1. An Introduction to FLUKA: a multipurpose Interaction and Transport MC code The FLUKA Code P.R. Sala ESI2009

2. 7 th FLUKA course, Paris Sept. 29-Oct. 3, 2008 2 FLUKA Developed and maintained under an INFN-CERN agreement Copyright 1989-2008 CERN and INFN http://www.fluka.org Main authors: A. Fassò, A. Ferrari, J. Ranft, P.R. Sala Contributing authors: G.Battistoni, F.Cerutti, T.Empl, M.V.Garzelli, M.Lantz, A. Mairani, V.Patera, S.Roesler, G. Smirnov, F.Sommerer, V.Vlachoudis      50 cm 65 cm p e-e- e in LAr Hadron-nucleus interactions Nucleus-Nucleus interactions Electron-photon int. Muon int. (inc photonuc) Neutrino int. Particle Transport multiple scattering Ionization Decay Low energy neutrons Combinatorial geo + voxels Magnetic field Analogue or biased

3. 33 The FLUKA international Collaboration M.Brugger, F. Cerutti, A. Ferrari, M. Mauri, G. Lukasik, S. Roesler, L. Sarchiapone, G. Smirnov, F. Sommerer,C. Theis, S. Trovati, H. Vinke, V.Vlachoudis CERN A. Fassò, J.Vollaire SLAC, USA J. Ranft Univ. of Siegen, Germany G. Battistoni, F. Broggi, M. Campanella, P. Colleoni, E. Gadioli, A. Mairani, S. Muraro, P.R. Sala INFN & Univ. Milano, Italy M. Carboni, C. D’Ambrosio, A. Ferrari, A. Mostacci, V. Patera, M. Pelliccioni, R. Villari INFN Frascati M.C. Morone Univ. Roma II, Italy A. Margiotta, M. Sioli INFN & Univ. Bologna, Italy K. Parodi DKFZ & HIT, Heidelberg, Germany A. Empl, L. Pinsky Univ. of Houston, USA K.T. Lee, T. Wilson, N. Zapp NASA-Houston, USA S. Rollet ARC Seibersdorf Research, Austria M. Lantz Chalmers Univ. of Technology, Sweden

4. Outline Fluka for calorimetry Energy deposition by ionization Electromagnetic processes Hadronic showers  shower development and  0 production: high energy Hadron-Nucleus interactions  non-compensation: “low energy” nuclear reactions neutrons  instrumental effects the example of quenching ALICE : fluka through VirtualMonteCarlo How to

5. Example: 300 GeV  in the ATLAS combined calorimeter test beam Layout of the experimental set-up (NIM A387,333(1997), NIM A449,461 (2000)) Test beams in 1994 and 1997, electrons, positive pions, muons LAr/Pb Fe-Scint preshower (LAr-Pb) dE/dx atomic interactions :

6. Calibration in electron scale (e/  correct), electronic noise added Proc. of Calor96 Same algorithm for all charged particles and all energies 300 GeV  in the ATLAS comb. calo test beam Discrete events: Discrete events: Delta-ray production above a user-defined threshold Continuous energy loss: Continuous energy loss: Cumulants approach to dE/dx fluctuations Multiple Coulomb Scattering with correlated PLC and lateral deflections dE/dx atomic interactions :

7. Ions dE/dx Dose vs depth distribution for 670 MeV/n 20 Ne ions on a water phantom. The green line is the FLUKA prediction The symbols are exp data from LBL and GSI Exp. Data Jpn.J.Med.Phys. 18, 1,1998 Fragmentation products Here more ingredients like effective charge and its fluctuations Applications to hadron therapy

8. Photoelectric: fluorescence, angular distribution, Auger, polarization Compton and Rayleigh: atomic bonds, polarization Pair production correlated angular and energy distribution; also  -pair production and direct e + e - for μ Photonuclear interactions; also for μ Bremsstrahlung : LPM, angular distribution,... also for μ Bhabha and Møller scattering Positron annihilation at rest and in flight μ capture at rest Optical photon (Cherenkov) production and transport Multiple or single scattering on option EMF ElectroMagneticFluka

9. P.R. Sala Esi 2009 CERN The KLOE calorimeter simulation The KLOE calorimeter at DA  NE, LNF (Italy) Calorimeter module 24 barrel modules Trapezoidal section (52 – 59)x23 cm 2 length: 430 cm Pb/Sci fibres structure 200 layers, lead foils + glue + fibres 1.2 mm Lead 1.35 mm 1.0 mm F. Bossi et al, (Kloe Collaboration) Riv. Nuovo Cimento 031 (2008) 531.

