Muon hodoscope URAGAN continuously detects the angular distribution of muons in a wide range of zenith angles and allows one to obtain information about variations, both in the intensity and in angular characteristics of the muon flux, caused by active processes in the heliosphere, the magnetosphere and atmosphere of the Earth. Various parameters of the muon flux anisotropy and methods of calculation of these parameters are discussed. Real-time processing of a continuous flow of multidimensional data from the muon hodoscope URAGAN is quite a challenge. In the article, methods of formation and primary analysis of the data, their processing in real time and obtaining time series of various parameters of integral counting rate and angular anisotropy of the muon flux, which are important for the physical analysis of modulation processes of cosmic rays in the heliosphere, are presented.

Secondary muons are generated in interactions of primary cosmic rays (CR) with nuclei of atoms of the atmosphere and keep quite well the directions of parent particles. Therefore, variations of primary CR caused by various phenomena associated with solar activity may be studied on the basis of the analysis of variations of the angular distribution of the muon flux measured in a real- time mode. This approach is the basis of the method of muon diagnostics developed in the Moscow Engineering Physics Institute using a specially designed muon hodoscope URAGAN (

The main advantage of wide-aperture muon hodoscopes compared to multidirectional muon telescopes is the possibility of reconstruction in real time of the track of each muon arriving from any direction of the upper hemisphere. To provide acceptable flows of processed and accumulated information, a matrix method of representing experimental data has been applied, which is described below.

Muon hodoscope (MH) URAGAN (_{2} + n-pentane. Sixteen gas discharge tubes with size 9 × 9 × 3500 mm^{3} and resistive cathode coating operated in a limited streamer mode are enclosed in a single plastic container. Each plane contains 320 tubes equipped with an external X-Y-strips coordinate readout system. Sensitive area of one SM is ~11.5 m^{2}. Trigger condition of the event detection is the coincidence of signals from the strips of 4 or more X-strip planes within the time gate of 250 ns. The scheme of the muon detection in the SM is shown in Figure

The muon hodoscope URAGAN. In the foreground, one of the supermodules is seen. On the left and at the background the other three SM a located.

Scheme of single particle detection in the SM.

As described in the article (

The angular distribution of the tracks for 1 minute measurement interval is stored in the forms of three types of matrices with dimensions of 90 × 90 cells: zenith and azimuth angles (θ, φ) _{a}_{i}, φ_{j}]; in projection angles (θ_{X}_{Y}_{pa}_{Xi}, θ_{Yj}]; in tangents of projection angles (tgθ_{X}_{Y}_{tg}_{Xi}, tgθ_{Yj}]. Different types of matrices are used for solution of different tasks. The matrix _{a}_{tg}_{pa}

Every matrix contains the angular distribution of muons measured during 1-minute interval. The sequence of such matrices gives a unique possibility to study the temporal changes of muon angular distributions. Depending on the analysis to be performed, matrices can be combined in different time intervals Δ

Data processing is carried out in a real-time mode. Time series of averaged over 1- and 60-min intervals atmospheric pressure, counting rates of reconstructed tracks (without the barometric and temperature corrections), and “live”-times for every supermodule are formed. These series are stored in 1- and 60-min daily files in a text format. At the beginning of each hour, an additional processing is carried out, for which the data of three SM (SM1, SM3 and SM4) are used, while SM2 is used mainly for methodical and calibration purposes. The purpose of data processing procedures is the creation of time series of the angular distribution of muons and of parameters of the counting rate analysis. Results of additional processing are:

time series of characteristics of angular distributions of 60-minute matrices _{a_1h};

time series of characteristics of the angular distributions of 60-minute matrices _{tg_1h};

time series of results of the wavelet analysis of 10- and 60-minute counting rates and characteristics of zenith-angular distributions;

image files of 60-minute matrices _{tg_1h} of variations in the angular distributions in the East-North (local geographic) and GSE (Geocentric Solar Ecliptic) coordinate systems;

image files of obtained time-series graphs.

Images of time series graphs and of matrices of variations of the angular distribution are presented at the web pages (

“Integral intensity mode” and “Hodoscopic mode”:

“Heliosphere” (60-minute muon flux variation analysis):

“Wavelets of URAGAN data”:

Changes of the atmospheric conditions modulate the muon flux at the Earth’s surface, and variations of the extra-atmospheric origin are of the same order. Therefore, to study the extra-terrestrial effects it is necessary first to correct all the matrices for the main atmospheric effects, barometric and temperature ones.

