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

Massimo Giovannozzi - CERN 2

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


Definition and issues - II


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!


Definition and issues - III


Here are some examples of indicators: Lyapunov exponent Tune difference (this indicator triggered several studies on accurate

computation of tunes in numerical simulations).


DA studies for LHC - I


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


DA studies for LHC - II Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA


10

11

12

13

14

15

16

0 15 30 45 60 75 90

DA

(s)

Angle (degrees)

Beam 1 Beam 2 Summary of DA at injection energy. The error bars represent the effect of 60 seeds


DA studies for LHC - III Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA


5

10

15

20

25

30

35

Min

imum

DA

(s)

Beam 1 Beam 2

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.


DA studies for LHC - IV Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA


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.


DA studies for LHC - V

Possibility to evaluate the DA for the machine as-built Possibility to evaluate impact of sorting on DA


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.


DA vs. time: models - I


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


Definition and issues - VII


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


DA vs. time: models - III


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.


DA vs. time: models - IV


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


DA vs. time: models - V


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.

15

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.

Fermilab APT seminar 5/11/2013 Massimo Giovannozzi - CERN

Benchmarking with real data – IISPS data: proton bunch at 55 GeV in coast

Estimates from purely diffusive model included.

16

Negative second order derivative cannot be reproduced by diffusive models!


Extensions - I


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.


Extensions – IIIntensity and luminosity evolution during physics fills


LHC

Tevatron


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


Luminosity evolution models - II What do we know from the LHC Run I


0

5

10

15

20

0 20000 40000 60000 80000 100000

Nor

mlis

ed in

tegr

ated

lum

inos

ity/fi

ll (1

033cm

-2)

Time in stable beams (s)

ATLASCMS

2011 LHC data.The two curves refer to the change of b* occurred during the year.


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.



Luminosity evolution models - IV


0

5

10

15

20

0 5 10 15 20 25 30 35 40

Nor

mal

ised

Inte

grat

ed lu

min

osity

/fill

(10-6

cm-2

)

Normalised time in stable beams (10-6 s)

ATLAS - 2011

CMS - 2011

ATLAS - 2012

2011 and 2012 LHC data.Dashed line: burn off onlyBlue squares: proposed model.


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).



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.

Massimo Giovannozzi - CERN


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


DA measurements: Beam 1 – IV2011 MD

Massimo Giovannozzi - CERN26


DA measurements: Beam 1 – VMD 2011


Effect of Q-kicker: large tails instead of a Gaussian beam

Beam size evolution during the MD


DA measurements: Beam 1 - VI MD 2011

Massimo Giovannozzi - CERN500 1000 1500

1.25

1.26

1.27

1.28

1.29 IMCO=-40 A

0 500 1000 1500 2000

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

Tim e s

Dyn

amic

Ape

rture

7 :0 0 am M C O 2 0 A

M C O 2 0 A

M C O 4 0 A

M C O 6 0 A

M C O 5 5 A

Another confirmation of the scaling law of intensity vs. time


Digression: simulations for Beam 1 DA measurements in 2011


0

2

4

6

8

10

12

14

16

18

20

-100 -80 -60 -40 -20 0 20 40 60 80 100

DA (s

igm

a)

Relative MCO strength

Particle loss Particle loss - nominal settings

Dinf Dinf - nominal settings


DA measurement: Beam 1 – VIIMD 2012


Same configuration as 2011 Scan MCDs

Scan MCOs (alternating signs)


Digression: simulations for Beam 1 DA measurements in 2012


0

2

4

6

8

10

12

14

16

18

20

-100 -80 -60 -40 -20 0 20 40 60 80 100

DA (s

igm

a)

Relative MCO strength

Particle loss Particle loss - nominal settings

Dinf Dinf - nominal settings

Signs -> +-+-+-+-Negative Dinf found: all phase space unstable!

MCO circuit in sector 1-2 was not available: simulations to be repeated and broken symmetry.


DA measurements: Beam 2 - VIIIMD 2011-12

Massimo Giovannozzi - CERN

Courtesy R. Tomás et al.


Conclusions - I


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.


Conclusions - II


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!


Thank you for your attention


The LHC dynamic aperture saga: overview, ideas and recent developments

Documents

Transcript of The LHC dynamic aperture saga: overview, ideas and recent developments