Stability diagrams of colliding beams in the Large Hadron Collider

Abstract

Most hadron synchrotrons rely on lattice nonlinearities for Landau damping of impedance driven coherent modes of oscillation. However, in a collider, the presence of beam-beam interactions strongly modifies the transverse amplitude detuning and therefore the resulting stability diagram. A numerical tool to evaluate the effect of beam-beam on the stability diagram has been developed and is used to discuss observations during different phases of the operational cycle of the Large Hadron Collider during the 2012 proton run. In particular, we show the evolution of the stability diagram when the strength of long range beam-beam interactions is increased, during the betatron squeeze. Also, we investigate the stability of beams colliding with a small transverse offset and compare to observations of instabilities when bringing the beams into collision and while leveling the luminosity.

Beam Instabilities in Hadron Synchrotrons

“…During the 2012 run of the LHC, instabilities were observed at the end of the squeeze with both polarities of the octupole [269], excluding this mechanism as a sole explanation for the instabilities observed, in particular when the contribution of long-range beam-beam interaction and the octupole contibute constructively to the stability diagram. Nevertheless, the size of the amplitude detuning is not the only consideration to take into account, as the dynamics of single particles is highly affected by both the long-range interactions and the lattice non-linearities.…”

“…59. Evolution of the stability diagram as the normalized separation between the beams is reduced during the betatron squeeze for the nominal LHC optics and beam parameters [269]. At the end of this operation, nominal LHC beams have a normalized separation of 10 σ.…”

“…While the effect of lattice non-linearities can be addressed analytically, the complex configuration of beambeam interactions leads to amplitude detuning with difficult analytical expressions [266,267], which render the solution of the dispersion relation difficult. This problem is easier addressed numerically, using single particle tracking to evaluate the amplitude detuning and numerical integration of the dispersion integral [268,269]. The non-linearities of beambeam interactions not only modify the amplitude detuning but can also significantly distort the particles distribution in the beam, affecting the strength of the Landau damping.…”

The HL-LHC Accelerator Physics Challenges

“…16 shows the negative imaginary part of the tune shift, −Im(∆Q), related to the Landau damping rate through 1/τ damp = 2πf rev Im(∆Q), as a function of the real part of the tune shift and of the beam-beam separation at the two main collisions points IP 1 and 5, but ignoring any collisions in IPs 2 and 8 [49]. This figure highlights the lack of stability for a transverse beam-beam separation around 2σ * , especially for the case where the Landau octupole magnets are powered at negative polarity (left picture).…”

“…15, which shows stability limits in complex tune plane computed separately for each of the following components for the nominal LHC parameters [49]: (1) the Landau octupoles, (2) the long-range bean-beam interactions, and (3) head-on collisions at the interaction points 1 and 5.…”