1. 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

2. 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

3. 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
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4. 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

5. 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

6. 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

7. 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 to 64.29!!
radius of curvature
equilibrium orbit
particles oscillating around design orbits
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8. Precision in controlling the tune
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9. 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

10. 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

11. 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%
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12. Precision in controlling the chromaticity
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13. 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 s injection plateau as measured in MB3028
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14. 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
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15. 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

16. 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

17. 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

18. 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