10. P.R. Sala Esi 2009 CERN GLUE FIBRES (198) LEAD base module replicas : 200 layers results with First Fluka simulation version (G. Battistoni, B. Di Micco, A. Ferrari, A. Passeri, V. Patera)

11. P.R. Sala Esi 2009 CERN COMPARISON WITH DATA –RESPONSE to PHOTONS Energy Resolution Curve : data Dots: FLUKA Resolution of the cluster centroid position along the module. A B Energy deposit M.Anelli et al., NIM A 598, 244 (2009) Jaroslaw Zdebik PhD thesis, also LNF-08/19

12. P.R. Sala Esi 2009 CERN Kloe: e.m. shower penetration depth Incoming photon Cluster centroid depth FLUKA DATA Cluster centroid Depth RMS depth

13. Hadronic Showers 100 GeV p on Pb shower longitudinal development Fraction of the beam energy converted into π 0 and  for interactions in Lead as a function of projectile energy

14. 14 The FLUKA hadronic Models Elastic,exchange Phase shifts data, eikonal P<3-5GeV/c Resonance prod and decay low E π,K Special High Energy DPM hadronization hadron Hadron-nucleus: PEANUT Sophisticated G-Intranuclear Cascade Gradual onset of Glauber-Gribov multiple interactions Preequilibrium Coalescence Evaporation/Fission/Fermi break-up  deexcitation

15. 15 Inelastic hN at high energies: DPM Problem: “soft” interactions → QCD perturbation theory cannot be applied. Interacting strings (quarks held together by the gluon-gluon interaction into the form of a string) Interactions treated in the Reggeon-Pomeron framework each of the two hadrons splits into 2 colored partons  combination into 2 colourless chains  2 back-to-back jets each jet is then hadronized into physical hadrons

16. 16 DPM and hadronization from DPM: Number of chains Chain composition Chain energies and momenta Diffractive events Almost No Freedom Chain hadronization Assumes chain universality Fragmentation functions from hard processes and e + e − scattering Transverse momentum from uncertainty considerations Mass effects at low energies The same functions and (few) parameters for all reactions and energies

17. 17  + + p  Ch + /Ch - + X (250 GeV/c) Inelastic hN interactions: examples  + + p   + + X (6 & 22 GeV/c) 6 GeV 22GeV M.E. Law et. Al, LBL80 (1972) Connected points: FLUKA Symbols w. errors : DATA Positive hadrons X2 Negative hadrons Dots: Exp. Data Histos : FLUKA

18. 18 Hadron-Nucleus interactions at high E Glauber cascade Quantum mechanical method to compute Elastic, Quasi-elastic and Absorption hA cross sections from Free hadron-nucleon scattering + nuclear ground state Multiple Collision expansion of the scattering amplitude Glauber-Gribov Field theory formulation of Glauber model Multiple collisions  Feynman diagrams High energies: exchange of one or more Pomerons with one or more target nucleons (a closed string exchange) G-INC with Formation zone (=materialization time): gives a condition for possible reinteraction inside a nucleus

19. 19 Effect of Glauber and Formation Zone No Glau No FZ Yes Glau Yes FZ Rapidity distribution of charged particles produced in 250 GeV  + collisions on Gold Points: exp. data (Agababyan et al., ZPC50, 361 (1991)).

20. 20 Nonelastic hA interactions at high energies: examples Recent results from the HARP experiment 12.9 GeV/c p on Al  + production at different angles Double differential  + production for p C interactions at 158 GeV/c, as measured by NA49 (symbols) and predicted by FLUKA (histograms)

21. Atlas combined calo test beam: 1994 data pion beams: longitudinal shower development and its fluctuations

22. The importance of low E interactions and nuclear physics 100 GeV p in a Fe absorber: space-averaged particle spectra Average binding energy losses for interactions in lead. The number of primary collisions are also reported

23. 23 Nuclear interactions in PEANUT: Target nucleus description (density, Fermi motion, etc) Preequilibrium stage with current exciton configuration and excitation energy (all non-nucleons emitted/decayed + all nucleons below 30-100 MeV) Glauber-Gribov cascade with formation zone Generalized IntraNuclear cascade Evaporation/Fragmentation/Fission model γ deexcitation t (s) 10 -23 10 -22 10 -20 10 -16

