Modelling of Electron Air Showers and Cherenkov Light
A.Mishev J. Stamenov
Institute for Nuclear Research and Nuclear Energy Bulgarian Academy of Sciences72 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
n 1
=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
c n
arccos1
the number Nc of photons emitted per path length s in this angle is
dN
dsdc c
n c
2
2
2
sin
Cherenkov light spectra
subroutine AUSGABAUSGAB
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
Chargedparticle
GAMMA = TOTE/MeC2 GAMMA>
Treshold
BETA = f(GAMMA)INDEX = INDEX of MEDIABETA = BETA*INDEXCALL CERE
NONO
NONO
NONO
Main program
YESYES
YESYES
muon
NONO
YESYES
Me=Mm
{Replacing the rest massof the electron}
YESYES
Simulation ofthe angle of emission
subroutine CERECERETETA = ACOSD(1/BETA){Cherenkov angle of emission }ANGLE = SIND2(TETA)STEP = TVSTEPCERPHOT = 390.0*ANGLE{number of the emitedCherenkov photons duringa transportation step;Cherenkov wavelenght bandis 350-500nm}CREG(IRL) = CREG(IRL)+CERPHOT{number of Cherenkov photonsin the region of interest}END OF CERE
Experimental setup
10 15 20 25 30
1
10
100
Nther
/Nexpt
Ntheor
,photons
Uout
expt ,mV
Source 60Co
A = 3.105 BqWater Tank 10x10x40 cm
Theory Experiment
H2O depth,cm
Experimental and theoretical responses of the small tank
10 100 1000
20
40
60
80
100
120
10cm H2O
20cm H2O
30cm H2O
N,
coin
cid
en
ces.
min
-1
U [mV]
Experimental response of the water tank for different depths
0.0 2.0x102 4.0x102 6.0x102 8.0x102 1.0x103
0.0
5.0x106
1.0x107
1.5x107
2.0x107
Statistical errors ~ 103photons
CORSIKA5.62 EGS4
Nto
t,pho
tons
Energy, GeV
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:
Equiprobable areas calculation
Start of cycle
First random impact point on the reflector
Second impact point on the reflector
Partial trajectory calculationand addition to the total trajectorybefore the photon extinction
End of cycle
Calculation of meantrajectory in the detector
Results output
END
Principle :
Ratio (PM area /total reflector area)
+Mean photon trajectory
Detection efficiency
Muon Cherenkov telescope
Water Cherenkov detector
1 10 100 1000
101
102
103
104
105
106
107
4He 1013eV
2.1013eV
5.1013eV
7.1013eV
1014eV
2.1014eV
5.1014eV
7.1014eV
1015eV
Q(R
), p
hoto
n/m
2
R, m
1 10 100
100
101
102
103
104
105
106
gamma
Q(R
), p
ho
ton
/m2
R, m
1012
5.1012
1013
5.1012
1014
Lateral distribution function of Cherenkov light forprimary helium
Lateral distribution function of Cherenkov light forprimary 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 1 PC 2 PC n
Main 1
Geometry and cross section calculation
Main 2
Data acquisition and analysis
Recommended
