FiDeL: the model to predict the magnetic state of the LHC Beam Dynamics meets Magnets – II 1st – 4th December 2014 Bad Zurzah FiDeL: the model to predict the magnetic state of the LHC Nicholas Aquilina University of Malta Acknowledgements: E. Todesco, N. Sammut

Overview Field description for the LHC (FiDeL) Magnetic measurements introduction and overview of the model Magnetic measurements Beam dynamics as observed through beam based measurements Precision and Control of the LHC precision in controlling the tune precision in controlling the chromaticity Conclusions FiDeL Beam dynamics (beam measurements) Magnetic measurements Control of the LHC 04/12/2014

FiDeL - overview provides the superconducting magnet integral field transfer function, such that the various powering circuits of the LHC supply the necessary currents FiDeL model predicts field errors and sets the corrector circuits to compensate for errors static components geometric contribution d.c. magnetisation contribution saturation contribution residual magnetisation contribution 04/12/2014

FiDeL - overview provides the superconducting magnet integral field transfer function, such that the various powering circuits of the LHC supply the necessary currents FiDeL model predicts field errors and sets the corrector circuits to compensate for errors dynamic components snapback decay snapback decay 04/12/2014

Magnetic measurements The FiDeL model consists of a set of semi-empirical equations Theses equations are based on the results obtained from individual measurements of the LHC magnets Two measurement cycles were used: loadline cycle, used to extract the static components machine cycle, used to extract the dynamic components 04/12/2014

Beam observables Orbit → b1 depends on the dipole Tune → b2=B2/B1 (B2 = main field of the quadrupole, B1 = main field of the dipole) need to be controlled within 10-3 units depends on the quadrupoles and the dipoles global measurement Chromaticity → b3 depends on the sextupole component (dipole, spool pieces) Beta-beating → b2=B2/B1 depends on the quadrupoles local measurement 04/12/2014

Tune and chromaticity in the LHC Tune: number of oscillations the particle goes through as it travels one revolution around the machine Set to a particular value not to have resonance Horizontal tune (at injection) = 64.28±0.005 Vertical tune (at injection) = 59.31±0.005 Chromaticity: variation of tune with relative momentum change inside a bucket, change in momentum of the particles is of the order of 10-3 for a chromaticity of 10 units, the change in tune is of the order of 0.01 enough for the tune to jump from 64.28 to 64.29!! radius of curvature equilibrium orbit particles oscillating around design orbits 04/12/2014

Precision in controlling the tune 04/12/2014

Tune behaviour during injection During the injection plateau, decay in the horizontal and vertical tunes was observed Origin of tunes decay during injection feed-down of sextupole errors due to off-axis beam traversal feed-down of sextupole errors will result in a change in tune with different signs in each plane – this source is excluded change in the strength of the dipoles decay of the dipoles was measured to be of the order of few arb. units as found in magnetic measurements and beam-based measurements – this source is excluded change in the strength of the quadrupoles all the quadrupole families in the LHC (5 families) contribute to the tune value – tune decay is due to the decay of the main field of all the families of quadrupoles in the LHC. This tune decay is modeled using the double exponential model and is now part of the FiDeL model. 04/12/2014

Tune behaviour during snapback Tune decay is followed by snapback 15 measurements taken from 2012 operation were analysed From this analysis, it was observed that the fitting parameters are linearly related – the snapback correlation factor The FiDeL model was updated to include the tune snapback using a correlation factor of 0.108 04/12/2014

Tune behaviour during ramp Precision of the FiDeL model can be studied by looking at the behaviour of the bare tune during the ramp Energy (TeV) Qh Qv precision working point 59.28 64.31 N/A 0.45 59.31 64.22 0.1% 3.5/4 59.25 64.28 0.05% 04/12/2014

Precision in controlling the chromaticity 04/12/2014

Expected b3 decay behaviour (based on magnetic measurements) 90% of the decay is over after the first 1000 s Static correction is enough δstd:- decay amplitude at t = 1000 s no dynamic behavior b3 behaviour during a 10000 s injection plateau as measured in MB3028 04/12/2014

Decay behaviour as observed in the LHC Decay behaviour in the LHC is slower than that observed during magnetic measurements After 30 minutes, decay is still dynamic dynamic correction required 04/12/2014

Updates to the decay model A static correction was being used asymptotic decay behaviour This was not enough, and chromaticity decay was still observed during injection chromaticity decay of 12 units A dynamic correction was implemented in the machine (in April 2011) based on beam based measurements chromaticity decay was corrected within 1-2 units 04/12/2014 injection on 21/02/2011 injection on 02/05/2011

Expected snapback behaviour (based on magnetic measurements) Snapback follows an exponential decay – snapback model The decay amplitude (∆bn) at the end of injection and the time for snapback to occurs (∆In) are linearly correlated – snapback correlation factor During magnetic measurements this correlation factor was found to be 0.176 04/12/2014

Beam-based measurements of snapback behaviour 8 beam based measurements were used to analyse the b3 snapback behaviour of the LHC The fitting parameters obtained from the analysed data all lie on the same line The correlation factor was found to be 0.22 04/12/2014

Conclusions The FiDeL model is a set of semi-empirical equations based on: Magnetic measurements Beam-based measurements Precision of FiDeL in controlling the tunes of the LHC The absolute precision of the FiDeL model for the quadrupoles at injection is of 0.1%, which is further improved to 0.05% once flat-top is reached The FiDeL model was updated to include the decay of the tunes during injection Snapback behaviour follows the tunes decay – snapback is modelled and included in the FiDeL model Precision of FiDeL in controlling the chromaticity of the LHC From magnetic measurements, a chromaticity decay of 22 units was expected On the other hand, the decay during magnetic measurements was much faster than that observed during beam based-measurements For this reason static correction was changed to dynamic correction FiDeL is able to control the chromaticity decay at injection within 1-2 units of chromaticity Snapback behaviour is confirmed to be in line with the model 04/12/2014