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Upgrade of the Monte Carlo Code CORSIKA to Simulate Extensive Air

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Upgrade of the Monte Carlo Code CORSIKA to Simulate Extensive Air FORSCHUNGSZENTRUM KARLSRUHE Technik und Umwelt Wissenschaftliche Berichte FZKA 6097B Upgrade of the Monte Carlo Co de CORSIKA to Simulate Extensive 20 Air Showers with Energies > 10 eV 1y D. Heck and J. Knapp Institut fur Kernphysik Contribution to: Fruhjahrstagung DPG, Sektion Teilchenphysik, March 23 - 27 1998 Freiburg 1 Universitat Karlsruhe, Institut fur Exp erimentelle Kernphysik, Postfach 3640, D-76021 Karlsruhe y now at: Department of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom Forschungszentrum Karlsruhe GmbH, Karlsruhe 1998 Abstract Upgrade of the Monte Carlo Co de CORSIKA to Simulate Extensive Air 20 Showers with Energies > 10 eV. To simulate extensive air showers at the highest observed energies the Monte Carlo program CORSIKA has b een upgraded. Some of the uncertainties of the hadronic interaction mo dels are discussed. The e ects of the Landau-Pomeranchuk-Migdal e ect onto the electromagnetic interactions are demonstrated. Sp ecial attention is paid to the reduction of computing time by the so-called thin sampling pro cedure. Various steps of realization are describ ed. The in uence of the thin sampling level on the computing time, the particle numb ers to b e stored, and the statistical uncer- tainty of observable quantities is shown. Zusammenfassung Erweiterung des Monte Carlo Programms CORSIKA zur Simulation von 20 ausgedehnten Luftschauern bei den hochsten Energien > 10 eV. Um ausgedehnte Luftschauer b ei den hochsten b eobachteten Energien simulieren zu konnen, wurde das Monte Carlo Programm CORSIKA erweitert. Einige der Un- sicherheiten, die von den hadronischen Wechselwirkungsmo dellen herruhren, werden diskutiert. Der Ein u des Landau-Pomeranchuk-Migdal-E ekts auf die elektromag- netischen Wechselwirkungen wird gezeigt. Besondere Aufmerksamkeit wird der Ver- minderung der Rechenzeit durch das sogenannte thin sampling Ausdunnen gewid- met. Die verschiedenen Ausbaustufen der Verwirklichung werden b eschrieb en. Der Ein u der Ausdunn-Energiesc hwelle auf die Rechenzeit, auf die Zahl der zu sp ei- chernden Teilchen und auf die statistische Unsicherheit b eobachtbarer Groen wird demonstriert. i ii Contents 1 Intro duction 1 2 Features of Hadronic Interaction Mo dels 1 3 Landau-Pomeranchuk-Migdal E ect 2 4 Computing Times without Thin Sampling 6 5 Stages of Thin Sampling 7 6 In uence of Thin Sampling Level 14 7 Conclusions 16 Acknowledgement 17 Bibliography 18 iii iv 1 Intro duction 15 The greatest mysteries of cosmic rays arise at the highest energies > 10 eV where the ux b ecomes so small that very extended detectors on the Earth surface are needed to collect statistically sucient events. Such exp eriments cannot observe the primary cosmic ray directly, rather they lo ok for the reaction pro ducts which are formed within the atmosphere - so-called extensive air showers EAS - and reach the ground. The reconstruction of parameters like primary energy, direction, and mass is not straight forward and is only p ossible by comparison with detailed simulations of the EAS development. Sp ecial interest is given to cosmic rays at 19 energies > 10 eV as their existence cannot to be explained consistently with known acceleration mechanisms and large distance traveling through space without o interaction with the 3 K background radiation. The exp erimental determination of the precise form of the sp ectrum at those energies would b e a great step towards the understanding of the highest energy particles in the universe. Some exp eriments to explore this energy range are now op erating or are to be real- ized in the near future. Such exp eriments are AGASA [1], HiRes [2], Yakutsk [3], and AUGER [4]. Understanding the exp erimental data and designing new exp eri- ments needs Monte Carlo programs to simulate EAS at the highest energies. These requests pushed the upgrade of the EAS simulation program CORSIKA COsmic 20 Ray SImulation for KASCADE for primary energies > 10 eV . 