The LHC dynamic aperture saga: overview, ideas and recent developments
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Transcript of The LHC dynamic aperture saga: overview, ideas and recent developments
The LHC dynamic aperture saga: overview, ideas and recent developments
Massimo GiovannozziCERN – Beams Department
Definition and physics/computational issues DA studies for LHC DA vs. time: models Benchmarking with real data Extensions Luminosity evolution model DA measurements Outlook
Acknowledgements: A. Bazzani, S. Fartoukh, E. Laface, F. Lang, E. MacLean, W. Scandale, F. Schmidt, E. Todesco, R. Tomás, G. Turchetti, C. Yu
Fermilab APT seminar 5/11/2013
Definition and issues - I
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The dynamic aperture is the region in phase in which bounded motion occurs.
So far only tracking allows computing theDA of a given system.
From a numerical point of view: A volume should be evaluated. This entails a scan
over the phase space variables. An appropriate choice of the steps in the variables is
required.NB: I will deal with protons -> symplectic
dynamics! The tracking has to be long-term
Fermilab APT seminar 5/11/2013
Definition and issues - II
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DA computations are CPU intensive. Fast tracking tools are required:
Optimised codes (e.g., kick codes) Parallel approach (this is only possible over the initial conditions).
As an alternative (maybe a dream…): find a dynamical quantity with a good correlation with DA, but less expensive in terms of CPU.
A trade-off between number of turns and number of initial conditions might be possible (e.g., use a dense set of initial conditions iterated a small number of turns).
Do not forget stable chaos and intermittency!
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Definition and issues - III
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Here are some examples of indicators: Lyapunov exponent Tune difference (this indicator triggered several studies on accurate
computation of tunes in numerical simulations).
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DA studies for LHC - I
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The dynamic aperture studies for the LHC absorbed a lot of resources for about two decades in terms of:
Theoretical studies in non-linear beam dynamics Software and analysis tools Specification magnetic field quality tables (with iterations with the
magnet builders) The large amount of information gathered during the
measurement stage of the magnets (warm and cold conditions)
Special tools developed (e.g., WISE) This allows:
Estimating the DA of the LHC as-built Estimating the impact of sorting on DA of the LHC as-built
Generate realistic realisations of the magnetic field errors, based on •Actual slot allocation
•Actual field quality
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DA studies for LHC - II Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA
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DA
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Beam 1 Beam 2 Summary of DA at injection energy. The error bars represent the effect of 60 seeds
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DA studies for LHC - III Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA
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Measured errors in all magnets (3.5 TeV), squeezed optics (no triplet correction) - after September 2008 incident
Measured errors in all magnets (3.5 TeV), injection optics -after September 2008 incident
Measured errors in all magnets (injection energy), injection optics -after September 2008 incident
Measured errors in all magnets (7 TeV), collision optics (triplet and D1 correction) - after September 2008 incident
Summary of minimum DA for several running configurations.
Fermilab APT seminar 5/11/2013
DA studies for LHC - IV Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA
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Impact of sorting.• Selected generic seeds• Each sequence of
errors is re-ordered.• The various dynamical
quantities are computed.
Yellow: all seeds (initial and re-ordered)Blue: selected seeds.
Fermilab APT seminar 5/11/2013
DA studies for LHC - V
Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA
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Impact of sorting.• Selected generic seeds• Each sequence of errors
is re-ordered.• The various dynamical
quantities are computed.Yellow: all seeds (initial and re-ordered)Blue: selected seeds.Red: average DA for as-built machine.
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DA vs. time: models - I
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Another strategy could be: is there a model to describe DA vs. time? In mathematical sense DA does not depend on time. Numerical simulations are performed with a specific
maximum number of turns (Nmax): the computed DA does depend on Nmax
How does DA depend on Nmax in numerical simulations?).
Studies have been performed recently to review the functional dependence on k of fit model
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Definition and issues - VII
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Dynamic aperture of a model of the LHC ring (left) in physical space: The red points represent the initial conditions stable up to 105 turns The blue points represent unstable conditions and their size is proportional to the number of
turns by which their motion is still bounded. The time-evolution of the DA is shown on the right.
The markers represent the numerical results The continuous line shows the fitted inverse logarithmic law. The dotted line represents D
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DA vs. time: models - III
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Is this a purely phenomenological fit? In fact not quite.
The physical picture is: For r < D
The motion is governed by KAM theorem. Fully stable region (only Arnold diffusion for a set of initial conditions of small measure -> irrelevant from the physical point of view).
For r > D
The motion follows Nekhoroshev theorem, i.e., the stability time N(r) of a particle at radius r is given by
This provides a pseudo-diffusion.
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DA vs. time: models - IV
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Two regimes found in 4D simulations: D , b, k are always positive. This implies a stable
region for arbitrary times. In 4D simulations with tune ripple or 6D
simulations: There could be situations in which no stable
region for arbitrary times exists. This corresponds to
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DA vs. time: models - V
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Fit of DA vs. time can lead to a number of extensions: Losses in hadron machines due to non-linear effects (single particle).
