Extensive air showers (EAS) are a cascade of electromagnetic radiation and ionized particles that produced in the atmosphere through the interaction of a primary cosmic ray with the atom of nucleus in the air producing a huge amount of secondary particles such as X-ray, electrons, neutrons, muons, alpha particles, etc. In this work, EAS effects were demonstrated by estimating the lateral distribution function (LDF) at ultrahigh energies of the various cosmic ray particles. The LDF of charged particles such as electron and positron pair production, gamma and muons particles was simulated at ultrahigh energies 10^16, 10^18 and 10^19 eV. The simulation was carried out using an air shower simulator called AIRES system version 2.6.0. The effect of the primary particles, energies and zenith angle on the LDF of charged particles produced in the EAS was taken into account. Comparison of LDF for charged particles and experimental results gave good agreement for electron and positron pair production and muons particles at 10^19 eV for 0 and 10 zenith angles
Some simple arguments are introduced for a possible explanation of the behavior of the lateral shower age of proton-initiated showers. The corresponding analytical treatment based on the proposed argument is then illustrated. Using the Monte Carlo simulation (MC) code CORSIKA, we have validated how the different characteristics associated with the lateral shower age predicted in the present analytical parametrization, can be understood. The lateral shower age of a proton-initiated shower and its correlations with the lateral shower ages of electron- and neutral pion-initiated showers supports …
The paper describes lateral density distributions of electrons and muons of cosmic ray extensive air showers (EAS) in the energy regime of the KASCADE experiment. Potential EAS observables are extracted while some suitable lateral distribution functions are introduced to describe these lateral density distributions of simulated/observed cosmic ray showers. Mass-sensitivity of these parameters are demonstrated particularly for the KASCADE electron and muon distributions data. Our studies indicate that the KASCADE data favours an idea of gradual change of cosmic ray mass composition from lighter…
Analyzing simulated extensive air shower (EAS) events generated with the Monte Carlo code CORSIKA, this paper critically studies the characteristics of lateral distribution of electrons in EAS around the knee energy region of the energy spectrum of primary cosmic rays. The study takes into account the issue of lateral shower age parameter as indicator of the stage of development of showers in the atmosphere. The correlation of lateral shower age parameter with other EAS observables is examined, using simulated data in the context of its possible use in a multi-parameter study of EAS, with a vi…
We present of measurements of radio emission from EAS at the frequency 32 MHz performed in 2008-2012. Showers were selected by zenith and azimuth directions, sampled by energy. A mean lateral distribution function was fitted to the data each interval. The paper presents unied approximation formula for all three energy intervals of lateral distribution, using connection between equation (1) and (2) coefficients with energy and geomagnetic angle. Here we analyze the connection between the shape of lateral distribution and the depth of the maximum shower development Xmax too.
The horizontal lateral density of a cosmic air shower with a non-zero zenith angle is asymmetric. The asymmetry consist of a stretching of the iso-density contours to ellipses and to a shift of the center of the elliptic contours with respect to the core of the shower. The shift is caused by atmospheric attenuation. The modeling of the attenuation results in an equation for the shift as a function of zenith angle and the size of the iso-density contours. A more accurate equation is obtained by investigating the shift in lateral densities of simulated showers. It is shown how the shift can be i…
A simple analytical argument is proposed for a possible explanation of the characteristics of the lateral shower age ($s$) of proton ($p$)/nuclei-initiated showers. The analytical argument states that lateral density distribution (LDD) of electrons of a $p$-initiated shower is due to superposition of several electromagnetic (EM) sub-showers developed at a very early stage in the atmosphere from the decay of neutral pions ($π^{0}$s). Thanks to the superposition property of the electron LDD in a $p$ shower, a plausible analytical parametrization has been worked out by giving well represented ana…
Distinguishing $γ$-ray and hadron initiated extensive air showers (EAS) based on lateral distribution of electrons has been studied by detailed Monte Carlo (MC) simulations. The possibility of using the local age parameter (LAP) of EAS for the gamma-hadron separation has been explored. It is found that separating $γ$-ray and hadron induced EAS on the basis of LAP can be useful for surface detector experiments those have no reliable muon measurement facilities.