2 Features of Hadronic Interaction Mo dels The most essential ingredient to simulate EAS at the highest energies is a hadronic interaction mo del which is able to extrap olate from lower energies covered by man made accelerators to predict the results of hadronic collisions at higher energies. This extrap olation is sub ject to considerable uncertainties. Within CORSIKA [5] we have ve high energy hadronic interaction mo dels available: DPMJET [6], HDPM [5, 7], QGSJET [8], SIBYLL [9], and VENUS [10]. A comparison of these mo dels is given in Ref. [11, 12, 13] which includes a discussion of their in uences onto the development of EAS. Three of these mo dels DPMJET, QGSJET, and SIBYLL handle hadronic interactions at the highest energies. Besides other features they predict also the hadronic interaction cross-section which determines the free path between twointeractions. The predicted inelastic proton-air cross-sections are shown in Fig. 1. Despite the extrap olation, the cross-section values of the three mo dels do not di er by more than 15 at the highest energies. Similarly the average transverse momentum which is carried away by the charged secondary particles is 19 5 predicted in accordance up to p =10 eV corresp onding with E 10 GeV , lab cm see Fig. 8 of Ref. [11] and the di erences between the considered mo dels are mo derate. Other extrap olations like the average multiplicity of secondary charged particles emerging from a hadronic collision are a ected byamuch larger uncertainty 1 650 (mb) p-air inel 600 Mielke et al. σ Yodh et al. 550 Gaisser et al. Baltrusaitis et al. 500 Honda et al. 450 400 VENUS 350 QGSJET SIBYLL 300 HDPM 250 DPMJET 2 3 4 5 6 7 8 9 10 11 10 10 10 10 10 10 10 10 10 10 plab (GeV/c) Figure 1: Inelastic p-air cross-sections for hadronic interaction mo dels available in CORSIKA together with exp erimental values derived from air shower exp eriments 5 [14, 15, 16, 17, 18]. The shaded band represents a t to the data b elow p < 10 GeV lab pair 2 according to the function = a log p+b log p+c . inel of more than a factor 2.5, as maybe deduced from Fig. 5 of Ref. [11]. 3 Landau-Pomeranchuk-Migdal E ect When an ultrarelativistic electron emits a low-energy photon via bremsstrahlung, the longitudinal momentum transfer b etween electron and the involved target nucleus can be very small. Because of the uncertainty principle this implies a long distance within which the momentum transfer takes place, known as the formation length. If anything happ ens to one of the two electromagnetic particles while traveling this formation length, the emission can b e disrupted. This is known as Landau-Pomeranchuk-Migdal LPM e ect [19, 20] and is caused predominantly by electron multiple scattering. This e ect b ecomes noticeable for interactions in air at normal temp erature and 16 pressure at energies ab ove 10 eV . Similarly in pair pro duction it suppresses + predominantly those events in which the energy is shared symmetrically by the e e - pair. The magnitude of this suppression dep ends on the pro duct E of the energy em air of inducing em-particle and of the air density at the interaction p oint. Consequently for pair pro duction and bremsstrahlung the LPM-e ect is most pronounced at high energies and low altitudes. In Figs. 2 and 3 the in uences of the LPM-e ect are shown 2 1 v•dN/dv -1 10 E = 1016eV e 17 Ee= 10 eV E = 3.1*1017eV e 18 Ee= 10 eV -2 E = 3.1*1018eV 10 LPM bremsstrahlung e 19 Ee= 10 eV altitude = 20 km E = 3.1*1019eV e 20 Ee= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional photon energy v = Eγ/E0 1 v•dN/dv -1 10 E = 1016eV e 17 Ee= 10 eV E = 3.1*1017eV e 18 Ee= 10 eV -2 E = 3.1*1018eV 10 LPM bremsstrahlung e 19 Ee= 10 eV altitude = 10 km E = 3.1*1019eV e 20 Ee= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional photon energy v = Eγ/E0 1 v•dN/dv -1 10 E = 1016eV e 17 Ee= 10 eV E = 3.1*1017eV e 18 Ee= 10 eV -2 E = 3.1*1018eV 10 LPM bremsstrahlung e 19 Ee= 10 eV altitude = 0 km E = 3.1*1019eV e 20 Ee= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional photon energy v = Eγ/E0 Figure 2: LPM-e ect for bremsstrahlung at various altitudes and electron energies. On the ordinate the pro duct of fractional photon energy v times the rate p er fractional photon energy dN =dv is given in arbitrary units. For the lowest energies it coincides with the Bethe-Heitler case. 16 20 for 3 altitudes and various energies b etween E =10 eV and 10 eV . These curves have b een established with a routine taken from the FORTRAN program AIRES 3 1 dN/du -1 10 E = 1017eV γ 18 Eγ= 10 eV LPM pair formation E = 3.1*1018eV γ 19 Eγ= 10 eV E = 3.1*1019eV altitude = 20 km γ 20 Eγ= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional electron energy u=Ee/E0 1 dN/du -1 10 E = 1017eV γ 18 Eγ= 10 eV LPM pair formation E = 3.1*1018eV γ 19 Eγ= 10 eV E = 3.1*1019eV altitude = 10 km γ 20 Eγ= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional electron energy u=Ee/E0 1 dN/du -1 10 E = 1017eV γ 18 Eγ= 10 eV LPM pair formation E = 3.1*1018eV γ 19 Eγ= 10 eV E = 3.1*1019eV altitude = 0 km γ 20 Eγ= 10 eV 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 fractional electron energy u=Ee/E0 Figure 3: LPM-e ect for pair pro duction at various altitudes and gamma-ray en- ergies.
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