7 Design and Principles of Linear Accelerators and Colliders
301
effect can be described using the disruption parameters D x and D y :
D x,y =
2Nr e σ z
γ σ x,y
σ x + σ y
.
(7.5)
If D x, y 1 each beam acts as a thin lens on the other beam with a focal length
f x, y = σ z /D x close to its centre. If D x 1 the beam particles oscillate in the field
of the other beam; ILC and CLIC have D x < 1 and D y 1. For D y ≥ 15 − 20
the beam-beam interaction becomes unstable. In this case very small beam-beam
offsets lead to a large loss of luminosity.
In order to increase the wall plug to beam power efficiency, η, two different
strategies exist. The first is to use superconducting structures to minimise the RF
losses in the structure itself. The second it to use normal conducting structures but
to increase the structure impedance and the beam current as much as possible to
maximise the power transfer to the beam. A limit arises from single and multi-bunch
beam instabilities, see Sect. 7.5.
At multi-TeV energies, the beamstrahlung parameter is much larger, Y 1,
which slightly changes the functional dependence of the luminosity on the number
of beamstrahlung photons to
L ∝ n
3
2
γ
√
γ
√
σ z
1
σ y
P b .
(7.6)
However, the fundamental considerations remain unchanged.
The beam-beam interaction is an important source of background. The disrupted
beam and the beamstrahlung photons need to be extracted from the detector without
large losses, this requires typically an exit hole of a few milliradian. In addition
secondary particles are produced.
The collision of beamstrahlung photons and beam particles produces low energy
electron-positron pairs, a process called incoherent pair production. The number
of these particles per bunch crossing can be of the order of 10 5 –10 6 . They are an
important source of background in the innermost layer of the vertex detector and
define a lower limit for its radius. Most of the particles go into the forward region
of the detector.
In a similar fashion, hadrons can also be produced in the collision, with a rate
ranging typically from one event every few bunch crossing to a few events per bunch
crossing. Most of the tracks of these events go into the forward region but they can
impact the jet reconstruction.
At high beam energies, if Y 1, beamstrahlung photons and the virtual photons
accompanying the beam particles can turn into electron-positron pairs due to the
strong beam fields, a process referred to as coherent pair production [37]. The
number of pairs can be a significant fraction of the number of beam particles. These
particles can lead to background in the forward region, depending on the detector
design.
301
effect can be described using the disruption parameters D x and D y :
D x,y =
2Nr e σ z
γ σ x,y
σ x + σ y
.
(7.5)
If D x, y 1 each beam acts as a thin lens on the other beam with a focal length
f x, y = σ z /D x close to its centre. If D x 1 the beam particles oscillate in the field
of the other beam; ILC and CLIC have D x < 1 and D y 1. For D y ≥ 15 − 20
the beam-beam interaction becomes unstable. In this case very small beam-beam
offsets lead to a large loss of luminosity.
In order to increase the wall plug to beam power efficiency, η, two different
strategies exist. The first is to use superconducting structures to minimise the RF
losses in the structure itself. The second it to use normal conducting structures but
to increase the structure impedance and the beam current as much as possible to
maximise the power transfer to the beam. A limit arises from single and multi-bunch
beam instabilities, see Sect. 7.5.
At multi-TeV energies, the beamstrahlung parameter is much larger, Y 1,
which slightly changes the functional dependence of the luminosity on the number
of beamstrahlung photons to
L ∝ n
3
2
γ
√
γ
√
σ z
1
σ y
P b .
(7.6)
However, the fundamental considerations remain unchanged.
The beam-beam interaction is an important source of background. The disrupted
beam and the beamstrahlung photons need to be extracted from the detector without
large losses, this requires typically an exit hole of a few milliradian. In addition
secondary particles are produced.
The collision of beamstrahlung photons and beam particles produces low energy
electron-positron pairs, a process called incoherent pair production. The number
of these particles per bunch crossing can be of the order of 10 5 –10 6 . They are an
important source of background in the innermost layer of the vertex detector and
define a lower limit for its radius. Most of the particles go into the forward region
of the detector.
In a similar fashion, hadrons can also be produced in the collision, with a rate
ranging typically from one event every few bunch crossing to a few events per bunch
crossing. Most of the tracks of these events go into the forward region but they can
impact the jet reconstruction.
At high beam energies, if Y 1, beamstrahlung photons and the virtual photons
accompanying the beam particles can turn into electron-positron pairs due to the
strong beam fields, a process referred to as coherent pair production [37]. The
number of pairs can be a significant fraction of the number of beam particles. These
particles can lead to background in the forward region, depending on the detector
design.