24. 24 (Generalized) IntraNuclear Cascade Primary and secondary particles moving in the nuclear medium Target nucleons motion and nuclear well according to the Fermi gas model Interaction probability  free + Fermi motion ×  (r) + exceptions (ex.  ) Glauber cascade at higher energies Classical trajectories (+) nuclear mean potential (resonant for  ) Curvature from nuclear potential  refraction and reflection Interactions are incoherent and uncorrelated Interactions in projectile-target nucleon CMS  Lorentz boosts Multibody absorption for ,  -, K - Quantum effects (Pauli, formation zone, correlations…) Exact conservation of energy, momenta and all addititive quantum numbers, including nuclear recoil

25. Equilibrium particle emission  Evaporation  Evaporation:  Weisskopf-Ewing approach  600 possible emitted particles/states (A<25) with an extended evaporation/fragmentation formalism  Inverse cross section with proper sub-barrier  Fission  Fermi Break-up  Fermi Break-up for A<18 nuclei  ~ 50000 combinations included with up to 6 ejectiles   de-excitation   de-excitation:  statistical + rotational + tabulated levels  Competition  Competition between evaporation and fission, on option competition also with gamma emission  The same algorithm for all reactions, including nucleus-nucleus interactions In ALL reaction steps, from first interaction to last  : Exact energy conservation including binding energy and recoil of residual nucleus Nuclear masses up to A=330, from experimental databases supplemented by calculated masses following the RIPL-2 IAEA report (2005).

26. 26 1 A GeV 208 Pb + p reactions Nucl. Phys. A 686 (2001) 481-524 Example of fission/evaporation Quasi-elastic Spallation Deep spallation Fission Fragmentation Evaporation DataData FLUKAFLUKA FLUKA after cascadeFLUKA after cascade FLUKA after preeqFLUKA after preeq

27. Low energy ( < 20MeV neutrons) The fraction of visible energy due to neutrons below 10-20 MeV is significant. Most of their kinetic E is spent via elastic interactions  recoils  non- ionizing or quenched. (except for interactions on Hydrogen). Most of the low energy neutron contribution comes from capture  rays. The capture probability is maximal in the thermal region: thermalization times can vary from  s to ms depending on the material composition Infinite calorimeter  visible E resolution  vs signal integration time

28. Energy range up to 20 MeV divided in 260 energy groups ( 30 thermal) and 40 groups for secondary gamma generation The library contains ≈230 different materials/temperatures/Self shielding Hydrogen cross sections available for different types of molecular binding (free, H 2 O, CH 2 ) Pointwise, fully correlated, with explicit generation of all secondary recoils, cross sections available for reactions in H, 6 Li, Ar and partially for 14 N and 10 B ( 4 He, 12 C and 16 O in preparation) gamma transport by the standard EM FLUKA modules For most materials, information on the residual nuclei produced by low-energy neutron interactions are available in the FLUKA library Low-energy neutron transport in FLUKA performed by a multigroup algorithm

29. Atlas Combined calo test beam: pions DATA Cut on mip in presampler Cut on beam position (beam chambers) SIMULATIONS Calibration in electron scale Scintillator quenching included Photostatistics convoluted Noise added Proton contamination taken into account Cut on preshower Energy reconstructed using the ``benchmark'' technique All parameters fixed to minimize  /E 0 at 300~GeV

30. Atlas combined calo test beam: 1994 data Experimental electron scale calibration available

31. Atlas combined calo test beam: resolution Energy resolution, 1994+1996 data 1996 Data Less electronic noise Better presampler No electron calibration Note the experimental point at 20 GeV 2 simulated curves: different algorithms for preshower reconstruction

32. ATLAS TILE Calorimeter (1994 setup) 180 cm (9 λ) 100 cm scintillator (3mm) iron (4mm) iron (5 mm) 1994 Test beam : 5 modules, positrons and positive pions beam, 20-300 GeV/c NIM A394,384 (1994) proton contamination in the beam measured (Cerenkov counters) in a later testbeam:

33. TILE Calorimeter: resolution and e/  FLUKA simulations with: Proton contamination Photostatistics convoluted offline Step-by-step signal quenching online Beam at 20 0 incidence

34. Tile Calorimeter: effect of quenching FLUKA simulations, 20 GeV/c 20 0 incidence diferent quenching parameters and effect of beam contamination on e/  and resolution

35. ALICE Test TPC

36. Truncated Mean (< 60%) „dE/dx“ Fluka compared to TPC Test Results Cluster Charge „Landau“ Spatial Resolution

37. Fluka compared to Silicon Pixel Detector Testbeam Results Si Pixel Detector Cluster Size Distribution

38. Neutron Background at the EMcal Position Late (> 30 ns) neutron production vertices

39. Optimization of the EMCAL time integration window using FLUKA

40. FLUKA: Analogue vs Biased mode FLUKA can run in both analogue or biased mode Analogue mode: Correlations and fluctuations are preserved Event-by-event analysis is possible Biased mode: Faster convergence to average results Rare events/contributions can be amplified Deep penetration problems are feasible FLUKA contains a variety of variance acceleration (biasing) techniques

