Here the results of calculations of pulses in Cherenkov light detectors for the Yakutsk array are presented. As long as the Vavilov-Cherenkov light is used to calibrate signals in scintillation detectors at the Yakutsk array it is vital for these measurements to be precise. The validity of measurements of the signal Q(400) used as the estimation parameter at the Yakutsk array has been confirmed. Our calculations show that the width of time pulses increases from nearly 50 ns at a distance of 100 m from the shower axis up to 700 ns at 1000 m.
It is a known problem of calibration of energy estimations of extensive air showers (EAS). At the Yakutsk array the Vavilov-Cherenkov light is used to calibrate signals in scintillation detectors [1]. Although our calculations show that for the same flux of Vavilov-Cherenkov light there should be much higher signals in scintillation detectors than it is measured in the experiment [2].
First, this contradiction may have different explanations. The hadron interaction model may not correctly describe the real processes at high energies. This question will be probed at LHC once it is operational. Alternatively, we may have a different chemical composition of primary cosmic rays -all our calculations were undertaken in the assumption of light chemical composition at high energies. Although recent experiments claim that the primary particles at those energies are protons [3], [4] (with exclusion of [5]).
Each detector array encounters the problem of full signal registration. Each detector after being triggered by some event (a particle hits the detector, the counting rate exceeds some level, a signal comes from another detector, etc.) collects the signal for some period of time, a so-called time gate. Time gates should be wide enough to collect possibly all particles coming to the detector. On the other hand, since we always have a background from low energy cosmic rays or the local sources (radioactivity, light pollution, etc.), the time gates should not be too wide in order to keep the signal to noise ratio high enough. So the time gates should be of about the disk thickness. At most detector arrays such as Haverah Park, Volcano Ranch, Yakutsk, the time gates were set to about 2 µs.
A. Watson in [6] suggested that the time gates at the Yakutsk array are too narrow to detect all particles and thus the signals are underestimated, that leads to In our previous paper [7] we have studied the problem of form and width of pulses in scintillation detector. In a few words though the signals in scintillation detectors at large distances from the shower axis (more than 1 km) exceed 2 µs (at 600 m signal width is well within 2 µs) and only part of the signal is measured the difference between the theory and the experiment is still too high to be explained solely by partial signal measurements. Therefore, additional analysis was required. In this paper we investigated another question -the form of the Cherenkov light pulse at the detector.
As well as in the previous work in this study we used CORSIKA 6.500 [8] with QGSJET-II [9]- [13] for high energy and Gheisha-2002d [14] for low energy calculations. Parameters of the atmosphere and the magnetic field were set to fit the conditions of the Yakutsk array. The time delay of arrival of the Vavilov-Cherenkov photons was calculated as the time between its arrival at the observation level and the time of arrival of the very first particle at the observation level. All calculations were carried out in the framework of a multilevel hybrid scheme [15], i.e. we calculated the database of Vavilov-Cherenkov light pulses at different distances from the shower axis from low energy showers from primary electrons, gamma and muons (some examples are shown in Fig. 123) and using source functions (also calculated in our previous simulations [7]) we calculated the impulses for high energy showers.
Source function describes the number of particles with energy in interval
Here E thr -some reasonable maximum energy threshold, maximum energy of particles in source functions; E min -some low energy threshold (naturally in case of the Vavilov-Cherenkov light for electrons and gammas it is 21 MeV, for muons -4 GeV); S e,γ,µ (E, x)) -source functions of electrons, gammas and muons respectively. But if the source functions were obtained numerically as a table of parameters (energy E i , depth of generation x i and weight w i if thinning procedure was applied) of low energy particles generated in the shower than this integral converts to a sum:
After all theese calculations for vertical showers from primary protons we obtained the following results.
In Fig. 4 the fraction of Vavilov-Cherenkov light collected within time τ at different distances from the shower axis is shown. As one can see the width of the Vavilov-Cherenkov light impulse at the distance of 100 m from the shower axis is less than 50 ns, at 400 m -200 ns, at 600 m -400 ns and at 1000 m it is less than 1 µs. Therefore, the time gates at the Yakutsk In addition we have calculated the form of the Vavilov-Cherenkov light forefront and backfront (see Fig. 5). As the forefront arrival time we took the moment when 5% of total signal is collected and the backfront was considered as the moment when 95% of all Cherenkov photons were collected. We found that the best fit is achieved by the power function σ = a • R b (with a f = 1.63 • 10 -3 , b f = 1.71, a b = 3.95 • 10 -2 and b b = 1.43 for forefront and backfront respectively) rather than
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