A Method for Estimation of the Parameters of the Primary Particle of an Extensive Air Shower by a High-Altitude Detector

A method for estimation of the parameters of the primary particle of an extensive air shower (EAS) by a high-altitude detector complex is described. This method was developed as part of the Pamir-XXI project. The results may be useful for other high-altitude projects and the EAS method in general. The specific configurations of optical detectors for Cherenkov EAS radiation and charged-particle detectors, the methods for data processing, and the attainable accuracy of reconstruction of parameters of primary particles (energy, direction, mass/type) are presented. The results primarily cover optical detectors that are suitable for studying EASs from primary nuclei in the range of energies E⁰ = 100 TeV–100 PeV and showers from primary γ-quanta with energies of E_γ ≥ 30 TeV. Grids of charged-particle detectors designed to determine the EAS direction and energy in the E⁰ = 1 PeV–1 EeV range are also considered. The obtained accuracy estimates are the upper limits of the actual experimental accuracies.     

EAS Phenomenology and Cosmic Ray Spectrum Ground Based Measurements

Primary cosmic ray energy spectrum around and above 1 PeV is of great interest due to its non-power-law behavior (“knee”) in PeV region found many years ago using the indirect EAS (Extensive Air Shower) method. The method is based on secondary particles measuring on Earth’s surface under a thick atmosphere. Traditionally, people use detectors sensitive to ionization produced mostly by secondary electromagnetic component and therefore any found changes in EAS size spectrum correspond to secondary components, which have to be recalculated to primary spectrum. Recently some new “knees” were claimed by high altitude experiments: at ∼45 TeV for all-particle spectrum (HAWC), for primary protons and helium: at ∼400 TeV (Tibet ASγ) and at ∼700 TeV (ARGO-YBJ) thus widening the “knee” region from ∼0.045 to 5 PeV. The natural explanation of such a strange spectrum behavior in a wide energy range could be found in the EAS phenomenological approach to the knee problem.

     

Radio signals from extensive air showers with the energies <Emphasis Type="Italic">E</Emphasis> <Subscript>0</Subscript> ≥ 10<Superscript>19</Superscript> eV according to data from the Yakutsk extensive air shower array

A radio instrument and results obtained from the measurements of the 32-MHz radio signal from particles of extensive air showers (EASs) with energies E₀ ≥ 1×10¹⁹ eV are reported in brief. The data were obtained at the Yakutsk EAS array in 1987–1989 (the first series of measurements) and in 2009–2014 (new series of measurements). The radio signal from EASs with energies above 10²⁰eV was detected at the Yakutsk EAS array for the first time, including the shower with the record energy of ~2×10²⁰ eV for the Yakutsk EAS array.     

The extensive air shower muon number spectrum beyond the knee in the cosmic-ray energy spectrum

The extensive air shower (EAS) muon number spectrum is obtained with increased statistics using the central muon detector of the EAS MSU array, which records muons with energies above 10 GeV. The dependence of the mass composition of primary cosmic rays on the energy is considered. The conclusion is confirmed that for energies from 3 × 10¹⁵ eV (the primary energy spectrum knee) up to 10¹⁷ eV a change in the composition associated with an increase in the proportion of heavy nuclei occurs; however, after the energy of 10¹⁷ eV, the proportion of heavy nuclei begins to decrease and the composition becomes lighter. A comparison with similar data from other experiments is conducted. The existence of an additional component of cosmic rays is confirmed; earlier an indication of its presence was derived from data on the EAS electron number spectrum.     

The mass composition of cosmic rays according to the data obtained using the TUNKA-25 setup

The data obtained using the Cherenkov TUNKA-25 extensive air shower (EAS) installation and the refined method were used to obtain the energy dependence of the average EAS depth maximum. The EAS distributions over the depth of the maximum were obtained for the energies of 5 × 10¹⁵ and 2 × 10¹⁶ eV. An analysis of the shape of distributions indicates that the model of interaction of the nuclei that yields the highest position of the maximum (QGSJET-01) is preferable. If this model is used to account for the maximum’s position, one finds that 〈InA〉 = 1.9±0.2 and helium is dominant in the mass composition at the energy of 5 × 10¹⁵ eV. A sharp increase in the mean mass of the composition is observed at energies in excess of 10¹⁶ eV.     

The knee in the primary-cosmic-ray spectrum,observed in the hadron component of extensive-air-shower cores at the mountain level

The spectra of the hadron component in extensive-air-shower (EAS) cores detected at the Tien Shan high-altitude scientific station of the Lebedev Institute of Physics, Russian Academy of Sciences, have been analyzed. Simulation was performed using the CORSIKA code within the QGSJET01 and QGSJET02 models under different assumptions about the primary-cosmic-ray (PCR) spectrum in the knee region. It is shown that the QGSJET01 model underestimates the energy of the hadron component of EAS cores at the mountain level. It is also shown that a pronounced knee in the experimental spectrum suggests a sharp (dγ ～ 1.5) change in the exponent of the proton spectrum slope at an energy of about 5 PeV.     

