The FLUKA Code
An Introduction to FLUKA:
a multipurpose Interaction and Transport MC code
P.R. Sala
ESI2009
FLUKA
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
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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
50 cm
K
p m
m
m
e in LAr
eDeveloped and maintained under
an INFN-CERN agreement
7th FLUKA course, Paris Sept. 29-Oct. 3, 2008
Copyright 1989-2008 CERN and INFN
p
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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
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Outline
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Fluka for calorimetry
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Energy deposition by ionization
Electromagnetic processes
Hadronic showers
 shower development and p0 production:
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high energy Hadron-Nucleus interactions
 non-compensation:
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“low energy” nuclear reactions
neutrons
 instrumental effects
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the example of quenching
ALICE : fluka through VirtualMonteCarlo
How to
dE/dx atomic interactions:
Example: 300 GeV m 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
preshower (LAr-Pb)
LAr/Pb
Fe-Scint
dE/dx atomic interactions:
300 GeV m in the ATLAS comb. calo test beam
Discrete events: Delta-ray production above a user-defined threshold
 Continuous energy loss: Cumulants approach to dE/dx fluctuations
 Multiple Coulomb Scattering with correlated PLC and lateral deflections

Same algorithm for all charged particles and all energies
Proc. of Calor96
Calibration in electron scale (e/m correct), electronic noise added
Ions dE/dx
Dose vs depth
distribution for 670
MeV/n 20Ne 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
EMF ElectroMagneticFluka
•Photoelectric: fluorescence, angular distribution, Auger,
polarization
•Compton and Rayleigh: atomic bonds, polarization
•Pair production correlated angular and energy distribution;
also m-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
The KLOE calorimeter simulation
The KLOE calorimeter
at DANE, LNF (Italy)
24 barrel
modules
Trapezoidal
section
(52 – 59)x23 cm2
length: 430 cm
Calorimeter module
Pb/Sci fibres structure
200 layers, lead foils +
glue + fibres
Lead
1.2 mm
F. Bossi et al, (Kloe Collaboration)
Riv. Nuovo Cimento 031 (2008) 531.
P.R. Sala Esi 2009 CERN
1.0 mm
1.35 mm
results with First Fluka simulation version
(G. Battistoni, B. Di Micco, A. Ferrari, A. Passeri, V. Patera)
base module
LEAD
replicas : 200
layers
GLUE
FIBRES (198)
P.R. Sala Esi 2009 CERN
COMPARISON WITH DATA –RESPONSE to PHOTONS
Resolution of the cluster centroid
position along the module.
Energy Resolution
E
E

