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Update on the modelling of crystal channeling for FLUKA

Update on the modelling of crystal channeling for FLUKA. P. Schoofs, F. Cerutti, A. Ferrari, G. Smirnov. Ref . :. Outline. Introduction Description of the model Frame of reference Continuous potential Interactions in Channeling Volume effects Exit kick Results

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Update on the modelling of crystal channeling for FLUKA

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  1. Update on the modelling of crystal channeling for FLUKA P. Schoofs, F. Cerutti, A. Ferrari, G. Smirnov Ref. : P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  2. Outline • Introduction • Description of the model • Frame of reference • Continuouspotential • Interactions in Channeling • Volume effects • Exit kick • Results • 2D distributions – Case study • Benchmarkingagainst UA9-H8 data • Conclusions P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  3. Introduction • Why an implementation of channeling inside FLUKA ? • Crystals are investigated as new possible solution for collimation @ CERN • Energydeposition and tracking of secondaries need to beevaluated • FLUKA is the Monte Carlo currentlyused to assessthese values in the collimation system • How doesitwork ? • Microscopic description avoiding the use of empiricalparameters • Crystalsdefined as a region of the FLUKA geometrylayout in which • Particlescanbe channeled if their transverse energy is smallenough • - Followchannelcurvature • - Undergoreducedamount of interactions • Interactions are carried on using FLUKA models • Quasi-channeled particlescanbereflected or captured Presently, a standaloneeventgenerator has been developed and benchmarked. Integrationinto FLUKA not yetcompleted. P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  4. Frame of reference • Crystal defined in FLUKA combinatorialgeometry • Object situated in the laboratory • Regionflagged as crystal  trigger channeling-relatedeffects • Crystal planes definedinside crystal by 2 vectors • A : along the channel direction • B : perpendicular to A, giving the crystal planes orientation • Vectors are independentfrom the region • Natural reproduction of miscut • Torsion • Change in the channel orientation alongB • Change the radius of curvatureproportional to excursion alongB P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  5. ContinuousPotential in a Crystal • Straight crystal • Lindhardformalism • For smallincoming angles relative to the crystal planes, successive interactions of the particlewith the lattice plane are correlated. • Hence, weconsider interactions with the plane as a whole • « Continuous » strings of atoms Continuouspotential • Moliere screening function • Thermal vibrations • Average the cont. pot. over the gaussian thermal motion • RMS amplitude = 0.075 Å at room temp. • Bent crystal • CentrifugalPotential • The effective potentialbarrier is reduced on the outerside • For a certain bending, the potentialwelldoes not existanymore • critical radius • Effective Potential Innerside Outerside dp P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  6. ContinuousPotential in a Crystal • Channeling condition • Energy of the transverse motion • PotentialEnergy ? • depends on the initial transverse position • random variable, uniform over • Particle is channeled if : • Maximal angle allowing channeling in a given crystal at a givenenergy = critical angle P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  7. Interactions in channeling • Oscillations • Particleoscillatebetweenplanes • Approx. : Harmonicpotential •  Sinusoidal oscillations • Oscillation amplitude depends on • Coulomb scattering • CH particles single-scattering mode • Transverse energymodified by interactions • According to , interaction withnucleicanberejected • Classicalview : particlenevercomescloser to the latticethan • Quantum form factor relating the momentumtransfer and impact parameter • Electrons takenintoaccount through the Fano correction • Dechanneling if goes above . P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  8. Interactions in Channeling • Nuclear Interactions • Scaling factor to the cross sections • = averagenucleidensity • Nucleardensity in the channel : • Folding of the density over the sine trajectory • Typicalscalingfactors range from 0 to 2.5 for individualparticles • Reduction rates of the order of 12 For 400GeV/c , R=13m, σx’ = 10 urad P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  9. Volume effects • Quasi-Channeling • Non channeled particles • Crystal bending Tangencyatsome point • Single-scattering mode • Volume capture • Tangencyregionbeginswhen • Transverse energy associated with the quasi-channeled particle • can be modified by Coulomb scatterings • IF : drops below  CAPTURE • Volume reflection • IF NOT : Particle escapes the region and is reflected • One-time kick towards the outerside of the bend • Exception : non-channeled particleswith • VR kick graduallyincreasing Possible Channeling Amorphous Quasi-channeling tangencyregion • [M. Bondarenco, arXiv:0911.0107v3, 2010] (Thanks to Daniele for pointingthis out ! ) P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  10. Exit kick • A particle exits channeling mode when • it is dechanneled or • it exits the crystal region of the geometry • Angularspreadat exit ? • Natural angle of the oscillatingparticle • Arc sine distribution • Width of the distribution depending on the oscillation amplitude of the particle, itselfdepending on the transverse energy value • Results in a steep exit distribution • Gaussianangle with • Providessatisfyingresultswrt the experimental data • BUT : parameter-related (eventhough not an entirelyarbitraryparameter) • Currentlythe adoptedmethod P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  11. Results • Qualitative comparison of angular scan with H8-RD22 • Distribution of particlesagainst crystal orientation and hor. outgoing angle wrt crystal orientation (out-cr) • Strip crystal in 400 GeV proton-beam – divergence σx’=8 urad • Using the hor. Kick (out-in) we have VR or. CH or. [Scandale, PRL 98, 2007] P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  12. Results • Otherexamples: • X divergence = 0 • Withstrong torsion (10urad/m), no hor. Divergence, σy=1 mm σy’=10 urad P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  13. Results • UA9-H8: • Single-passexperiment • Crystal placed in the center • 5 siliconstrip detectors around • Track reconstruction : up- and downstream  yieldsdeflection angles • (Preliminary) data analysis: • Determination of the crystal torsion • Crystal efficiencyafter torsion compensation courtesy M. Pesaresi P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  14. Results • Benchmarkingagainst UA9-H8 data : channeling orientation • 2 different types of crystals • Quasi-Mosaic • Strip • Bending angle • ~50 urad for LHC • ~100-200 urad for the SPS • LHC strip crystal (STF 71 – R.1191) • SPS strip crystal (STF 50 – R.889) • LHC QM crystal (QMP 28 – R.1028) P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  15. Results • Volume reflection orientation • SPS strip crystal (STF 50 – R.892) • (NB: Log scale to betterappreciate VC) • Overall good agreement P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  16. Conclusions • Semi-classicalmicroscopic model of channeling • Description of dechanneling, volume reflection and volume capture • Takesintoaccount torsion and miscut • Uses FLUKA interaction models • Good agreement withresultsfrom UA9-H8 experiment • for the channeling peak description • for the dechanneling distribution • volume capture rate • But : • Slightunderestimation of the dechanneling rate • Exit kick determinationstill an open question • In the future : • Finish implementationinsidecore FLUKA • EMD ? Alteredionization in channeling ? • Longer term : negativelychargedparticles, axial channeling,… Acknowledgement to the UA9 collaboration ! P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  17. Thanks for your attention ! P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  18. Backup P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  19. Backup P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  20. Backup P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  21. Backup P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

  22. Backup P. Schoofs, Update on the modelling of CC for FLUKA, CollUSM#28

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