The particle lateral distribution function (LDF) of air showers at a given altitude is sensitive to the mass composition and primary energy of cosmic rays. Studies of the LDF are difficult to perform due to experimental effects such as sampling bias, as well as shower-to-shower fluctuations in particle density. The High Altitude Water Cherenkov (HAWC) observatory, a dense air shower array located in central Mexico at 4100 m a.s.l., is well-suited to perform detailed event-by-event studies of the LDF of multi-TeV cosmic-ray showers. The detector is instrumented with 1,200 photomultipliers (PMTs…
Lateral distributions of electrons in air showers initiated by photons of ultra high energies ($10^{18}-10^{22}$ eV) obtained on the basis of numerical solution of adjoint cascade equations are presented. An extended analysis has been made considering separately the Landau-Pomeranchuk-Migdal (LPM) effect and the interaction of photons and electrons with the geomagnetic field (GMF) with respect to the scaling formalism for lateral distributions. It is shown that one-parametric scaling description of the lateral distribution of electrons remains valid up to the highest energies considering the L…
New analysis of lateral distributions (LD) of electrons, muons and charged particles in extensive air showers generated by $10^{15}-10^{19}$ eV cosmic rays has been made with respect to the scaling formalism for LD and air shower universality paradigm. It is found that lateral distributions of electrons and muons, when considered separately, are well described by one-parametric scaling functions, while for the charged particles mixture distributions the scaling description is not accurate in radial distance range where electrons and muons give a comparable contribution to the local particle de…
The lateral distribution function (LDF) for coherent electromagnetic radiation from air showers initiated by ultra-high-energy cosmic rays is calculated using a macroscopic description. A new expression is derived to calculate the coherent radio pulse at small distances from the observer. It is shown that for small distances to the shower axis the shape of the electric pulse is determined by the `pancake' function, describing the longitudinal distribution of charged particles within the shower front, while for large distances the pulse is determined by the shower profile. This reflects in a di…
The antenna array LOPES is set up at the location of the KASCADE-Grande extensive air shower experiment in Karlsruhe, Germany and aims to measure and investigate radio pulses from Extensive Air Showers. The coincident measurements allow us to reconstruct the electric field strength at observation level in dependence of general EAS parameters. In the present work, the lateral distribution of the radio signal in air showers is studied in detail. It is found that the lateral distributions of the electric field strengths in individual EAS can be described by an exponential function. For about 20% …
In this work, the effects of the extensive air showers (EAS) were described by estimating the lateral distribution function (LDF) at very high energies of various cosmic ray particles. LDF was simulated for charged particles such as the electron and positron pair production, gamma, muons and all charged particles at very high energies 10^16, 10^18 and 10^19 eV. The simulation was performed using air shower simulator system (AIRES) version 2.6.0. The effect of primary particles, energies, thinning energy and zenith angle on the charged LDF particles produced in the EAS was taken into account. T…
In this work the estimation of the lateral distribution function in Extensive Air showers was performed by using a system for air shower simulations which is called AIRES version 2.6 for different hadronic models like (QGSJET99, SIBYLL and SIBYLL1.6). The simulation was fulfilled in the high energy range (10^15-10^19 eV) for different primary particles like (gamma, protons and iron nuclei) for vertical showers. This simulation can be used to reconstruct the type and energy of the particle that generated Extensive Air showers for charged particles that registered with different arrays.
Using Monte Carlo simulation of extensive air showers, we showed that the maximum depth of showers, $X_{max}$ can be estimated using $P=Q(100)/Q(200)$, the ratio of Cherenkov photon densities at 100 and 200 meters from the shower core, which is known as the steepness parameter of the lateral distribution of Cherenkov radiation on the ground. A simple quadratic model has been fitted to a set of data from simulated extensive air showers, relating the steepness parameter and the shower maximum depth. Then the model has been tested on another set of simulated showers. The average difference betwee…
The Sydney University Giant Air-shower Recorder (SUGAR) measured the muon component of extensive air showers with a unique array of muon detectors. The SUGAR data allow us to reconstruct the empirical dependence of muon density on the distance from the axis of the shower, the lateral distribution function (LDF). We compare the shape of this function with the predictions of hadronic-interaction models, QGSJET-II-04 and EPOS-LHC, in the energy range 10^17.6 - 10^18.6 eV. We find a difference between the observed data and the simulation: the observed muon density falls faster with the increased c…
The lateral density distributions (LDD) of inclined cosmic ray air shower are asymmetric and the corresponding iso-density contours are of increasing eccentric ellipses with zenith angles of different showers. The polar asymmetry of the iso-density contours introduces a significant shift of the EAS core, which is quantitatively expressed as a gap length (GL) parameter between the EAS core and the center of the modified density pattern consisting of several equi-density ellipses. The LDD of EAS particles is usually approximated by a particular type of lateral density function (LDF) which is gen…
The simulation of the Cherenkov light lateral distribution function (LDF) in Extensive Air Showers (EAS) was perfomed with the CORSIKA code in the energy range 10^13-10^16 eV for configuration of the Tunka-25 EAS array. On the basis of this simulation we obtained sets of approximating functions for primary protons, iron nuclei and gamma-quanta for zenith angles Theta<=20. The comparison of the calculated Cherenkov light LDF with that measured with the Tunka-25 array has shown an opportunity of primary particle identification and definition of its energy around the "knee".