Fermilab APT seminar 5/11/2013 Massimo Giovannozzi - CERN
Benchmarking with real data – ITevatron data: proton bunch at injection
Estimates from purely diffusive model included.
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Nice agreement for all models!
Experimental data from: T. Sen et al. “Beam Losses at Injection Energy and During Acceleration in the Tevatron”, IPAC03, p. 1754.
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Benchmarking with real data – IISPS data: proton bunch at 55 GeV in coast
Estimates from purely diffusive model included.
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Negative second order derivative cannot be reproduced by diffusive models!
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Extensions - I
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Evolution of DA in presence of beam-beam effects.Nb=0.10×1011 Nb=1.15×1011 Nb=1.70×1011
The proposed model holds for:- Non-linear single particle
dynamics- Weak-strong beam-beamIt is then tested on luminosity data from LHC.
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Extensions – IIIntensity and luminosity evolution during physics fills
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LHC
Tevatron
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Luminosity evolution models - I
The inverse logarithm model seems to fit well al data considered so far (LHC and other circular accelerators/colliders).
For luminosity evolution: No consideration of, e.g., burn off effect: an “effective” fit has
been considered and proved to work well, but the fit parameters might have little physical content.
A correct approach would require disentangling pseudo-diffusive effects (inverse logarithm) from the rest.
The boundary conditions: try to find a relatively simple model to allow analytical considerations.
LHC Run I provided lots of data to probe new models…Massimo Giovannozzi - CERN 19
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Luminosity evolution models - II What do we know from the LHC Run I
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Time in stable beams (s)
ATLASCMS
2011 LHC data.The two curves refer to the change of b* occurred during the year.
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Luminosity evolution models - III
Is it possible to factor out the contribution of the pseudo-diffusive effects?
Is it possible to normalise the data to find a “sort” of universal (at least for LHC) curve?
The answer is positive: For the time being only the plain proton burn off has
been included. Emittance evolution (e.g., radiation or rest gas
interaction) can be included.
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Luminosity evolution models - IV
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ATLAS - 2011
CMS - 2011
ATLAS - 2012
2011 and 2012 LHC data.Dashed line: burn off onlyBlue squares: proposed model.
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DA measurements - I
What is the DA of the real machine? No lifetime problems or slow losses at injection. During aperture measurements (with beams probing high
amplitudes) no sign of slow losses was found. This observation indicates that DA should be of the same order of mechanical aperture, i.e., about 10 s.
Measurement campaign launched: Two MD sessions organised (2011, 2012). Objective: benchmark numerical simulations against
measurements (e.g., for HERA a factor of two was found).
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Fermilab APT seminar 5/11/2013
DA measurements - II Two strategies applied:
Beam 1: Blow up the beam until slow losses are observed. Record evolution of beam intensity. Fit beam intensity with proposed models. Compare with fit parameters from numerical simulations of DA.
Beam 2: Kick the beam in order to push it towards high amplitudes until
large losses are obtained (standard method). Requires rather strong kick (aperture kicker). Compare amplitude of beam losses with numerical simulations of
DA.
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DA measurements: Beam 1 - III
Two MD sessions: 2011
Almost half of the time lost… Q-kicker used to blow up the beam emittance: not easy to induce
a symmetric blow up. Performed scans over the strength of MCOs using the same
polarity in all sectors. 2012
Much more efficient MD… Transverse damper used to blow up the beam emittance: easy
and reproducible blow-up. Performed scans over MCOs and MCDs. Used different alternating signs schemes (suggested by
Stephane).Massimo Giovannozzi - CERN
Strong chromatic effects
Almost cancelled chromatic effects (but symmetry broken
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DA measurements: Beam 1 – IV2011 MD
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DA measurements: Beam 1 – VMD 2011
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Effect of Q-kicker: large tails instead of a Gaussian beam
Beam size evolution during the MD
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DA measurements: Beam 1 - VI MD 2011
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Another confirmation of the scaling law of intensity vs. time
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Digression: simulations for Beam 1 DA measurements in 2011
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Dinf Dinf - nominal settings
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DA measurement: Beam 1 – VIIMD 2012
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Same configuration as 2011 Scan MCDs
Scan MCOs (alternating signs)
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Digression: simulations for Beam 1 DA measurements in 2012
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Signs -> +-+-+-+-Negative Dinf found: all phase space unstable!
MCO circuit in sector 1-2 was not available: simulations to be repeated and broken symmetry.
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DA measurements: Beam 2 - VIIIMD 2011-12
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Courtesy R. Tomás et al.
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Conclusions - I
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The LHC project has triggered several studies in non-linear beam dynamics.
Several tools and techniques have been devised to achieve the goal of estimating the dynamic aperture.
Latest proposals based on DA vs. time models Intensity vs. time Luminosity vs. time Luminosity models
Next step: try to find a diffusive model providing an equivalent behaviour of the DA vs. time
All confirmed by the analysis of available measured data.
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Conclusions - II
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The work done seems to have been fruitful: the LHC does not suffer from any single-particle non-linear effects.
DA measurements have been performed and data analysis is in progress.
HL-LHC will require even more sophisticated tools in view of new physics challenges!
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Thank you for your attention
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