Studies of Head-on Collisions at the LHC
The layout of experimental regions in the LHC is shown in Fig. 4.23. The beams
travel in separate vacuum chambers and cross in the experimental areas where they
share a common beam pipe. In these common regions the beams experience headon collisions as well as a large number of long range beam–beam encounters [166].
This arrangement together with the bunch filling scheme of the LHC as shown in
Fig. 4.24 [166, 167] leads to very different collision pattern for different bunches,
often referred to as “PACMAN” bunches. The number of both, head-on as well
as long range encounters, can be very different for different bunches in the bunch
trains and lead to a different integrated beam–beam effect [167]. This was always
a worry in the LHC design and the effects have been observed in an early stage of
the commissioning. Strategies have been provided to minimize these effects, e.g.
different planes for the crossing angles [166, 167].
4.6.4.1 PACMAN Bunches
The bunches in the LHC do not form a continuous train of equidistant bunches
spaced by 25 ns, but some empty space must be provided to allow for the rise
time of kickers (Fig. 4.24). These gaps and the number of bunches per train are
determined by requirements from the LHC injectors. The whole LHC bunch pattern
is composed of 39 smaller trains (each with 72 bunches) separated by gaps of various
length followed by a large abort gap for the dump kicker. Due to the symmetry,
E. Metral et al.
When we re-write the luminosity as
L =
N 2 kf
4πσ x σ y
=
Nkf
4πσ x
N
σ y
(4.64)
we get an idea of what is happening. In e + e − colliders the horizontal beam size
σ x is usually much larger than the vertical beam size σ y and changes very little.
In order for the luminosity to increase proportionally to the intensity N, the factor
N/σ y must be constant. This implies that with increasing current the vertical beam
size increases in proportion above the beam–beam limit. This has been observed in
all e + e − colliders and since the vertical beam size is usually small, this emittance
growth can be very substantial before the life time of the beam is affected or beam
losses are observed [163].
The dynamics of machines with high synchrotron radiation is dominated by the
damping properties and the beam–beam limit is not a universal constant nor can it
be predicted. Simulation of beams with many particles can provide an idea of the
order of magnitude [164, 165].
4.6.4 Studies of Head-on Collisions at the LHC
The layout of experimental regions in the LHC is shown in Fig. 4.23. The beams
travel in separate vacuum chambers and cross in the experimental areas where they
share a common beam pipe. In these common regions the beams experience headon collisions as well as a large number of long range beam–beam encounters [166].
This arrangement together with the bunch filling scheme of the LHC as shown in
Fig. 4.24 [166, 167] leads to very different collision pattern for different bunches,
often referred to as “PACMAN” bunches. The number of both, head-on as well
as long range encounters, can be very different for different bunches in the bunch
trains and lead to a different integrated beam–beam effect [167]. This was always
a worry in the LHC design and the effects have been observed in an early stage of
the commissioning. Strategies have been provided to minimize these effects, e.g.
different planes for the crossing angles [166, 167].
4.6.4.1 PACMAN Bunches
The bunches in the LHC do not form a continuous train of equidistant bunches
spaced by 25 ns, but some empty space must be provided to allow for the rise
time of kickers (Fig. 4.24). These gaps and the number of bunches per train are
determined by requirements from the LHC injectors. The whole LHC bunch pattern
is composed of 39 smaller trains (each with 72 bunches) separated by gaps of various
length followed by a large abort gap for the dump kicker. Due to the symmetry,