Based on extensive air shower simulations it is shown that the electron distributions with respect to the two angles, determining electron direction at a given shower age, for a fixed electron energy and lateral distance, are universal. It means that the distributions do not depend on the primary particle energy or mass (thus, neither on the interaction model), shower zenith angle or shower to shower fluctuations, if they are taken at the same shower age. Together with previous work showing the universality of the distributions of the electron energy, of the lateral distance (integrated over a…
Observational evidence from Auger and earlier experiments shows a deficit of signal in a surface detector compared to predictions, which increases as a function of zenith angle, when the energy of the event is fixed by fluorescence measurements. We explore three potential explanations for this: the "Cronin effect" (growth of high-transverse momentum cross sections with nuclear size), the need for more particles at high transverse momentum in p- p collisions than currently predicted by high energy hadronic models used for air shower simulations, and the possibility that secondary interactions i…
We explore the feasibility of estimating primary cosmic ray composition at ultra high energies from the study of lateral age parameter of Extensive Air Showers (EAS) at ground level. Using different types of lateral distribution functions, we fit the particle density of simulated EAS to find the lateral age parameter. We discuss the chemical composition calculating the merit factor for each parameter distribution. The analysis considers three different primary particles (proton, iron and gamma), four different zenith angles (0°, 15°, 30° and 45°) and three primary energies (10^{17.25} eV, 10^{…
The simulation of Cherenkov photon's lateral density and arrival time distributions in Extensive Air Showers (EASs) was performed with the CORSIKA code in the energy range: 100 GeV to 100 TeV. On the basis of this simulation we obtained a set of approximating functions for the primary $γ$-ray photons, protons and iron nuclei incident at zenith angles from 0$^\circ$ to 40$^\circ$ over different altitudes of observation. Such a parameterisation is important for the primary particle identification, for the reconstruction of the shower observables and hence for a more efficient disentanglement of …
We investigate features of the lateral distribution function (LDF) of the radio signal emitted by cosmic ray air-showers with primary energies $> 0.1$~EeV and its connection to air-shower parameters such as energy and shower maximum using CoREAS simulations made for the configuration of the Tunka-Rex antenna array. Taking into account all significant contributions to the total radio emission, such as by the geomagnetic effect, the charge excess, and the atmospheric refraction we parameterize the radio LDF. This parameterization is two-dimensional and has several free parameters. The large numb…
Muons with a high transverse momentum (p_T) are produced in cosmic ray air showers via semileptonic decay of heavy quarks and the decay of high p_T kaons and pions. These high p_T muons have a large lateral separation from the shower core muon bundle. IceCube is well suited for the detection of high p_T muons. The surface shower array can determine the energy, core location and direction of the cosmic ray air shower while the in-ice array can reconstruct the energy and direction of the high p_T muon. This makes it possible to measure the decoherence function (lateral separation spectrum) at di…
A Monte Carlo (MC) simulation study of cosmic ray (CR) extensive air showers (EAS) has been carried out in the energy regime of the KASCADE experiment. From the characteristics of lateral distributions of electrons and muons of simulated EAS, some important EAS observables are extracted by a novel approach, and their CR mass-sensitivity is demonstrated. The study takes into account the issue of the experimental lateral density profiles of EAS electrons and muons after introducing the notion of the local age and segmented slope parameters, aimed to extract information on CR mass composition fro…
In this study, the necessity of the simulation study for exploring the interactions of ultra-high energy particles cosmic rays was examined. Different hadronic interaction models such as (SIBYLL, QGSJET, and EPOS) were simulated by using air showers simulation AIRES system (version 19.04.00). Also, the charged particle density of Extensive Air Showers (EAS) was calculated by estimating the lateral distribution function (LDF). Moreover, the LDF simulation of the two primary particles (proton and iron nuclei) was performed, taking into account their primary energies effect and the zenith angle o…
CoREAS is a Monte Carlo code for the simulation of radio emission from extensive air showers. It implements the endpoint formalism for the calculation of electromagnetic radiation directly in CORSIKA. As such, it is parameter-free, makes no assumptions on the emission mechanism for the radio signals, and takes into account the complete complexity of the electron and positron distributions as simulated by CORSIKA. In this article, we illustrate the capabilities of CoREAS with simulations carried out in different frequency ranges from tens of MHz up to GHz frequencies, and describe in particular…
IceTop, the surface component of the IceCube detector, has been used to measure the energy spectrum of cosmic ray primaries in the range between 1.58 PeV and 1.26 EeV. It can also be used to study the low energy muons in air showers by looking at large distances (> 300m) from the shower axis. We will show the muon lateral distribution function at large lateral distances as measured with IceTop and discuss the implications of this measurement. We also discuss the prospects for low energy muon studies with IceTop.
