Abstract
An important number of coherent beam instability mechanisms can be observed in a particle accelerator, depending if the latter is linear or circular, operated at low, medium or high energy, with a small or a huge amount of turns (for circular machines), close to transition energy or not (below or above), with only one bunch or many bunches, with counter-rotating beams (such as in colliders) or not, if the beam is positively or negatively charged, if one is interested in the longitudinal plane or in the transverse plane, in the presence of linear coupling between the transverse planes or not, in the presence of nonlinearities or not, in the presence of noise or not, etc. Building a realistic impedance model of a machine is a necessary step to be able to evaluate the machine performance limitations, identify the main contributors in case an impedance reduction is required, and study the interaction with other mechanisms such as optics (linear and nonlinear), RF gymnastics, transverse damper, noise, space charge, electron cloud, and beam–beam (in a collider). Better characterising an instability is the first step before trying to find appropriate mitigation measures and push the performance of a particle accelerator, as some mitigation methods are beneficial for some effects and detrimental for some others. For this, an excellent instrumentation is of paramount importance to be able to diagnose if the instability is longitudinal or transverse, single bunch, or coupled bunch, involving only one mode of oscillation or several, and the evolution of the intrabunch motion with intensity is a fundamental observable with high-intensity high-brightness beams. Finally, among the possible mitigation methods of coherent beam instabilities, the ones perturbing the least the single-particle motion (leading to the largest necessary dynamic aperture and beam lifetime) and easiest to implement for day-to-day operation in the machine control room should be preferred.
Highlights
This led to several new instability mechanisms such as the destabilising effect of resistive transverse dampers [6] and the losses of transverse Landau damping due to linear coupling [7], noise [8], and beam–beam [9]
There is still a lot to be done on Landau damping and its possible loss, looking in more detail to theories, simulations, and measurements
In the CERN LHC, for instance, the required current in the Landau octupoles is predicted to be reduced by an order of magnitude for zero chromaticity. (For the beam and machine parameters used during the last year of Run 2, in 2018, this corresponded to ∼ 2000 A without damper and ∼ 200 A with damper, knowing that the maximum current available in the Landau octupoles is ∼ 550 A.) a resistive transverse damper destabilises the single-bunch motion below the transverse mode coupling instability (TMCI) intensity threshold, introducing a new kind of instability, which has been called ITSR instability [6]
Summary
As the machines performance was pushed, new mechanisms were revealed and nowadays the challenge consists in studying the interplays between all these intricate phenomena, as it is very often not possible to treat the different effects separately. This led to several new instability mechanisms such as the destabilising effect of resistive transverse dampers [6] and the losses of transverse Landau damping due to linear coupling [7], noise [8], and beam–beam [9].
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