Investigation of the possibility of registration
of wide atmospheric showers at the “RUSALKa”(Mermaid) facility.
Guskov A., JINR (Dubna)
Methods of simulation analysis are applied in physics for prediction of behavior of various systems in different conditions. Simulation analysis makes it possible to estimate the functionality of expensive experimental facilities and to choose their optimal configuration before they are created. Thus, experimental facilities are not designed “by eye”, but are optimized in accordance with the results of simulation analysis, which shall provide an opportunity to spare workforce and funds for their creation. The simulation analysis is also irreplaceable with already existing experimental facilities, because it allows us to understand whether a certain facility operates in the expected way.
The simulation analysis in physics of elementary particles is carried out by random drawing of processes specific to this particular field of physics – reactions of birth, decay and interaction of different particles. You should not be confused with the word “random”, though the time of various events, types of involved particles, their streamline and their energy are all random variables rather than arbitrary ones. Their distributions fully correspond to probable regularities that are well known in particle physics. For instance, at the decay of π0-meson into two gamma rays in the reference frame, where π0-meson is at rest, the direction of emission of one of the gamma rays is chosen at random (which is fully consistent with the reality). At that, the direction of emission of another gamma ray is not arbitrary and is connected with the direction of emission of the first gamma according to the law of conservation of momentum. Due to a wide use of random varieties this method of simulation is often called Monte Carlo method (named after the place of a famous casino location).
Simulation of registration of wide atmospheric showers by the “MERMAID” facility was performed by means of the AIRES  software package. This package is one of the standard means of simulation of interaction of primary cosmic rays with the Earth’s atmosphere and of the development of atmospheric showers. This package includes both the processes of physics of elementary particles (interaction of particles with atomic nuclei, their dissipation, decay, etc.) and such peculiarities as composition of atmosphere, variability in its density with respect to altitude deviation, earth curvature and even the availability of the geomagnetic field. This package is used by the AUGER  collaboration – one of the widely recognized leaders in the exploration of cosmic rays of superhigh energies.
For every particle of primary cosmic rays AIRES gives coordinate, angular, energetic and time distributions for all secondary particles that have reached the Earth’s surface. The radial distribution ρ(R) of different secondary particles reaching the Earth’s surface for vertical shower generated by proton with the energy E = 1017 EeV is shown in Fig. 1. Insofar as the probability of registration of hard gamma rays by the stations of the “MIRMAID” facility is quite small, the electrons / positrons located close to the shower axes and muons located at distances of more than 600 m are considered to be the main detection particles. The specific energy spectrum of the secondary particles is shown in Fig. 2.
|Lowest kinetic energy, GeV||0.02||0.01||0.001||0.01||0.14||0.14|
|Probability of registration||1||1||0.02||1||1||0.01|
Each station of the “MIRMAID” facility was simulated as the system of two adjacent plates, each of which had the area of 0,5 m2. The shower was considered to be registered by the station if at least one of the secondary particles was received (and registered) by each of the plates, provided that the arrival time of the particles on each of the plates differed by no more than 1 ms. Insofar as there is no universal detector which would register absolutely all particles in all energy ranges, there were taken into account only the particles with the energy above a certain threshold depending on their type. The lowest kinetic energy of a particle necessary for its registration, as well as the probability of the registration for each type of particles is shown in Table 1.
The time structure of a shower is also very important because the time information received by each of the stations is used both for establishment of the registration fact and for establishment of the direction of its development. The time of arrival of a shower front with respect to the time of arrival along the shower axes for vertical (θ = 00) and slanting (θ = 300) showers with the energy of E = 1017 EeV is shown in Fig. 3.
The simulation showed that the radius of the curvature of the shower time front amounts to about 10 km. Insofar as the size of the “MIRMAID” facility is only 300m in all (see Fig. 4), the shower front may be roughly reckoned as flat. The typical time form of a signal for the station located at the distance of 150 m from the axes of the vertical shower with the energy of E = 1017 EeV is shown in Fig. 5. The characteristic duration of the signal is 50-100ns, which can be compared with an accuracy of the absolute time instance by means of GPS.
