CORSIKA, Extensive Air Shower simulation

introduction CORSIKA SummaryWhat are Extensive Air Showers?• charged particle cascades that arise in the atmospherewhen cosmic rays hit the Earth• consist of plenty of different particles (e ± , p, n, µ ± , π ± , π 0 ,K ± )• shower front moves with almost speed of light towards theEarth during development through the atmosphere

introduction CORSIKA Summaryshower components• initiated by collision ofprimary with particles ofthe atmosphereatmospheric depth 1000 g/cm 2• three main showercomponents• hadronic one (mostly pand n)• elm. one containselectrons, positrons andgammasfed by π 0 decayselm.componenthadroniccomponentmyoniccomponentobservationlevel• muonic one, mostpenetrating part

introduction CORSIKA Summaryshower components• initiated by collision ofprimary with particles ofthe atmosphereatmospheric depth 1000 g/cm 2• three main showercomponents• hadronic one (mostly pand n)• elm. one containselectrons, positrons andgammasfed by π 0 decayselm.componenthadroniccomponentmyoniccomponentobservationlevel• muonic one, mostpenetrating part

introduction CORSIKA Summaryshower components• initiated by collision ofprimary with particles ofthe atmosphereatmospheric depth 1000 g/cm 2• three main showercomponents• hadronic one (mostly pand n)• elm. one containselectrons, positrons andgammasfed by π 0 decayselm.componenthadroniccomponentmyoniccomponentobservationlevel• muonic one, mostpenetrating part

introduction CORSIKA Summaryshower components• initiated by collision ofprimary with particles ofthe atmosphereatmospheric depth 1000 g/cm 2• three main showercomponents• hadronic one (mostly pand n)• elm. one containselectrons, positrons andgammasfed by π 0 decayselm.componenthadroniccomponentmyoniccomponentobservationlevel• muonic one, mostpenetrating part

introduction CORSIKA Summaryshower components• initiated by collision ofprimary with particles ofthe atmosphereatmospheric depth 1000 g/cm 2• three main showercomponents• hadronic one (mostly pand n)• elm. one containselectrons, positrons andgammasfed by π 0 decayselm.componenthadroniccomponentmyoniccomponentobservationlevel• muonic one, mostpenetrating part

introduction CORSIKA Summaryshower discprimary particleshower axis• shower has lateral extent• shower disc is roughly 1mthick• charged particles can besampled by grounddetectorsthickness ≈ 1mshower coreΘzenith angleΘdetectors

introduction CORSIKA SummaryWhat are the main reactions that occur?• elm. component:π 0 → 2γ, γ → e + + e − and e − → e − + γ• muonic component:π ± → µ ± + ν ¯ µ ,• hadronic component:π and fragments of primary nuclei interact with air nucleifrom atmosphere

introduction CORSIKA Summaryenergy flow

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for elm. cascades• simple branching model forelm. cascade• alternating Bremsstrahlungand pair production aftereach interaction length• N = 2 t , t depth in X 0 ;E(t) = E 0 /2 t• N max = E 0 /E c = 2 tmax• depth of shower maximum∝ to logarithmic energy• in maximum E c is reached

introduction CORSIKA SummaryHeitler model for hadronic part• simple branching model forhadronic cascade• π + A → π 0 + 𠱕 hadronic interaction untilpion decays/reachescritical energy[J. Matthews, Astropart. Physics 22(2005)387]

introduction CORSIKA SummaryHeitler model for hadronic part• simple branching model forhadronic cascade• π + A → π 0 + 𠱕 hadronic interaction untilpion decays/reachescritical energy[J. Matthews, Astropart. Physics 22(2005)387]

introduction CORSIKA SummaryHeitler model for hadronic part• simple branching model forhadronic cascade• π + A → π 0 + 𠱕 hadronic interaction untilpion decays/reachescritical energy[J. Matthews, Astropart. Physics 22(2005)387]

introduction CORSIKA Summaryfluctuations

introduction CORSIKA SummaryCORSIKACOsmic Ray SImulation for KAscadeKArlsruhe Shower Core and Array DEtector• program for detailed simulation of extensive air showers• particles are tracked on their way through the atmosphere• alternative interaction models to describe the high energyreactions• in particle decays all branches down to 1% level are takeninto account

introduction CORSIKA SummaryHow to simulate extensive air showers?• Follow all the particles and register their interactions.• Transport and reactions are determined by randomnumbers according to probability density functions. (MonteCarlo method)• to attain in the end detector related EAS observables (e.g.N e , N µ , X max )

introduction CORSIKA Summaryrelevant parameters• Environment: atmospheric models, magnetic field of theEarth• Particle: type, energy, position, momentum, time• Range estimation: cross section σ, life time τ• Particle transport: ionization energy loss dE/dX , multiplescattering (for leptons), deflection in magnetic field, in theend particle reaches observation level or cut• Interaction/decay with production of secondaries: hadronicinteraction models, particle decay (branching ratio > 1%),electromagnetic interaction (EGS4)• Secondary particles: are stored on stack

introduction CORSIKA SummaryAtmosphere

introduction CORSIKA Summarydifferent atmospheres

introduction CORSIKA SummaryMagnetic Fieldtotal strength of Earth’s magnetic field in nT

