A Monte Carlo simulation of cosmic rays interactions with the Earth s atmosphere

Transcription

1 Laboratori Nazionali del Gran Sasso, Italy September 8-2, 200 A Monte Carlo simulation of cosmic rays interactions with the Earth s atmosphere P.Zuccon, B.Bertucci, B.Alpat, R.Battiston, G.Battistoni 2, W.J. Burger, G.Esposito, A.Ferrari 2,3, E.Fiandrini, G.Lamanna, P.Sala 2,3 INFN Italy 2 INFN Sezione di Milano Italy 3 CERN Switzerland

2 Introduction Great interest in accurate simulation of CR interaction with atmosphere: Atmospheric νs Radiation satellite altitudes Key points: - CR primary fluxes - Model of the Atmosphere - Interaction Model - Geomagnetic Effects on primaries and secondaries - Cross-check with experimental data

3 Outline Description of the simulation: Generation technique Geomagnetic Field The model of the atmosphere Interaction package Comparison with AMS data on protons and leptons Conclusions & Future plans

4 Uniform generation of an isotropic proton flux in the kinetic energy range GeV, on a spherical surface at 40 Km a.s.l. Power law spectrum modified for solar modulation effect from a fit to AMS data. Each proton is back-traced until: The generation technique a) It reaches the distance of 0 Earth's radii from the Earth's center. ( allowed trajectory) b) It touches again the production sphere. (forbidden trajectory) EARTH

5 Magnetic Field Model Magnetic field in the Earth's proximity is the sum of two components. INTERNAL FIELD Generated by the Earth International Geomagnetic Reference Field distributed by NASA - 0 harmonics EXTERNAL FIELD Generated by the solar wind interaction with the geomagnetic field Tsyganenko '96 improved to speed up calculations distributed by NASA. Calculated only above 2 Earth's radii Altitude (Earth s Radii) Total Field Intensity (=Intensity at Earthís surface) External Field/Total Field

6 The Model of Atmosphere It is based on the MSIS-E-90 distributed by NASA 60 homogeneous layers between 0 and 20 Km Interaction probablity as a function of altitude Chemical composition as a function of altitude Earth s Radii (637.4 Km) Nuclear Int. lenght λ I EM Int. lenght X 0 density (g/cm 3 ) Total density N 2 O 2 O Altitude (Km) Altitude (Km) Ex. A particle following a circular orbit at 20 Km a.s.l. will travel for 0 4 Earth's radii before to feel an interaction length

7 The Interaction model FLUKA 2000 Authors: A.Ferrari, P.Sala, G.Battistoni(see TAUP200) Key advantages: Theory driven approach Continuosly checked against experimental data Intrinsically 3D

8 Details of the simulation A sample of ~3 0 6 protons has been generated in the kinetic energy range GeV using a spectrum fitted from AMS data. This statistic corresponds to an equivalent time exposure of the full area covered by AMS orbits of ~2 seconds. The normalisation of fluxes is absolute and it is calculated taking into account our detecting area and the Equivalent Time Exposure. We use as a detector a spherical surface matching the AMS orbit recording each particle within the AMS FoV.

9 Down going proton Flux 0 < θ M < 0,2 0,2 < θ M < 0,3 0,3 < θ M < 0,4 Flux (m 2 sr. MeV s.) ,4 < θ M < 0,5 0,5 < θ M < 0,6 0,6 < θ M < 0,7 0,7 < θ M < 0,8 0,8 < θ M < 0,9 0,9 < θ M < Kinetic Energy (GeV) AMS data Solid Line This simulation Red Line "real" secondary flux

10 Up going proton Flux - 0 < θ M < 0,2 0,3 < θ M < 0, ,5 < θ M < 0,6 0,7 < θ M < 0, Kinetic Energy (GeV) AMS data Solid Line This simulation Red Line "real" secondary flux

11 Motion of a trapped particle in the geomagnetic field Three type of motion: ) Gyration around the field line 2) Bouncing between northern and southern hemispheres Longitudinal drift Mirror point Field line Bouncing 3) Drift around the Earth

12 Drift shells examples L=.05 B m =0.4 G Atmosphere limit Short Lived shell The mirror point is always in the atmosphere so particles can only bounce once from northern to southern mirror points L=.05 B m =0.3 G Atmosphere limit Long Lived shell The mirror point is in the atmosphere only above the SAA the particle interact only in this area

13 Secondary protons end points map degree Short lived T < 0.3 s degree degree Long lived T > 0.3 s Only from primaries detected for geomagnetic latitude < 0.4 degree

14 Downgoing charged lepton fluxes Electrons and Positrons Flux (m 2 sr. MeV s.) e- downward 0 < θ M < 0,3 e- downward 0,3 < θ M < 0,7 e+ downward 0 < θ M < 0,3 e+ downward 0,3 < θ M < 0,7 Flux (m 2 s sr MeV) - Flux (m 2 s sr MeV) Ratio Electrons Positrons Kinetic Energy (GeV) Geomagnetic latitude (rad) AMS data Black line This simulation Red line "real" flux AMS data This simulation

15 Electrons and Positrons Flux (m 2 sr. MeV s.) Downgoing charged lepton fluxes e- downward e+ downward 0 < θ < 0,3 0 < M θ < 0,3 M AMS data Black line This simulation Green line only primaries with Ek>30 GeV e- downward 0,3 < θ M < 0,7 e+ downward 0,3 < θ M < 0,7 The green histogram shows that at low latitude positrons and electrons originate from protons of different energy Kinetic Energy (GeV) E e - W e + Estward protons inject positrons in the shells dump electrons in the Atm p p Westward protons inject electrons in the shells dump positrons in the Atm

16 Conclusions A good agreement between simulation and measured data is shown both on protons and on electrons. This simulation constrained by AMS data can be used to assess the radiation enviromment in near-earth orbits and is a new reliable tool for more accurate calculations of particle fluxes in atmosphere Future Plans Add the He component to the primary flux Cross check with muons fluxes measurements in the atmosphere Extend the energy range of the primaries up to TeV to do a full neutrino fluxes calculation

17 Integrated fluxes in 9 bins on geomagnetic latitude Flux (m 2 sr. s.) - 0 Primary proton flux Secondary measured proton flux Secondary real proton flux Ratio Sec./Prim. Ratio real Sec./Prim Geomagnetic latitude(rad) Geomagnetic latitude (rad)

18 ν µ reaching the Earth for vertical showers ν µ yelds ν µ Ratios Secondary/Primary Flux(m 2 sr. s.) - E ν >.3 GeV 0.4 < E ν <.3 GeV 0. < E ν < 0.4 GeV E ν >.3 GeV 0.4 < E ν <.3 GeV 0. < E ν < 0.4 GeV Geomagetic latitude (rad) Geomagetic latitude (rad) triangles: ν µ from secondary protons open circles: ν µ from primary protons

19 νe reaching the Earth for vertical showers ν e yelds ν e Ratios Secondary/Primary Flux(m 2 sr. s.) - 0 E ν >.3 GeV 0.4 < E ν <.3 GeV 0. < E ν < 0.4 GeV Flux(m 2 sr. s.) - E ν >.3 GeV 0.4 < E ν <.3 GeV 0. < E ν < 0.4 GeV Geomagetic latitude (rad) Geomagetic latitude (rad) triangles: ν e from secondary protons open circles: ν e from primary protons