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 N c of photons emitted per path length s in this angle is

Cherenkov light spectra

AUSGAB subroutine AUSGAB REAL INDEX,BETA,GAMMA { refractive index, velocity, Lorenz factor } CHARGE=IQ(NP) {charge of the particle} TOTE=E(NP) {energy of the particle} Region of interest Charged particle GAMMA = TOTE/M e C 2 GAMMA> Treshold BETA = f (GAMMA) INDEX = INDEX of MEDIA BETA = BETA*INDEX CALL CERE NO NO NO Main program YES YES muon NO YES M e =M m {Replacing the rest mass of the electron} YES Simulation of the angle of emission CERE 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 nm} CREG(IRL) = CREG(IRL)+ CERPHOT {number of Cherenkov photons in the region of interest} END OF CERE

Experimental setup

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

Comparison between EGS4 and CORSIKA code simple atmospheric model in EGS4 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 EGS4's UPHI subroutine

Flow diagram of EGS4

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

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

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