introduction CORSIKA SummaryMagnetic FieldInclination angle

introduction CORSIKA SummaryMagnetic FieldDeclination angle

introduction CORSIKA SummaryParticles in CORSIKA

introduction CORSIKA SummaryCharmed Particles in CORSIKA

introduction CORSIKA SummaryRange of particle for interactionThe probability P int to traverse a layer with thickness χ withoutinteraction is:P int (χ) = 1λ inte −χ/λ int.The individually traversed matter thickness χ isχ = −ln(RNDM) · λ int with random number 0 < RNDM < 1.The mean free path λ int is given by λ int = Σ3 i=1 n iA iΣ 3 i=1 n iσ i,int.with A i atomic weight of atmosphere’s component iand σ i energy dependent cross section of component i.atomic fractions n i of air:n 1 (N 2 ) = 0.7848,n 1 (O 2 ) = 0.2105,n 1 (Ar) = 0.0047

introduction CORSIKA SummaryRange of particle for decayThe probability P D to traverse a path l without decay isP D (l) = 1l De −l/l DThe individually traversed path length l is l = −ln(RNDM) · l Dwith random number 0 < RNDM < 1.The mean free path l D is given by l D = cτγβ.

introduction CORSIKA SummaryCross section

introduction CORSIKA SummaryCross sections

introduction CORSIKA Summaryionization energy lossenergy loss of charged particle traversing matter of thickness λis described by Bethe-Bloch stopping power formuladE i = λz2β 2 κ 1(ln(γ 2 − 1) − β 2 + κ 2 )very high energy muons suffer additional loss byBremsstrahlung and e + e − pair production

introduction CORSIKA SummaryWhy so many different interaction models?Different interaction models produce different mean values forshower variables. Scattering of mean values gives estimationon systematic uncertainties due to different extrapolations ofaccelerator data to high energy and forward direction.Different models follow slightly different approaches to describeinteractions (jet model, pomeron exchange, Gribov-Reggetheory).

introduction CORSIKA Summarylateral density functions for H and Fe primaries at 1000 gcm 2 ,mean values from 50 showers with 1PeV primary energy each

introduction CORSIKA Summarylongitudinal profiles for H and Fe primaries, mean values from50 showers with 1PeV primary energy each

introduction CORSIKA SummaryEnergy Spectrum of Cosmic Rays

introduction CORSIKA Summaryexample applicationSimulations are needed to interprete data.

introduction CORSIKA SummaryDownloading the program:Installation• ftp corsika-6735.tar.gz (and QGSDAT-II-03 for QGSjetIImodel) from ftp://ftp-ik.fzk.de/pub/corsika/v670• unpack using: tar -zxvf corsika-6735.tar.gz• move QGSDAT-II-03 to corsika-6735/run/• run install script in subdirectory corsika-6735• select options• source: www-ik.fzk.de/corsikadocumentation and further information available• since 2009 100% GNU compatible installation scriptcoconut• for normal linux installation (gcc and g77) alternatively./corsika-install can be used

introduction CORSIKA Summarymost important options• high energy hadronic interaction model: QGSjetII, Epos• low energy hadronic interaction model: FLUKA, GHEISHA• date and time: used only for printing in output file• detector geometry:• Horizontal flat (Auger, KASCADE-Grande, Grapes)• Non flat (volume) (Magic, HESS)• Vertical string detector (Antares, IceCube)• ROOTOUT: output in root file format using COAST

introduction CORSIKA Summarysteering via input fileIf installation succeeded binary can be found in the /runsubdirectory, can be executed and is controlled via steering file.

introduction CORSIKA Summary• storage amount and cpu time increase linearly withprimary energy• one single 10 20 eV shower needs ≈1 year CPU time,several TB storage amount

introduction CORSIKA Summarythinning option, for highest energieschoose ǫ and weight w ifollow all particles with E > E thin = ǫ · E 0typical values for thinning level ǫ are 10 −7 ... 10 −4kept particle resembles w i particles of its kindcomparison for 1 10 19 eV showerCPU time disk spaceno thinning few months few 100 GBǫ ≈ 10 −7 7h 20MBǫ ≈ 10 −6 1h 2MB→optimal thinning [M. Kobal et al., Astropart. Phys.15(2001)259]

introduction CORSIKA Summaryadvantages• cpu time saving• storage amount is reduced• good compromise betweenbenefit and cost for optimalvalues of ǫ and wshortcomings• additional artificialfluctuations are introduced(increased by √ w)• problems to apply furthersimulations to output file(e.g. detector simulation,geant)

introduction CORSIKA Summaryalternative programsAIRESCONEXCOSMOSFLUKAGEANT4HEMASMOCCASENECAtranscript of MOCCA to Fortran (Sciutto)hybrid with cascade equations (Kalmykov et al.)hybrid with subshower library (Kasahara et al.)multi-purpose detector Monte Carlo (Ferrari et al.)multi-purpose detector Monte Carlo (CERN)used for MACRO (Battistoni, Forti et al.)split algorithm, thinning, Pascal (Hillas)hybrid with cascade equations (Drescher et al.)

introduction CORSIKA Summary• CORSIKA is currently best available tool for 3d simulationof extensive air showers!• for further details look at http://www-ik.fzk.de/corsika