6 Design and Principles of Synchrotrons and Circular Colliders
255
Fig. 6.29 Crab Waist collision scheme
transformation is a vertical betatron function twist according to:
β y = β
∗
y +
(s − x/2θ )
2
β ∗
y
(6.70)
In this case, the β y waist of one beam is twisted to be oriented along the central
trajectory of the other beam. As a consequence, all particles, independently of
their x position, collide at the minimum β y spot of both beams, with an increase
of few percent in the geometric luminosity due to the β y redistribution along the
overlapping beams area. A sketch of this shown in Fig. 6.29.
However the main CW effect is to suppress the betatron and synchro-betatron
resonances which would arise due to the vertical motion modulation induced by
the horizontal oscillations. This increases the space for the working betatron tunes
255
Fig. 6.29 Crab Waist collision scheme
transformation is a vertical betatron function twist according to:
β y = β
∗
y +
(s − x/2θ )
2
β ∗
y
(6.70)
In this case, the β y waist of one beam is twisted to be oriented along the central
trajectory of the other beam. As a consequence, all particles, independently of
their x position, collide at the minimum β y spot of both beams, with an increase
of few percent in the geometric luminosity due to the β y redistribution along the
overlapping beams area. A sketch of this shown in Fig. 6.29.
However the main CW effect is to suppress the betatron and synchro-betatron
resonances which would arise due to the vertical motion modulation induced by
the horizontal oscillations. This increases the space for the working betatron tunes