We present a measurement of the energy spectrum of the light mass group of cosmic rays (protons and helium) with the High Altitude Water Cherenkov (HAWC) Observatory in the energy interval from $10$ TeV to $200$ TeV. The spectrum covers the energy range between direct and indirect measurements, where precision data on the composition of cosmic rays are needed. The spectrum was constructed by applying an unfolding technique on a proton plus helium enriched sub-sample ($>90\%$ abundance) of cosmic ray air showers selected from the HAWC cosmic-ray data. The subset contains $3.8 \times 10^{9}$ air…
By means of Monte Carlo simulations of extensive air showers (EAS), we have performed a comprehensive study of the shower to shower fluctuations affecting the longitudinal and lateral development of EAS. We split the fluctuations into physical fluctuations and those induced by the thinning procedure customarily applied to simulate showers at EeV energies and above. We study the influence of thinning on the calculation of the shower to shower fluctuations in the simulations. For thinning levels larger than 10^(-5) - 10^(-6), the determination of the shower to shower fluctuations is hampered by …
Cosmic ray air showers emit radio pulses at MHz frequencies, which can be measured with radio antenna arrays - like LOPES at the Karlsruhe Institute of Technology in Germany. To improve the understanding of the radio emission, we test theoretical descriptions with measured data. The observables used for these tests are the absolute amplitude of the radio signal, and the shape of the radio lateral distribution. We compare lateral distributions of more than 500 LOPES events with two recent and public Monte Carlo simulation codes, REAS 3.11 and CoREAS (v 1.0). The absolute radio amplitudes predic…
Using a large set of simulated extensive air showers, we investigate universality features of electron and positron distributions in very-high-energy cosmic-ray air showers. Most particle distributions depend only on the depth of the shower maximum and the number of particles in the cascade at this depth. We provide multi-dimensional parameterizations for the electron-positron distributions in terms of particle energy, vertical and horizontal momentum angle, lateral distance, and time distribution of the shower front. These parameterizations can be used to obtain realistic electron-positron di…
Scaling properties of nuclei- and photon-initiated air showers are examined in wide primary energy range ($10^{14}÷10^{22}$~eV) taking into account Landau-Pomeranchuk-Migdal and geomagnetic field effects. It is shown that the invariance in lateral distribution and also the universal dependence between shower age and root mean square radius of electron component exist up to the highest energies. The implications of shower universality for reanalysis, cross-checking and validation of the results of different experiments together with decreasing of the influence of hadronic model uncertainties ar…
This paper presents the set of measurements of ultra-high energy air shower radio emission at frequency 32 MHz in period of 2008-2012. The showers are selected by geomagnetic and azimuth angles and then by the energy in three intervals: 3*10^16 3*10^17 eV, 3*10^17 6*10^17 eV and 6*10^17 5*10^18 eV. In each energy interval average lateral distribution function using mathematically averaged data from antennas with different directions are plotted. In the paper, using experimental data the dependence of radio signal averaged amplitude from geomagnetic angle, the shower axis distance and the energ…
The LOPES experiment, a digital radio interferometer located at KIT (Karlsruhe Institute of Technology), obtained remarkable results for the detection of radio emission from extensive air showers at MHz frequencies. Features of the radio lateral distribution function (LDF) measured by LOPES are explored in this work for a precise reconstruction of two fundamental air shower parameters: the primary energy and the shower Xmax. The method presented here has been developed on (REAS3-)simulations, and is applied to LOPES measurements. Despite the high human-made noise at the LOPES site, it is possi…
In this paper, we present results obtained from the measurements of radio emission at frequency of 32 MHz with energy more than 10$^{19}$ eV. Generalized formula that describe lateral distribution and depends on main characteristic of the air showers: energy E$_0$ and depth of maximum X$_{max}$ was derived. The formula has a good agreement with data at average and large distances from shower axis. Employing the ratio of radio emission amplitude at distances 175 m and 725 m we determined the depth of maximum X$_{max}$ for air shower with energy 3.7$\cdot$10$^{19}$ eV, which in our case is equal…
We have investigated some features of the density and arrival time distributions of Cherenkov photons in extensive air showers using the CORSIKA simulation package. The main thrust of this study is to see the effect of hadronic interaction models on the production pattern of Cherenkov photons with respect to distance from the shower core. Such studies are very important in ground based $γ$-ray astronomy for an effective rejection of huge cosmic ray background, where the atmospheric Cherenkov technique is being used extensively within the energy range of some hundred GeV to few TeV. We have fou…
