1 / 93

930 likes | 1.02k Views

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

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

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**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**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**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.**The integral form:**here E0 – energy of the primary particle; Pb (E,xb) – boundary condition; xb– point of interaction of the primary particle.**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΄**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.**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.**Source functions for low energy electrons and gamma quanta**x=min(E0;E/ε)**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**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**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**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**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**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**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**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**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**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**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**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**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**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**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**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Energyby under threshold: 1 - by electrons; 2 - by photons;**3 - by pair; 4 - sum of 1, 2, 3**Cascade curves: - NKG; - LPM; lines -**individualLPM curves**Cascade curves: - NKG; - LPM; lines -**individualLPM curves**Muon density in gamma-induced showers:______ - BH; ______**- LPM; ■ – Plyasheshnikov, Aharonian; - our individual points**Muon density in gamma-induced showers:1 - AGASA; 2 - Homola**et al.; 3 - BH; 4 - Plyasheshnikov, Aharonian; 5, 6 - our calculations; 7 - LPM**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

More Related