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Update of the Sixtrack scattering routine. Claudia Tambasco, Belen Salvachua, Stefano R edaelli, Roderik Bruce, Daniele Mirarchi. Collimation Working Group 31/03/2014 . Acknowledgements. Thanks to whole the collimation team , in particular to L.Lari , A.Marsili , G.Cavoto .

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Update of the Sixtrack scattering routine

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update of the sixtrack scattering routine

Update of the Sixtrack scattering routine

Claudia Tambasco, Belen Salvachua, Stefano Redaelli, Roderik Bruce, Daniele Mirarchi

Collimation Working Group 31/03/2014


Thanks to whole the collimation team, in particular to L.Lari, A.Marsili, G.Cavoto.

Thanks to A. Lechner and the FLUKA team:

Providing FLUKA cross sections:

Comparison FLUKA/Sixtrack cross sections will continue (R.Bruceet al.)

Ionization losses:

Implementation of the Landau tail for the Ionization energy loss (D.Mirarchi et al.)

Thesis on Cern Library at:


  • SixTrack scattering routine updates:
    • Carbon density
    • Ionization losses
    • Coulomb scattering correction
    • Nuclear interactions
  • Results:
    • 3.5 TeV global losses
    • 3.5 TeV data/simulations comparison at TCTs
    • 7 TeV impacts at collimators
    • 7 TeV Cleaning Efficiency
  • Ongoing work
  • Conclusions

Why do we need to update the SixTrack scattering routine?

  • Scattering routine developed in 1990’s (by T. Tranker and J.B Jeanneret)
  • Recent measurements of cross section processes

Better description of interaction with matter

After the long shutdown, LHC will reach the designed proton energy of 7 TeV and the luminosity peak of 10^34 [cm-2 s-1] :

Higher Luminosity and Energy

More beam losses, more energy deposition on the machine equipment

quench of the superconducting magnets

Even more important Collimation System:

More accurate prediction of the Cleaning efficiency

  • Improving the physics model of the scattering routine allows to increase the power of predictions for higher energy simulations
sixtrack scattering routine
SixTrack scattering routine
  • Simulates scattering mechanisms of the protons within the collimator jaws
  • developed in 1990’s (by T. Tranker and J.B Jeanneret)

Ionization (Bethe-Bloch equation)



Small angle:

Multiple Coulomb scattering

Large angle:

Rutherford Scattering

Coulomb scattering:

Nuclear interactions

scattering with the nucleons

Effective number of nucleons


Scattering routine changes:

Nuclear Interactions:

  • Proton-proton SD cross section
  • Proton-proton elastic cross section
  • Proton-proton total cross section
  • Proton-Nucleus inelastic cross section
  • Proton-Nucleus total cross section
  • Proton-Nucleus elastic cross section
  • updated according to recent experimental data

Review of electromagnetic processes:

  • Ionization
  • Coulomb scattering

and Carbon density (see next slide for the value implemented)


Update Carbon density

Previous Carbon in SixTrack

AC150K Carbon


TCP and TCSP collimators

Used as TCP/TCSG

Carbon jaw by default

Graphitic carbon, but its compaction rate is far from full so its nominal density is significantly lower, i.e. 1.65 g/cm^3.


Update of ionization energy loss

In many Monte Carlo programs the ionization energy loss is simulated by implementing a continue loss that is described by the Bethe-Bloch equation:

Previous SixTrack version: used a constant value to describe the energy lost by ionization which was an approximation of the Bethe-Bloch.

New SixTrack version: implemented the Bethe-Bloch equation for the complete list of collimator materials.

Used before for simulations at all energies


Multiple Coulomb Scattering correction

Multilple Coulomb Scattering: added logarithmic part in rms angle formula:

Old SixTrack version: the logarithm part in the rms angle formula was missing

New SixTrack version: added missing logarithmic part

Adding the logarithmic part increases the rms of the scattered angle distribution

With the new implementation the difference on the rms reaches up 20% for Tungsten

Carbon 60 cm

RMS: 0.00292

RMS: 0.00242

New SixTrack

Old SixTrack


Proton-proton scattering

  • Experimental data from LHC experiments are available for p-p total and elastic cross sections at 3.5 TeV and 4 TeV beam energy
  • New SixTrack version: implemented recent parameterizations from COMPETE collaboration

New parameterizations:

Before: linear fit used

7 TeV

Differential pp ELASTIC cross-section:

Slope Parameter

New parameterization:


Single diffractive cross section

Old SixTrack version: implementation from an old theory of K. Goulianos (1983)

Further experimental data showed the necessity to develop a new theory

New SixTrack version: implementation from updated theory from same author

“Renormalization of hadronic diffraction and the structure of the pomeron”,

K. Goulianos Physic Letters B 358 1995

New parameterization:

Larger momentum change w.r.t. elastic scattering

pp SD cross section

The previous version underestimated the total proton-proton SD cross section


Minor Updates: p-Nucleus cross sections

  • Proton-Nucleus total cross section:
  • new collision length from PDG (max variation ~2% )
  • Proton-Nucleus inelastic cross section:
  • new interaction length from PDG (max variation ~3% )

Proton-Nucleus elastic cross section: automatically updated since it is calculated by subtracting the other contributions


Results: Global losses at 3.5 TeV

Impacts at collimators and aperture

Change on Cleaning Q8-Q11

Old SixTrack 3.5 TeV

New SixTrack 3.5 TeV

TCSG IP6 new: ~1.5 e-4

old: ~4 e-5


Results: Check improvement with data

  • Look at the TCT losses in IP1 and IP5
  • SixTrack gives the primary impacts at collimators, then BLM response factors from FLUKA are needed [E.Skordis, R.Bruce]

3.5 TeV Experimental Data vs simulation at TCTs

Perfect machine

Thanks to R.Bruce

for experimental data

Thanks to FLUKA

For BLM response factors


Only Sixtrack

By a factor of ≈3 closer to data w.r.t. the old routine

The new SixTrack version provides a better agreement with the experimental data

A new estimation of the cleaning inefficiency at 7 TeV has been carried out


New predictions of the losses at 7 TeV:

impacts at collimators

B1 horizontal halo case



~by a factor 4 more losses in TCSG in IP6


New predictions of the losses at 7 TeV

New SixTrack at 7TeV

Beam 1 Horizontal halo distribution




New predictions of the losses at 7 TeV (DS region)

DS regions:



More losses on the cold magnets by a factor of≈ 1.8 w.r.t. the previous routine


Ongoing work

  • Paper in preparation includes:
  • Description of all the updates
  • 7 TeV predictions of the new simulations
  • Parametric study of cleaning and impacts at TCTs and TCSG in IP6 for:
    • Ionization energy Bethe-Bloch vs most probable value of the Landau Distribution and the tails
    • Singe Diffractive cross section variation: ±10%, ±20, …, ±90%


From PDG

  • The physics model of the SixTrack scattering routine has been updated and improved
  • The effects of the new SixTrack version has been studied by data-simulation comparison at 3.5 TeV

3 times closer to the data w.r.t. the old SixTrack version

  • A study on the cleaning inefficiency prediction at 7 TeV has been carried out

1.8 times more losses on the cold magnets w.r.t. the old SixTrack version

  • Data-simulations comparison at 3.5 TeV in the imperfect machine case

further agreement expected (see R. Bruce talk)

Follow up of the work in the team:

Further comparisons with other codes (FLUKA/SixTrack/Merlin/Geant)

Further physics model improvement (Bethe-Bloch/Landau tails)

New SixTrack release contains already the presented changes

(R.Bruce, D.Mirarchi, A.Rossi)