6 Design and Principles of Synchrotrons and Circular Colliders
235
IP
x x
x
Fig. 6.23 Collisions with different vertical β-functions
IP
x x
x
Fig. 6.24 All collisions at a minimum of the vertical β-functions using a crabbed waist scheme
One possible consequence can be the coupling between the transverse and and
longitudinal plane. Such a coupling is particularly bad for flat beams since the
vertical beam size will increase significantly.
In Fig. 6.23 the vertical β-function is indicated and the result of this effect is that
the particles collide at positions with different vertical β-functions.
This can be mitigated [42] by making the vertical waist (β min
y ) amplitude
dependent in the horizontal plane Fig. 6.24. All particle collide now at the minimum
of the vertical β-function.
It should be emphasized that the main purpose of such a scheme is not to reduce
a geometrical loss but to reduce the coupling. Therefore it is of interest only for flat
beams.
This scheme is established using two sextupoles.
6.4.4 Integrated Luminosity and Event Pile Up
The maximum luminosity, and therefore the instantaneous number of interactions
per second, is very important, but the final figure of merit is the so-called integrated
235
IP
x x
x
Fig. 6.23 Collisions with different vertical β-functions
IP
x x
x
Fig. 6.24 All collisions at a minimum of the vertical β-functions using a crabbed waist scheme
One possible consequence can be the coupling between the transverse and and
longitudinal plane. Such a coupling is particularly bad for flat beams since the
vertical beam size will increase significantly.
In Fig. 6.23 the vertical β-function is indicated and the result of this effect is that
the particles collide at positions with different vertical β-functions.
This can be mitigated [42] by making the vertical waist (β min
y ) amplitude
dependent in the horizontal plane Fig. 6.24. All particle collide now at the minimum
of the vertical β-function.
It should be emphasized that the main purpose of such a scheme is not to reduce
a geometrical loss but to reduce the coupling. Therefore it is of interest only for flat
beams.
This scheme is established using two sextupoles.
6.4.4 Integrated Luminosity and Event Pile Up
The maximum luminosity, and therefore the instantaneous number of interactions
per second, is very important, but the final figure of merit is the so-called integrated