Behavior of the EAS in late stages of its development

In late stages of the extensive air shower (EAS) development (s ≥ 1.2–1.3) contributions to the electromagnetic component are made not only by hadrons but also partially by muons. In this case, the cascade curves are higher in comparison with the classical theory. If the number of particles is converted into the shower energy, this effect is not small in the energy range E ₀ = 10¹³?10¹⁶ eV. In the numerical simulation of the experiment, it is important to make sure that the energy cutoff thresholds for muons and electrons are close to each other (this is usually ignored).     

Dependence of the energy spectrum of UHE cosmic rays on the latitude of an extensive air shower array

Several energy spectra of cosmic rays with energies E ₀ ≥ 10¹⁷ eV measured at the Yakutsk EAS, AGASA, Haverah Park, HiRes, Auger, and SUGAR arrays are considered. It is shown that the fairly good mutual agreement of the spectrum shapes can be achieved if the energy of each spectrum is multiplied by a factor K specific for each spectrum. These factors exhibit a pronounced dependence on the latitude of the above-mentioned arrays.     

Energy spectrum and mass composition of primary cosmic rays at energies 10<Superscript>15</Superscript>–10<Superscript>18</Superscript> eV

Data on muon and electron components of extensive air showers (EAS) (obtained with the EAS MSU array) were used to derive the primary cosmic ray (PCR) mass composition. It is shown that for energies beyond the knee at energy 3 × 10¹⁵ eV the abundance of heavy nuclei increases with energy. But at energies above 10¹⁷ eV the abundance of light nuclei starts to grow. The primary cosmic ray spectrum in the range 10¹⁵–10¹⁸ eV is analyzed. It is shown that at energies above 10¹⁷ eV the additional component appears and it differs from the bulk of Galactic cosmic rays generated by shocks in SN remnants.     

Causality violation in spatially closed space-times

Some results are obtained which establish conditions under which causality violation cannot occur in space-times admitting a compact, but not necessarily acausal, spacelike hypersurface. For example, it is shown that causality violation can occur in a space-time admitting a compact spacelike slice and obeying fairly reasonable energy conditions only if it is “singular” in the sense that some “causal interval”J ⁺(p) ∩J ^? (q) has noncompact closure.     

Searching for preferential arrival directions of ultrahigh-energy cosmic rays on the Moscow State University EAS array

There is evidence for possible clustering in the arrival directions of extensive air showers (EASs). A program for analyzing EAS arrival directions has been developed to investigate this problem and the database of the Moscow State University EAS array for 1982–1989 has been analyzed. The distributions in equatorial coordinates have been derived for cosmic rays with energies E ≥ 2 × 10¹⁵ eV and zenith angles <40°. The uniformity of the derived distributions is verified using various statistical tests.     

Properties of giant air showers and the problem of estimating the primary-particle energy

The main errors in energy estimation in individual events detected at the Yakutsk EAS array are analyzed. The data on the fraction of muons are considered. For inclined showers with energies exceeding 10¹⁹ eV, it is much larger than the value given by approximation at lower energies. This difference may be due to new processes arising upon interaction between particles with such energies, which leads to a significant increase in the muon component in the total primary-particle energy.     

An impact-parameter model for multiplicity distributions

We study a model for hadron-hadron scattering in which at each value of impact parameter the multiplicity follows a Poisson distribution whose mean is determined by the profile function. This model permits a calculation of the full multiplicity distribution once the profile function is given. Geometrical scaling and KNO scaling are linked together; the rise in σ_el/σ_tot at the \(Sp\bar pS\) implies a violation of KNO scaling. The energy dependence of moments of the multiplicity distribution is “predicted” quite well. Implications for hard-scattering models are discussed.     

Astrophysical and structural peculiarities of extensive air showers with energy E 0 ≥ 1017 eV from Yakutsk EAS array data

The astrophysical characteristics of primary cosmic rays (PCRs) and the structure of extensive air showers (EASs) with energy E ₀ ≥ 10¹⁷ eV are simultaneously analyzed using the Yakutsk EAS array data acquired in the period 1974–2005. Enhanced and reduced particle fluxes are shown to come from the disk of the Supergalaxy (the Local Supercluster of galaxies) at E ₀ ≥ 5 × 10¹⁸ eV and E ₀ ≤ (2?3) × 10¹⁸, respectively. The development of air showers with E ₀ ≥ (3?5) × 10¹⁸ eV differs significantly from that at lower energies. This is interpreted as a manifestation of the possible interaction between extragalactic PCRs and the matter of this spatial structure.     

