Effects of beam-beam interactions on luminosity

decay rates at the LHC in 2012Anton Esmail-Yakas, 2015

For completion of the 3rd year of the Physics with a Year in Europe Msci at Imperial College London in relation with École

Polytechnique Fédérale de Lausanne as part of the Swiss European Mobility Program.

Special thanks to Xavier Buffat for help with the analysis and Danilo Banfi for help with the initial Python codes

used

Main supervisor: Tatiana PieloniSupervisor from Imperial College London: Gavin Davies

Supervisor from EPFL: Leonid Rivkin

Aims

• Analyse different available models for luminosity decay

• Analyse the dependency of decay rates on BBIs

• Analyse the time dependency of decay rates

Different fitting methods

• Simple exponential model• C = 0, variable C

• Tevatron model (“Fitting the luminosity decay in the Tevatron, E. McCrory et al., 2005)

•Brightness model (Xavier Buffat)

Simple exponential model

• (C = 0)

• + C (C variable)

Constant decay rate

Tevatron model

Theory attempts to account for IBS, beam burn-up due to luminosity, and beam-beam interactions.

Time varying decay rate

Brightness model

Assumes 2 different processes of decay – slow process () (e.g. IBS)Fast process () that is present for brightness larger than (e.g. incoherent growth due to a resonance)

Two decay rates – C varying in initial hoursC = 0 in later hours

C = 0 fit

C varying fit

Brightness fit

Tevatron fit

Residual analysis – Whole FillC = 0 fit qualitatively worse.

3 other fits produce similar results.

Residual analysis – 1st Hour

Whole fill does not model 1st hour accurately – need to fit 1st hour separately

Little difference between Variable C fit and other models when fitting first hour.

Filling scheme 2710

- First half 2012

Decay rates pop out for bunches missing IP2s and IP8s

Luminosity and Specific luminosity decay rates follow the same pattern

Strong and varying correlations with the LRs

Bunches seem to also follow HOs – only noticeable when they are missing

Very different pattern over whole fill compared to 1st hour

Some shifts at bunches with different HOs/LRs

Related to drop in HOs?

Negative correlation with LRs?Or a different effect? IBS?

Specific luminosity decays show some relation to HOs

Whole fill decay shows stronger relation to HOsrather than LRs?Likely due to stronger effect of HOs persisting throughout fill

Filling scheme 2998

- Second half2012

Decay rates pop out for bunches missing IP8s

Luminosity and Specific luminosity decay rates follow the similar pattern

Very different patterncompared to fill 2710

Strong and varying correlations with the LRs

Also for spec. lumi.

Very different pattern over whole fill compared to 1st hour

Drops in decay rates for bunches with fewer total LRs

But no bunch by bunch correlation with LRs

Large change in pattern after 1st hour

Expanding time window

Similar change in pattern

Equivalent analysis using 1hr sliding window – results are very different and not consistent enough to produce results for each hour

Modelling sections by single hours is not effective outside of the first hour

However, the expanding window is not necessarily better, as it only shows a different pattern for the first hour, and misses it in the following hours – e.g. hours 1-2, as seen below…

Decay rate vs time analysisDecay rate is calculated by an expanding window as for the bunch-bunch analysis, though expanding in 5 minute steps.

Sharp drop after first hoursThough somewhat unreliable due to expanding window

More examples…

• Importance of model used to fit luminosity – simple exponential (C=0) is not suitable. Models based around varying decay regimes are much better• Importance of the time period that is looked at – currently no model can

fit to the whole fill and still accurately model behaviour contained within the first hour. Need to find a better model for consistent time analysis• Effects in the first hours are VERY different to effects over the whole fill –

Strong BBI dependencies – not yet obvious the nuances within this• Studies on a larger number of fills and relating to injection intensities of

fills would be useful

Closing ideas…

Thank you!

Questions?