0.057
E (GeV )
L 
1.2cm
E (GeV )
Curve : data
Dots: FLUKA
M.Anelli et al., NIM A 598, 244 (2009)
Jaroslaw Zdebik PhD thesis , also LNF-08/19
B
A
Energy deposit
P.R. Sala Esi 2009 CERN
Kloe: e.m. shower penetration depth
Cluster centroid Depth
Cluster centroid
depth
Incoming
photon
FLUKA
DATA
RMSdepth
P.R. Sala Esi 2009 CERN
Hadronic Showers
100 GeV p on Pb
shower longitudinal development
Fraction of the beam energy
converted into π0 and 
for interactions in Lead
as a function of projectile energy
The FLUKA hadronic Models
Hadron-nucleus: PEANUT
Elastic,exchange
Phase shifts
data, eikonal
hadron
low E
π,K
Special
P<3-5GeV/c
Resonance prod
and decay
hadron
Sophisticated
G-Intranuclear Cascade
Gradual onset of
Glauber-Gribov multiple
interactions
Preequilibrium
High Energy
DPM
hadronization
Coalescence
Evaporation/Fission/Fermi break-up
 deexcitation
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Inelastic hN at high energies: DPM
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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
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DPM and hadronization
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from DPM:
Number of chains
Chain composition
Chain energies and momenta
Diffractive events
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Almost No Freedom
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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
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Inelastic hN interactions: examples
p+ + p  p+ + X (6 & 22 GeV/c)
p+ + p  Ch+/Ch- + X (250 GeV/c)
Positive
hadrons X2
Negative
hadrons
Connected points: FLUKA
Symbols w. errors : DATA
Dots: Exp. Data
Histos : FLUKA
6 GeV
M.E. Law et. Al, LBL80 (1972)
22GeV
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Hadron-Nucleus interactions at high E
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Glauber cascade
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Glauber-Gribov
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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
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
1
plab
RA  r0 A  x for  2
pT  M 2
3
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Effect of Glauber and Formation Zone
Rapidity distribution of charged particles produced in 250 GeV p+
collisions on Gold
Points: exp. data (Agababyan et al., ZPC50, 361 (1991)).
No Glau
No FZ
Yes Glau
Yes FZ
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Nonelastic hA interactions at high energies: examples
Recent
results
from the
HARP
experiment
12.9 GeV/c
p on Al
p+
production
at
different
angles
Double differential p+ production
for p C interactions at 158 GeV/c, as
measured by NA49 (symbols) and
predicted by FLUKA (histograms)
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Atlas combined calo test beam: 1994 data
pion beams: longitudinal shower development and its fluctuations
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
Nuclear interactions in PEANUT:
Target nucleus description (density, Fermi motion, etc)
t (s)
Glauber-Gribov cascade with formation zone
10-23
Generalized IntraNuclear cascade
10-22
Preequilibrium stage with current exciton configuration and
excitation energy
(all non-nucleons emitted/decayed + all nucleons below 30-100 MeV)
Evaporation/Fragmentation/Fission model
γ deexcitation
10-20
10-16
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(Generalized) IntraNuclear Cascade
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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(r) + exceptions (ex. p)
Glauber cascade at higher energies
Classical trajectories (+) nuclear mean potential (resonant for p)
Curvature from nuclear potential  refraction and reflection
Interactions are incoherent and uncorrelated
Interactions in projectile-target nucleon CMS  Lorentz boosts
Multibody absorption for p, m-, KQuantum effects (Pauli, formation zone, correlations…)
Exact conservation of energy, momenta and all addititive
quantum numbers, including nuclear recoil
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Equilibrium particle emission
 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 for A<18 nuclei
 ~ 50000 combinations included with up to 6 ejectiles
  de-excitation:
 statistical + rotational + tabulated levels
 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).
Example of fission/evaporation
1 A GeV
208Pb
+ p reactions Nucl. Phys. A 686 (2001) 481-524
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Data
FLUKA
FLUKA after cascade
FLUKA after preeq
Quasi-elastic
Spallation
Evaporation
Fission
Deep spallation
Fragmentation
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Low energy ( < 20MeV neutrons)
The fraction of visible energy due to neutrons below 10-20 MeV is
significant.
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Most of their kinetic E is spent via elastic interactions recoils nonionizing 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 ms to ms depending on the material composition
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Infinite calorimeter
 visible E
resolution 
vs
signal integration
time
Low-energy neutron transport in FLUKA
performed by a multigroup algorithm
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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, H2O, CH2)
Pointwise, fully correlated, with explicit generation of all secondary
recoils, cross sections available for reactions in H, 6Li , Ar and partially
for 14N and 10B (4He, 12C and 16O 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
Atlas Combined calo test beam: pions
SIMULATIONS
Calibration in electron scale
DATA
Scintillator quenching included
Cut on mip in presampler Photostatistics convoluted
Cut on beam position
Noise added
Proton contamination taken
(beam chambers)
into account
Cut on preshower
Energy reconstructed using the ``benchmark'' technique
2
E0  EEM  a  Qhad  b  EEM 3  a  Qhad1  c  EEM
All parameters fixed to minimize /E0 at 300~GeV
Atlas combined calo test beam: 1994 data
Experimental electron
scale calibration
available
2
E0  EEM  a  Qhad  b  EEM 3  a  Qhad1  c  EEM
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
ATLAS TILE Calorimeter (1994 setup)
1994 Test beam : 5 modules, positrons
and positive pions beam, 20-300 GeV/c
NIM A394,384 (1994)
180 cm
(9 λ)
proton contamination in the beam measured
(Cerenkov counters) in a later testbeam:
scintillator (3mm)
iron (4mm)
iron (5 mm)
TILE Calorimeter: resolution and e/p
Beam at
200 incidence
FLUKA simulations with:
Proton contamination
Photostatistics convoluted offline
Step-by-step signal quenching online
Tile Calorimeter: effect of quenching
Qvis 
Q
dE
1  kB
dx
FLUKA simulations,
20 GeV/c
200 incidence
diferent quenching
parameters and
effect of beam
contamination
on e/p
and resolution
ALICE Test TPC
Fluka compared to TPC Test Results
Spatial Resolution
Cluster Charge „Landau“
Truncated Mean
(< 60%)
„dE/dx“
Fluka compared to Silicon Pixel
Detector Testbeam Results
Cluster Size Distribution
Si Pixel Detector
Neutron Background at the EMcal
Position
Late (> 30 ns) neutron production vertices
Optimization of the EMCAL time
integration window using FLUKA
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
how?
FLUKA is available from www.fluka.org and from NEA
 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

