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E. Metral et al.
around the interaction regions. Such a scheme was used in LEP in the second phase
[171].
Contrary to the majority of the colliders, the LHC collides particles of the same
type which therefore must travel in separate beam pipes. At the collision points of
the LHC the two beams are brought together and into collision. During that process
it is unavoidable that the beams travel in a common vacuum chamber for more than
120 m. In the LHC the distance between the bunches is only 25 ns and therefore
the bunches will meet in this region. In order to avoid the collisions, the bunches
collide at a small crossing angle of 285 μrad. While two bunches collide at a small
angle (quasi head-on) at the centre, the other bunches are kept separated by the
crossing angle. However, since they travel in a common beam pipe, the bunches
still feel the electromagnetic forces from the bunches of the opposite beam. When
the separation is large enough, these so-called long-range interactions should be
weak.
4.6.7.1 Long-Range Beam–Beam Effects
Although the long-range interactions distort the beams much less than a headon interaction, their large number and some particular properties require careful
studies:
• They break the symmetry between planes.
• While the effect of head-on collisions is strongest for small amplitude particles,
they mostly affect particles at large amplitudes.
• The tune shift caused by long-range interactions has opposite sign in the plane of
separation compared to the head-on tune shift.
• They cause changes of the closed orbit [153].
• They largely enhance so-called PACMAN effects [168].
4.6.7.2 Opposite Sign Tune Shift
The opposite sign of the tune shift can easily be understood when we average the
oscillation of a small amplitude particle as it samples the focusing force of the
beam–beam interaction. When the separation is larger than ~1.5σ , the focusing
(slope of the force as a function of the amplitude) changes the sign and the resulting
tune shift assumes the opposite sign.
To some extend this property could be used to partially compensate long-range
interactions when a configuration is used where the beams are separated in the
horizontal plane in one interaction region and in the vertical plane in another
one.
E. Metral et al.
around the interaction regions. Such a scheme was used in LEP in the second phase
[171].
Contrary to the majority of the colliders, the LHC collides particles of the same
type which therefore must travel in separate beam pipes. At the collision points of
the LHC the two beams are brought together and into collision. During that process
it is unavoidable that the beams travel in a common vacuum chamber for more than
120 m. In the LHC the distance between the bunches is only 25 ns and therefore
the bunches will meet in this region. In order to avoid the collisions, the bunches
collide at a small crossing angle of 285 μrad. While two bunches collide at a small
angle (quasi head-on) at the centre, the other bunches are kept separated by the
crossing angle. However, since they travel in a common beam pipe, the bunches
still feel the electromagnetic forces from the bunches of the opposite beam. When
the separation is large enough, these so-called long-range interactions should be
weak.
4.6.7.1 Long-Range Beam–Beam Effects
Although the long-range interactions distort the beams much less than a headon interaction, their large number and some particular properties require careful
studies:
• They break the symmetry between planes.
• While the effect of head-on collisions is strongest for small amplitude particles,
they mostly affect particles at large amplitudes.
• The tune shift caused by long-range interactions has opposite sign in the plane of
separation compared to the head-on tune shift.
• They cause changes of the closed orbit [153].
• They largely enhance so-called PACMAN effects [168].
4.6.7.2 Opposite Sign Tune Shift
The opposite sign of the tune shift can easily be understood when we average the
oscillation of a small amplitude particle as it samples the focusing force of the
beam–beam interaction. When the separation is larger than ~1.5σ , the focusing
(slope of the force as a function of the amplitude) changes the sign and the resulting
tune shift assumes the opposite sign.
To some extend this property could be used to partially compensate long-range
interactions when a configuration is used where the beams are separated in the
horizontal plane in one interaction region and in the vertical plane in another
one.