Barometric effect is the anti-correlation of cosmic ray intensity with the pressure at the observation level. Temperature effect is caused by changes of the temperature at all altitudes of the atmosphere. Corrected angular matrix ^{corr}(θ,φ,

where θ and φ are zenith and azimuth angles for matrix cell centers; _{T} and Δ_{P} are corrections for temperature and barometric effects. Barometric correction is calculated as

where _{0} = 993 mbar is the averaged over a long time period pressure at the registration level,

where _{0}(θ) is the over a long period averaged number of reconstructed events for zenith angle θ, _{T}(_{SMA}(_{SMA}(

Information about the temperature profile of the atmosphere can be obtained from the following sources (

Information from direct measurements of air temperature with the help of meteorological balloon flights. For example, for URAGAN data correction the information from the Central Aerological Observatory (

The alternative sources are weather forecasting models of the atmosphere. One of them is the numerical forecasting model of the atmosphere GDAS (The Global Data Assimilation System). GDAS output data are available 8 times a day for the whole globe (1 degree latitude-longitude grid) and for 23 constant pressure levels (from 1000 to 20 mbar). Retrospective archive data (since 2005) are in the open access (

In Figure

10-minute average counting rates of the URAGAN hodoscope without and with corrections for meteorological effects.

For the study of the response of muon flux variations registered by the muon hodoscope URAGAN, the local anisotropy vector

The _{h} parameter is sensitive to the changes in the interplanetary magnetic field induced by the active processes on the Sun. The variations of the horizontal projection of the vector of local anisotropy can be used to identify the time intervals of the increased anisotropy, which are observed during the passage of various irregularities in the solar wind and the interplanetary magnetic field in the Earth’s vicinity. Study of the muon flux anisotropy during periods of heliospheric disturbances is based on the comparison of data of satellite detectors and muon hodoscope URAGAN. To estimate the state of the interplanetary space, the values of the modulus of the magnetic induction vector _{sw} were used in the work. To estimate the state of the magnetosphere, the values of the geomagnetic activity index _{p} were used (_{sw}, _{p}-index, counting rate

Temporal changes in parameters _{sw}, _{p}-index, counting rate and the parameter of the local anisotropy according to URAGAN for the period from September 9 to October 10, 2016.

The horizontal lines in the graphs indicate the boundaries for the determination of perturbations in the interplanetary space (_{sw}), the Earth’s magnetosphere (_{p}) and the cosmic-ray muon flux (

As can be seen from the upper graphs, the ejection affected the interplanetary magnetic field. The increase in the values of magnetic induction began on September 18, the maximum was reached on September 19 and amounted to 18.9 nT. There was also a disturbance in the values of the solar wind speed, its maximum occurred on September 20 and amounted to 727 km/s. The perturbations of these parameters in the interplanetary space were confirmed by the geomagnetic activity index _{p} = 4.

The response of the muon hodoscope to the CME was visible one day after ejection. Three distinct peaks were repeated at regular intervals once per day and are clearly seen on the last graph. The projection of the relative anisotropy vector _{h} in

Muon hodoscope is a cosmic-ray detector designed to study the relations between the spatial and temporal variations of the cosmic ray muon flux and various dynamic processes in the heliosphere and magnetosphere of the Earth. Development of the URAGAN hodoscope offers a chance to attain a new qualitative level in investigating and monitoring processes in the near-Earth space, in particular those of a dangerous character. For implementation of fast and effective primary processing of a large flow of multidimensional information from the muon hodoscope URAGAN in a real time, a matrix approach to data representation was proposed and realized. Characteristics of the anisotropy of the angular distribution of muons provide a convenient tool for the study of the processes of cosmic ray flux modulation of atmospheric and extra-terrestrial origin.

This work was performed in the Scientific and Educational Center NEVOD with the state financial support provided by the Russian Scientific Foundation (RSF), project No. 17-17-01215 “Creation of a method for early diagnostics of geomagnetic storms based on digital processing of time series of observational matrices of a muon hodoscope”.

The authors have no competing interests to declare.