41. how? FLUKA is available from www.fluka.org and from NEAwww.fluka.org Written in Fortran Input from data-cards Customizable user-routines available Built-in scoring Geometry: Combinatorial + lattice + voxel, with debugging and 2D viewer External 3D geometry visualization tool available (SimpleGeo by C. Theis), internal one under development Courses for beginners twice a year (next in Mumbay, India, Oct. 2009) User support through mailing list

42. Flair FLUKA Advanced Interface Flair FLUKA Advanced Interface [http://www.fluka.org/flair]http://www.fluka.org/flair Input:  Filtering Cards  Show card links  Units: i.e. 20 GeV/c (ToDo)  Data validation  Import/Export on various formats Process:  Debugging  Compilation  Run monitoring  Merging

43. Flair FLUKA Advanced Interface Flair FLUKA Advanced Interface [http://www.fluka.org/flair]http://www.fluka.org/flair Plotting, Databases of materials, isotopes etc

45. 45 Preequilibrium emission For E >  production threshold  only (G)INC models At lower energies a variety of preequilibrium models Two leading approaches The quantum-mechanical multistep model: Very good theoretical background Complex, difficulties for multiple emissions The semiclassical exciton model Statistical assumptions Simple and fast Suitable for MC Statistical assumption: any partition of the excitation energy E * among N, N = N h +N p, excitons has the same probability to occur Step: nucleon-nucleon collision with N n+1 =N n +2 (“never come back approximation) Chain end = equilibrium = N n sufficiently high or excitation energy below threshold N 1 depends on the reaction type and cascade history

46. 7 th FLUKA course, Paris Sept. 29-Oct. 3, 2008 46 FLUKA Applications  Cosmic ray physics  Neutrino physics  Accelerator design (  n_ToF, CNGS, LHC systems)  Particle physics: calorimetry, tracking and detector simulation etc. (  ALICE, ICARUS,...)  ADS systems, waste transmutation, (  ”Energy amplifier”, FEAT, TARC,…)  Shielding design  Dosimetry and radioprotection  Space radiation  Hadrontherapy  Neutronics

47. 7 th FLUKA course, Paris Sept. 29-Oct. 3, 2008 47 FLUKA Developed and maintained under an INFN-CERN agreement Copyright 1989-2008 CERN and INFN http://www.fluka.org Main authors: A. Fassò, A. Ferrari, J. Ranft, P.R. Sala Contributing authors: G.Battistoni, F.Cerutti, T.Empl, M.V.Garzelli, M.Lantz, A. Mairani, V.Patera, S.Roesler, G. Smirnov, F.Sommerer, V.Vlachoudis >2000 users

48. The ATLAS EM calorimeter Energy resolution 10-100 GeV: Detail of the FLUKA geometry and 287 GeV electron beam deposited energy Stars : fluka Dots: expt. (RD3 collab.) impact position response vs. electron impact position Longitudinal Development

49. dE/dx atomic interactions Experimental 1 and calculated energy loss distributions for 2 GeV/c positrons (left) and protons (right) traversing 100μm of Si J.Bak et al. NPB288, 681 (1987) Discrete events: Discrete events: Delta-ray production above a user-defined threshold Continuous energy loss: Continuous energy loss: Cumulants approach to dE/dx fluctuations

50. 50 Equilibrium particle emission (evaporation, fission and nuclear break-up) Probability per unit time of emitting a particle j with energy E Probability per unit time of fissioning From statistical considerations and the detailed balance principle, the probabilities for emitting a particle of mass m j, spin S j, ħ and energy E, or of fissioning are given by: (i, f for initial/final state, Fiss for fission saddle point) ρ’s: nuclear level densities U’s: excitation energies V j ’s: possible Coulomb barrier for emitting a particle type j B Fiss : fission barrier Q j ’s: reaction Q for emitting a particle type j σ inv : cross section for the inverse process Δ’s: pairing energies Neutron emission is strongly favoured because of the lack of any barrier Heavy nuclei generally reach higher excitations because of more intense cascading

51. Small Angle Absorber (SAA) Complex integration issues: Inner interface  Vacuum system, bake-out, bellows, flanges Outer interface  Tracking chambers, recesses Tungsten Lead 2°2° 0.8°

52. Optimization of the Small Angle Absorber performed with FLUKA Example: Can Pb be replaced by Cu ?