Thermal conductivity of gold and silver at high pressures

The thermal diffusivities of gold and silver have been measured under pressure up to 2.5 GPa at room temperature. From the measured data the pressure dependence of the thermal conductivity, λ, has been calculated. The values found for the pressure coefficient λ^?1$\text{δλ}\text{δP}$ were 3.9 × 10^?2GPa^?1 for gold and 4.0 × 10^?2 GP silver at atmospheric pressure. The results are compared to theoretical predictions of the pressure dependence and also to previous experimental results for copper and aluminium. For the noble metals, small angle or “vertical” scattering of electrons is shown to have a stronger volume dependence than “horizontal” scattering.     

Study of complex impedance spectroscopic properties of the KFeP2O7 compound

The KFeP₂O₇ compound was prepared by the conventional solid-state reaction. The sample was characterized by X-ray powder diffraction. The AC electrical conductivity and the dielectric relaxation properties of this compound have been investigated by means of impedance spectroscopy measurements over a wide range of frequencies and temperatures, 200 Hz–5 MHz and 553–699 K, respectively. Both impedance and modulus analysis exhibit the grain and grain boundary contribution to the electrical response of the sample. The temperature dependence of the bulk and grain boundary conductivity were found to obey the Arrhenius law with activation energies Eg?=?0.94 (3)?eV and Egb?=?0.89 (1)?eV. The grain-and-grain boundary conductivities at 573 K are 1.07?×?10^?4 and 1.16?×?10^?5 (Ω^?1 cm^?1). The scaling behavior of the imaginary part of the complex impedance suggests that the relaxation describes the same mechanism at various temperatures. The near value of the activation energies obtained from the equivalent circuit, conductivity data, and analysis of M″ confirms that the transport is through ion hopping mechanism.     

Cosmic ray energy spectrum from measurements of air showers

This review focuses on high-energy cosmic rays in the PeV energy range and above. Of particular interest is the knee of the spectrum around 3 PeV and the transition from cosmic rays of Galactic origin to particles from extra-galactic sources. Our goal is to establish a baseline spectrum from 1014 to 10^20 eV by combining the results of many measurements at different energies. In combination with measurements of the nuclear composition of the primaries, the shape of the energy spectrum places constraints on the number and spectra of sources that may contribute to the observed spectrum.     

High-energy cosmic ray muons in the Earth’s atmosphere

We present the calculations of the atmospheric muon fluxes at energies 10–10⁷ GeV based on a numerical-analytical method for solving the hadron-nucleus cascade equations. It allows the non-power-law behavior of the primary cosmic ray (PCR) spectrum, the violation of Feynman scaling, and the growth of the total inelastic cross sections for hadron-nucleus collisions with increasing energy to be taken into account. The calculations have been performed for a wide class of hadron-nucleus interaction models using directly the PCR measurements made in the ATIC-2 and GAMMA experiments and the parameterizations of the primary spectrum based on a set of experiments. We study the dependence of atmospheric muon flux characteristics on the hadronic interaction model and the influence of uncertainties in the PCR spectrum and composition on the muon flux at sea level. Comparison of the calculated muon energy spectra at sea level with the data from a large number of experiments shows that the cross sections for hadron-nucleus interactions introduce the greatest uncertainty in the energy region that does not include the knee in the primary spectrum.     

Electrical conductivity and defect structure of Ni-doped and “CO-reduced” Ni-doped SrTiO3 single crystals

The electrical conductivities of Ni-doped and “CO-reduced” Ni-doped SrTiO₃ single crystals were measured at temperatures 700–1200°C and P_o2's of 10^?7–10^?1 atm. Plots of log σ vs $\text{1}\text{T}$ at constant P_o2's were found to be linear, and the activation energies appeared to be 0.92 eV for Ni-doped SrTiO₃ and 0.50 eV for “CO-reduced” Ni-doped SrTiO₃ single crystals, respectively. Plots of log σ vs log P_o2 at constant temperature were found to be linear with an average slope of ?$\text{1}\text{4}$ for SrTiO₃:Ni and of ?$\text{1}\text{6}$ for “CO-reduced” SrTiO₃:Ni single crystals, respectively. The electrical conductivity dependencies on P_o2 indicate that a triply ionized titanium interstitial and an oxygen vacancy model are applicable to Nidoped and “CO-reduced” Ni-doped SrTiO₃ single crystals, respectively. The small polaron conduction was suggested on “CO-reduced” Ni-doped SrTiO₃ single crystal from the temperature dependence of conductivity.     

Elektronenpolarisation im Energiebereich unterhalb 50 eV durch Streuung an freien Hg-Atomen

The angular dependence of spin polarizationP(Θ) of electrons elastically scattered by a beam of mercury atoms is measured in a double scattering experiment for electron energies of 45±1 eV; 23±1 eV; 7±1 eV; and 3,5±1 eV. Maximum degree of polarization obtained isP(100°)=0,39±0,07; electron energy 7±1 eV; electron current 10^?12–10^?11 A.