Evaluation of the closest tune approach and its MAD-X implementation

The closest tune approach (ΔQmin) is a measure of the transverse coupling in an accelerator. The current method for evaluating the ΔQmin in MAD-X based on tune matching is time consuming and can have issues with convergence. We first review existing analytical estimates of ΔQmin to assess their accuracy. A new analytical estimate is also proposed, which features the best performance. This new estimate is included in version 5.07.01 of MAD-X. Correction of the transverse coupling based on the minimization of this new estimate shows improved performance in terms of resulting correction level and CPU time

Simulations of Sextupolar Contribution to Amplitude Detuning in the LHC

Nonlinear dynamics can impact circular machines’ performance and stability. A measurement of the machine nonlinearities can be obtained by characterizing the amplitude detuning: the dependency of the tune as a function of the amplitude of particle oscillations. It has been shown that the direct amplitude detuning coming from octupoles changes by a factor 2 depending on the nature of the betatron oscillations (free or forced oscillations). This study aims to investigate the hypothesis of the sextupolar amplitude detuning exhibiting similar behavior to that of octupolar amplitude detuning. To test this hypothesis, numerical simulations for LHC were performed with MAD-X, both for an AC dipole driving the beam and for free oscillations. Analysis of the tracking data confirmed the expected behavior

Amplitude dependent closest tune approach

Recent observations in the LHC point to the existence of an amplitude dependent closest tune approach. However this dynamical behavior and its underlying mechanism remain unknown. This effect is highly relevant for the LHC as an unexpectedly closest tune approach varying with amplitude modifies the frequency content of the beam and, hence, the Landau damping. Furthermore the single particle stability would also be affected by this effect as it would modify how particles with varying amplitudes approach and cross resonances. We present analytic derivations that lead to a mechanism generating an amplitude dependent closest tune approach

MD1405: Demonstration of forced dynamic aperture measurements at injection

Accurate measurements of dynamic aperture become more important for the LHC as it advances into increasingly nonlinear regimes of operations, as well as for the High Luminosity LHC where machine nonlinearities will have a significantly larger impact. Direct dynamic aperture measurements at top energy in the LHC are challenging, and conventional single kick methods are not viable. Dynamic aperture measurements under forced oscillation of AC dipoles have been proposed as s possible alternative observable. A first demonstration of forced DA measurements at injections energy is presented

Report from LHC MD 2171: Amplitude dependent closest tune approach from normal and skew octupoles

Simulation-based studies predict significant amplitude-dependent closest tune approach can be generated by skew octupole sources in conjunction with their normal octupolar counterparts. This has the potential to significantly influence Landau damping at small β∗, where skew octupole errors in the experimental IRs, together with b4 introduced by the Landau octupoles, is predicted to cause large distortion of the tune footprint. This MD aimed to perform a first exploration of these predictions with beam, by enhancing skew octupole sources in the IRs at injection and measuring amplitude detuning with free kicks in the plane approaching the coupling resonance

Report from LHC MD 1399: Effect of linear coupling on nonlinear observables in the LHC.

Simulation work during Run 1 established that linear coupling had a large impact on nonlinear observables such as detuning with amplitude and dynamic aperture. Linear coupling is generally taken to be the largest single source of uncertainty in the modelling of the LHC’s nonlinear single particle dynamics. ThisMD sought to verify that such behaviour, to this point only observed in simulation, translated into the real machine

An alternative method to measure amplitude dependence of the closest tune approach

In the linear regime, a minimum closest approach of the fractional horizontal and vertical tunes exists, due to linear coupling between the transverse planes. Simulation-, theoretical-, and beam-based studies of the LHC in Run 1 and 2 however, also demonstrated the existance of an amplitude dependence of the closest tune approach. This Ampiltude DEpendent Closest-Tune-Approach (ADECTA “Add-Ek-Ta”) is a topic of interest due to its potential to generate large distortions of the tune footprint in the vaccintity of the Qx − Qy = n resonance, which may then impact Landau damping. The measurement technique utilized in previous beam-based studies features a number of significant limitations however, most particularly that it is impractical to apply at top-energy in the LHC. This note presents the result of tests of an alternative measurement technique which can overcome limitations of the previous method

Report from MD380: Nonlinear errors in experimental insertions and off-momentum dynamic aperture

Nonlinear errors in low-¯¤ insertions can have a significant impact upon the beam dynamics. In particular reductions in the LHC dynamic aperture of the order of 3 ¾nominal (105 turns) are expected due to the presence of such errors in IR1 and IR5 at ¯¤ = 0.4m. This represents a slight risk to 40 cm operation in 2016. More optimistically correction of nonlinear errors in experimental insertions has led to significant gains in luminosity production in other accelerators: a ¸ 4% increase in integrated luminosity per fill was achieved in RHIC from the correction of such errors. The nonlinear errors of the ATLAS and CMS insertions were therefore studied at top energy during machine development time in 2015. During one of these studies it was also possible to perform AC-dipole kicks at injection, which have indicated a reduction in dynamic aperture off-momentum

MD2065: Emittance exchange with linear coupling

In order to better understand the luminosity imbalance between ATLAS and CMS that was observed in 2016, it was proposed to perform a test whereby the horizontal and vertical emittances are exchanged by crossing the tunes in the presence of linear coupling. The luminosity before and after the exchange could be compared to see if the imbalance stems purely from the uneven emittances or if there is an additional mechanism in play. However, due to limited machine availability only tests at injection were able to performed