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The large-scale coordinate-tracking detector TREK for registration of inclined EAS is being developed in MEPhI. The detector is based on multiwire drift chambers from the neutrino experiment at the IHEP U-70 accelerator. Their key advantages are a large effective area (1.85 m2), a good coordinate and angular resolution with a small number of measuring channels. The detector will be operated as part of the experimental complex NEVOD, in particular, jointly with a Cherenkov water detector (CWD) with a volume of 2000 cubic meters and the coordinate detector DECOR. The first part of the detector named Coordinate-Tracking Unit based on the Drift Chambers (CTUDC), representing two coordinate planes of 8 drift chambers in each, has been developed and mounted on opposite sides of the CWD. It has the same principle of joint operation with the NEVOD-DECOR triggering system and the same drift chambers alignment, so the main features of the TREK detector will be examined. Results of the CTUDC development and a joint operation with NEVOD-DECOR complex are presented.

The neutron component of EAS has not been practically studied for many years. Creation of the neutron detector arrays PRISMA-32 and PRISMA-YBJ demonstrated the effectiveness of such investigations. It is important to underline that recording the EAS neutron component is carried out over the whole array area. Development of a new larger scale neutron detector array (URAN) in MEPhI will continue these studies. During the construction of the URAN array, a new design of en-detectors based on the scintillator with natural boron and new electronics was developed. The use of new electronics with a switchable sampling rate allows one to reach EAS fast timing accuracy up to 10 ns. The en-detectors of the URAN are located on the roofs of the buildings. The sensitive area of each detector is 0.36 m2, while the array's starting area is ∼ 103 m2. Total number of the initial array detectors is 72. They are subdivided into 6 independent clusters each of 12 en-detectors, connected with the central data acquisition station.

Influence of various theoretical and experimental uncertainties on results of underground muon flux calculations is estimated on the basis of a semi-analytical solution of muon spectrum transport equation. Status and accuracies of theoretical formulae for muon interaction cross sections and energy loss rate are discussed. A brief review of recent improvements in theoretical treatment of muon interactions is given. A necessity of a comprehensive verification of different muon transport codes is stressed.

A systematic outline of the theory of the pair meter — a method of measuring the muon energy via multiple production of electron-positron pairs in thick layers of matter — is given. Possible variants of the technique of derivation of the muon energy in the pair meter are considered in unified terms on the basis of the maximum likelihood method. Analytical expressions for the energy measurement error have been obtained. An asymptotic limit of the measurement error at high energies has been found. The important role of the background process — the inelastic interaction of muons with nuclei — is elucidated. The problem of optimization of the pair meter for measuring the spectrum of cosmic ray muons is formulated and solved. The results of numerical simulation for the real pair meter are compared with the experimental data of the pair meter of the MUTRON arrangement. The pair meter technique can be used for the spectrometry of muons in the energy region ≳10 12 eV in new experimental arrangements.