Modelling of Electron Air Showers and Cherenkov Light

Modelling of Electron Air Showers and Cherenkov Light A. Mishev J. Stamenov Institute for Nuclear Research and Nuclear Energy Bulgarian Academy of Sciences 72 Tsarigradsko chausse, Sofia 1784, BULGARIA

The Cherenkov radiation is emitted if the velocity v of charged particles exceeds the speed of light, which is given by the local refractive index of the medium n and the vacuum speed of light c The condition is =v/c , where n is the local refractive index of the medium, v the speed of the charged particle and c the speed of light. Neglecting the wavelength dependence of n the emission angle c of Cherenkov photons relative to the charged particle direction is the number Nc of photons emitted per path length s in this angle is

Cherenkov light spectra

subroutine AUSGAB subroutine CERE TETA = ACOSD(1/BETA) {Cherenkov angle of emission } ANGLE = SIND 2(TETA) STEP = TVSTEP CERPHOT = 390. 0*ANGLE {number of the emited Cherenkov photons during a transportation step; Cherenkov wavelenght band is 350 -500 nm} CREG(IRL) = CREG(IRL)+ CERPHOT {number of Cherenkov photons in the region of interest} END OF CERE REAL INDEX, BETA, GAMMA {refractive index, velocity, Lorenz factor } CHARGE=IQ(NP) {charge of the particle} TOTE=E(NP) {energy of the particle} NO Region of interest YES muon YES NO Charged particle NO Me=Mm {Replacing the rest mass of the electron} GAMMA = TOTE/Me. C 2 GAMMA> Treshold NO YES BETA = f(GAMMA) INDEX = INDEX of MEDIA BETA = BETA*INDEX CALL CERE Simulation of the angle of emission Main program

Experimental setup

Experimental response of the water tank for different depths Experimental and theoretical responses of the small tank

simple atmospheric model in EGS 4 21 layers of 5 km thickness chemical composition Nitrogen, Oxygen and Argon variation of the refractive index in function of the local density of the atmosphere is taken into account The angle of Cherenkov photons emission is simulated with a full analogy with EGS 4's UPHI subroutine Comparison between EGS 4 and CORSIKA code

Flow diagram of EGS 4

Simplified schematic algorithm of "TRAMEAN"(Mean Trajectory) Monte Carlo code: START Data input: -material and geometrical conditions; -mean athmospheric extinction of Cerenkov photons; -initial number of created photons

Muon Cherenkov telescope Water Cherenkov detector

Lateral distribution function of Cherenkov light for primary helium Lateral distribution function of Cherenkov light for primary gamma

Cross section calculation Transportation step calculation Analytical energy losses calculation User’ s control set NO Step < set YES Continue to the next interaction

PC 1 PC 2 PC n Geometry and cross section calculation Main 1 Main 2 Data acquisition and analysis