Flair
FLUKA Advanced Interface [http://www.fluka.org/flair]
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
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
Flair
FLUKA Advanced Interface [http://www.fluka.org/flair]
Plotting , Databases of materials, isotopes etc
Preequilibrium emission
For E > p 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 = Nh +Np, excitons
has the same probability to occur
Step: nucleon-nucleon collision with Nn+1=Nn+2 (“never come back
approximation)
Chain end = equilibrium = Nn sufficiently high or excitation energy below
threshold
N1 depends on the reaction type and cascade history
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RF
FLUKA Applications
CMS
Point 4
Momentun
Cleaning
Point 5
LHC Dump
Point 3.3
Point 3.2
The LHC
Loss Regions
Point 6
Regions of high losses
(e.g., Collimators,…)
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Point 7
Cosmic ray physics
Neutrino physics
ALICE
Accelerator design ( n_ToF, CNGS, LHC systems)
LHCb
ATLAS
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
Point 2
Regions with low losses
(e.g., due to residual gas)
Point 8
Point 1
7th FLUKA course, Paris Sept. 29-Oct. 3, 2008
46
Betatron
Cleaning
FLUKA
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
Developed and maintained under an INFN-CERN agreement
Copyright 1989-2008 CERN and INFN
>2000 users
http://www.fluka.org
7th FLUKA course, Paris Sept. 29-Oct. 3, 2008
47
The ATLAS EM calorimeter
287 GeV
electron
beam
Stars : fluka
Dots: expt.
(RD3 collab.)
Energy resolution 10-100 GeV:
 9.2  0.3%
 9.8  0.4%
Exp :
E

E
Fluka :
E

E
Longitudinal Development
impact position
response vs. electron impact position
deposited energy
Detail of the FLUKA geometry and
dE/dx atomic interactions
Discrete events: Delta-ray production above a user-defined threshold
Continuous energy loss: Cumulants approach to dE/dx fluctuations
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)
Equilibrium particle emission (evaporation, fission and
nuclear break-up)
From statistical considerations and the detailed balance principle, the
probabilities for emitting a particle of mass mj, spin Sj,ħ and energy E, or
of fissioning are given by:
(i, f for initial/final state, Fiss for fission saddle point)
Probability per unit time of
emitting a particle j with energy E
Probability per unit time of
fissioning
• ρ’s: nuclear level densities
• U’s: excitation energies
• Vj’s: possible Coulomb barrier
for emitting a particle type j
• BFiss: fission barrier
PJ

2S

j
 1 m j c
p 2 3
PFiss 
1
U i Q j   f

Vj
U i  BFiss
2 p  0
r f U f 
 E  EdE
ri U i  inv
r Fiss U i  BFiss  E 
dE
ri U i 
• Qj’s: reaction Q for emitting a
particle type j
• σinv: 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
50
Small Angle Absorber (SAA)
2°
0.8°
Lead
Tungsten

Complex integration issues:

Inner interface

 Vacuum system, bake-out, bellows, flanges
Outer interface
 Tracking chambers, recesses
Optimization of the Small Angle
Absorber performed with FLUKA
Example: Can Pb be replaced by Cu ?