For the investigation of the dependence of the coincidence counting between two stations dN / dt on the distance L between them, the flow of the primary cosmic rays was being simulated in accordance with the experimental data (see Fig. 6 ) with the energy range of 1013 – 5 x 1019 EeV. The obtained dependence is shown in Fig. 7. It may be roughly described by the formula
and the distance L is expressed in meters. It is interesting to compare this dependence with the results of experimental measurements of the counting of station pairs, which were performed in the years of 2008 and 2009. Judging from Fig. 8 it is clear that the counting of some station pairs lies considerably lower than the expected curve. This, perhaps, points to the fact that the effectiveness of registration of particles by separate stations is low. The distribution of showers registered according to their energies by two stations located at the distance of L = 100 m, which was obtained at the result of simulation is shown in Fig. 9.
Apart from coincidence of the time of arrival of signals between stations in a certain time window Δt, that was generated by the development of wide atmospheric showers, there is also a possibility of random coincidences of signals initiated by separate random particles of secondary cosmic rays or by the noises of photomultiplier detectors being the main unit of every station. If the counting of each station amounts to N, then the number of random coincidences Nrandom in the interval of Δt shall be equal to
Taking into account a well-known experimental fact that typical counting of each station amounts to about 1 c-1, it shall be possible to estimate the counting of random coincidences Nrandom in the window Δt = 1 ms. It shall amount to about 30 random coincidences per year.
It  is  clear  from the results of simulation that in order to ensure the counting of coincidences between two stations generated by showers to be at least one order of magnitude more than the counting of random coincidences, the stations should be located at the distance of no more than 300 – 400 meters from each other. The choice of the size of the “MIRMAID” facility has been based on the results of simulation.
There was also performed the simulation of registration of wide atmospheric showers by all seven stations of the “MIRMAID” facility. Fig. 10 shows the number of coincidences at n stations expected within the period of one year. For instance, if the facility is working perfectly, there could be expected the registration of up to 1700 showers, which would send the signal to each of the seven stations. However, since the effectiveness of real stations may be considerably lower than 100%, an actual registered number of the coincidences at seven stations might be considerably lower. If we take the effectiveness of each station equal to 80% (which is quite optimistic estimation), then the coincidence counting throughout seven stations will fall up to 350 per year. In the cause of simulation there was established such an important parameter as the product of effective area of the facility by the effective solid angle overlapped by it. This variable bounds the number of primary cosmic particles passing through a unit area from a single solid angle in a unit of time, and the facility reference system:
For coincidences throughout seven stations and the primary particles’ energies higher than 1015 EeV (only showers caused by the particles with these particular energies can cover all seven stations) (SeffΩeff) = 1 x 10-4 km 2 x sr.
The systematic error of the estimate of the counting of the events is mainly caused by two factors: accuracy of the spectrum of primary cosmic rays and the change of the secondary particles’ flow during their passing through the substance under the stations (roofs, concrete ceilings etc.) The contribution of the first factor may be estimated from experimental data given in Fig. 6 . It is approximately 30%. The change of the flow of the secondary particles of the shower passing through the layer of the concrete has been investigated by means of the GEANT  software package. It was shown that the change of the flow was determined by two competitive processes: the absorption of low-energy particles of the shower and the birth of new particles. The first process dominates decreasing the flow of the particles, provided that the width of the layer is less that 2X0, where the variable X0 is called radiation length and determines the typical distance between the successive acts of interactions for the electrons and hard gamma rays (for the concrete of X0=11.5 sm). The second process results in the increase of the flow of the particles with the width of the concrete layer of (2 – 9)X0.
Further increase of the concrete layer will result in decrease of the flow because of the absorption of both primary particles and those born inside the concrete. The dependence of the flow of the secondary particles on the width of the concrete layer that has been passed through is shown in Fig. 11, and the contribution into the systematic error of the estimate of the coincidence counting connected with the change of the flow of the secondary particles, was estimated at the level of ±40%. Thus, the estimate of the full systematic error calculated in the form of the geometric sum of two contributions considered above, is 50%.
 C. Amsler et al. (Particle Data Group), Physics Letters B667,1 (2008)