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First energy estimates of giant air showers with help of the hybrid scheme of simulations

First energy estimates of giant air showers with help of the hybrid scheme of simulations. L.G. Dedenko M.V. Lomonosov Moscow State University, 119992 Moscow, Russia. CONTENT. Introduction 5-level scheme - Monte-Carlo for leading particles - Transport equations for hadrons

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First energy estimates of giant air showers with help of the hybrid scheme of simulations

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  1. First energy estimates of giant air showerswith help of the hybrid scheme of simulations L.G. DedenkoM.V. Lomonosov Moscow State University,119992 Moscow, Russia

  2. CONTENT • Introduction • 5-level scheme - Monte-Carlo for leading particles - Transport equations for hadrons - Transport equations for electrons and gamma quanta - The LPM showers - The primary photons - Monte-Carlo for low energy particles in the real atmosphere - Responses of scintillator detectors • The basic formula for estimation of energy • The relativistic equation for a group of muons • Results for the giant inclined shower detected at the Yakutsk array • Conclusion

  3. ENERGY SCALE

  4. SPACE SCALE

  5. Transport equations for hadrons: here k=1,2,....m – number of hadron types; - number of hadrons k in bin E÷E+dE and depth bin x÷x+dx; λk(E) – interaction length; Bk – decay constant; Wik(E′,E) – energy spectra of hadrons of type k produced by hadrons of type i.

  6. The integral form: here E0 – energy of the primary particle; Pb (E,xb) – boundary condition; xb– point of interaction of the primary particle.

  7. The decay products of neutral pions are regarded as a source function Sγ(E,x) of gamma quanta which give origins of electron-photon cascades in the atmosphere: Here – a number of neutral pions decayed at depth x+ dx with energies E΄+dE΄

  8. The basic cascade equations for electrons and photons can be written as follows: where Г(E,t), P(E,t) – the energy spectra of photons and electrons at the depth t; β – the ionization losses; μe, μγ – the absorption coefficients; Wb, Wp – the bremsstrahlung and the pair production cross-sections; Se, Sγ– the source terms for electrons and photons.

  9. The integral form: where At last the solution of equations can be found by the method of subsequent approximations. It is possible to take into account the Compton effect and other physical processes.

  10. Source functions for low energy electrons and gamma quanta x=min(E0;E/ε)

  11. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  12. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  13. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  14. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  15. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  16. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  17. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  18. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  19. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  20. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  21. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  22. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  23. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  24. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  25. Balance of energyby 1 - the primary photon; 2 - electrons; 3 - photons and 4 - under threshold in e-ph shower; 5 - sum of 1,2,3; 6 - total sum

  26. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  27. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  28. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  29. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  30. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  31. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  32. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  33. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  34. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  35. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  36. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  37. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  38. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  39. Energyby under threshold: 1 - by electrons; 2 - by photons; 3 - by pair; 4 - sum of 1, 2, 3

  40. B-H SHOWERS

  41. Cascade curves: - NKG; - LPM; lines - individualLPM curves

  42. Cascade curves:______ - NKG; ______ - LPM

  43. Cascade curves: - NKG; - LPM; lines - individualLPM curves

  44. Cascade curves:______ - NKG; ______ - LPM

  45. Cascade curves:______ - NKG; ______ - LPM

  46. Cascade curves:_____ - NKG; ______ - LPM

  47. Muon density in gamma-induced showers:______ - BH; ______ - LPM; ■ – Plyasheshnikov, Aharonian; - our individual points

  48. Muon density in gamma-induced showers:1 - AGASA; 2 - Homola et al.; 3 - BH; 4 - Plyasheshnikov, Aharonian; 5, 6 - our calculations; 7 - LPM

  49. For the grid of energies Emin≤ Ei ≤ Eth (Emin=1 MeV, Eth=10 GeV) and starting points of cascades 0≤Xk≤X0 (X0=1020 g∙cm-2) simulations of ~ 2·108 cascades in the atmosphere with help of CORSIKA code and responses (signals) of the scintillator detectors using GEANT 4 code SIGNγ(Rj,Ei,Xk) SIGNγ(Rj,Ei,Xk) 10m≤Rj≤2000m have been calculated

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