560
M. Lamont et al.
the left-hand side a schematic picture for the dependence of the beam-beam force
on the particle oscillation amplitude and on the right-hand side as an example the
resulting tune foot print for the nominal LHC collisions covering particle amplitudes
from 0 to 6σ (the particles with zero amplitudes are located at the tip of the tune foot
print). Note that the LHC tune foot print shown features the effect of both head-on
and long range collisions.
With increasing instantaneous luminosity, the number of concurrent interactions
increases. The number of collisions per bunch crossing, the pile-up, is given by
μ =
L
f rev n b
σ tot
(9.75)
where σ tot is the total cross-section for the interaction of beam particles.
The maximum acceptable pile-up may be limited by the capabilities of the
installed experimental detectors, e.g. due to a limited read-out rate or detector
dead time. It may also be limited by the accelerator itself, e.g. due to heating or
radiation limits. If this is the case, it imposes an additional limit for the instantaneous
luminosity; increasing the luminosity per colliding bunch pair (through intensity or
beam size at the IP) increases the pile-up proportionally. The luminosity of a collider
operating at the pile-up limit can be optimized through luminosity levelling, which
will be discussed in Sect. 9.8.7.
Similarly, the acceptable pile-up density in the luminous region around the IP
may be limited e.g. by the detector resolution. Apart from reducing the overall pileup, this can be mitigated by increasing the size of the luminous region or changing
the bunch distribution.
9.8.3 Collider with Strong Synchrotron Radiation Damping
In circular colliders with strong synchrotron radiation the amplitude growth due
to the beam-beam interaction is stabilized by the synchrotron radiation damping
yielding an increased but stable beam size at the IP. As a result, the instantaneous
luminosity no longer increases quadratically, but rather linearly, with the bunch
current above a certain limit of the beam-beam force and the beam-beam tune
shift reaches asymptotically a maximum value. This maximum value defines the
so called beam-beam limit in a collider with strong radiation damping. The actual
value of the beam-beam limit varies between different colliders and depends on
the actual operating point (the horizontal and vertical tunes) and the strength of
the synchrotron radiation damping. Figure 9.17 shows as an example the measured
vertical beam-beam parameter in LEP as a function of the bunch current for the LEP
operation with beam energies of 98 GeV and 101 GeV.
In an ideal storage ring without coupling and vertical dispersion, the vertical
beam size shrinks to a minimum value which is in theory only limited by the
quantum fluctuation of the synchrotron radiation. In the horizontal plane this effect
M. Lamont et al.
the left-hand side a schematic picture for the dependence of the beam-beam force
on the particle oscillation amplitude and on the right-hand side as an example the
resulting tune foot print for the nominal LHC collisions covering particle amplitudes
from 0 to 6σ (the particles with zero amplitudes are located at the tip of the tune foot
print). Note that the LHC tune foot print shown features the effect of both head-on
and long range collisions.
With increasing instantaneous luminosity, the number of concurrent interactions
increases. The number of collisions per bunch crossing, the pile-up, is given by
μ =
L
f rev n b
σ tot
(9.75)
where σ tot is the total cross-section for the interaction of beam particles.
The maximum acceptable pile-up may be limited by the capabilities of the
installed experimental detectors, e.g. due to a limited read-out rate or detector
dead time. It may also be limited by the accelerator itself, e.g. due to heating or
radiation limits. If this is the case, it imposes an additional limit for the instantaneous
luminosity; increasing the luminosity per colliding bunch pair (through intensity or
beam size at the IP) increases the pile-up proportionally. The luminosity of a collider
operating at the pile-up limit can be optimized through luminosity levelling, which
will be discussed in Sect. 9.8.7.
Similarly, the acceptable pile-up density in the luminous region around the IP
may be limited e.g. by the detector resolution. Apart from reducing the overall pileup, this can be mitigated by increasing the size of the luminous region or changing
the bunch distribution.
9.8.3 Collider with Strong Synchrotron Radiation Damping
In circular colliders with strong synchrotron radiation the amplitude growth due
to the beam-beam interaction is stabilized by the synchrotron radiation damping
yielding an increased but stable beam size at the IP. As a result, the instantaneous
luminosity no longer increases quadratically, but rather linearly, with the bunch
current above a certain limit of the beam-beam force and the beam-beam tune
shift reaches asymptotically a maximum value. This maximum value defines the
so called beam-beam limit in a collider with strong radiation damping. The actual
value of the beam-beam limit varies between different colliders and depends on
the actual operating point (the horizontal and vertical tunes) and the strength of
the synchrotron radiation damping. Figure 9.17 shows as an example the measured
vertical beam-beam parameter in LEP as a function of the bunch current for the LEP
operation with beam energies of 98 GeV and 101 GeV.
In an ideal storage ring without coupling and vertical dispersion, the vertical
beam size shrinks to a minimum value which is in theory only limited by the
quantum fluctuation of the synchrotron radiation. In the horizontal plane this effect