Galactic cosmic rays are the high-energy particles that stream into our solar system from distant corners of our Galaxy and some low energy particles are from the Sun which are associated with solar flares. The Earth atmosphere serves as an ideal detector for the high energy cosmic rays which interact with the air molecule nuclei causing propagation of extensive air showers. In recent years, there are growing interests in the applications of the cosmic ray measurements which range from the space/earth weather monitoring, homeland security based on the cosmic ray muon tomography, radiation effe…
Cherenkov light lateral distribution function (CLLDF) simulation was fulfilled using CORSIKA code for configurations of Tunka EAS array of different zenith angles. The parameterization of the CLLDF was carried out as a function of the distance from the shower core in extensive air showers (EAS) and zenith angle on the basis of the CORSIKA simulation of primary proton around the knee region with the energy 3.10^15 eV at different zenith angles. The parameterized CLLDF is verified in comparison with the simulation that performed using CORSIKA code for two zenith angles.
The ARGO-YBJ experiment, a full coverage extensive air shower (EAS) detector located at high altitude (4300 m a.s.l.) in Tibet, China, has smoothly taken data, with very high stability, since November 2007 to the beginning of 2013. The array consisted of a carpet of about 7000 m$^2$ Resistive Plate Chambers (RPCs) operated in streamer mode and equipped with both digital and analog readout, providing the measurement of particle densities up to few particles per cm$^2$. The unique detector features (full coverage, readout granularity, wide dynamic range, etc) and location (very high altitude) al…
The aim of this report of the Working Group on Hadronic Interactions and Air Shower Simulation is to give an overview of the status of the field, emphasizing open questions and a comparison of relevant results of the different experiments. It is shown that an approximate overall understanding of extensive air showers and the corresponding hadronic interactions has been reached. The simulations provide a qualitative description of the bulk of the air shower observables. Discrepancies are however found when the correlation between measurements of the longitudinal shower profile are compared to t…
The lateral distribution function of high energy muons in EAS around the knee ($5.9\le \lg N_e \le 7.1$) has been measured for near vertical showers ($θ\le 20^{\circ}$, effective muon threshold energy is 230 GeV). The measurements have been performed at the Baksan Underground Scintillation Telescope (BUST). The electromagnetic component is measured by the "Andyrchy" EAS array, located above the BUST. The knee in EAS size spectrum is found to be at $\lg N_e \approx 6.3$. The experimental results are compared with Monte Carlo simulations.
One of the uncertainties in interpretation of ultra-high energy cosmic ray (UHECR) data comes from the hadronic interaction models used for air shower Monte Carlo (MC) simulations. The number of muons observed at the ground from UHECR-induced air showers is expected to depend upon the hadronic interaction model. One may therefore test the hadronic interaction models by comparing the measured number of muons with the MC prediction. In this paper, we present the results of studies of muon densities in UHE extensive air showers obtained by analyzing the signal of surface detector stations which s…
We observe a correlation between the slope of radio lateral distributions, and the mean muon pseudorapidity of 59 individual cosmic-ray-air-shower events. The radio lateral distributions are measured with LOPES, a digital radio interferometer co-located with the multi-detector-air-shower array KASCADE-Grande, which includes a muon-tracking detector. The result proves experimentally that radio measurements are sensitive to the longitudinal development of cosmic-ray air-showers. This is one of the main prerequisites for using radio arrays for ultra-high-energy particle physics and astrophysics.
The main interest of the present work is in analyzing the lateral distribution function (LDF) of Cherenkov radiation from particles that produced in Extensive Air Showers (EAS). The simulation of Cherenkov radiation LDF is fulfilled by utilizing the CORSIKA program at 1 PeV of the primary energy around the knee region for many primaries for vertical showers for Tunka-133 array conditions. Depending on the numerical simulation results of Cherenkov light LDF, sets of parameterized polynomial functions are resetted for several particles as a function of primary particle type. The comparison betwe…
An in-depth characterization of coherent radio Cherenkov pulses from particle showers in dense dielectric media, referred to as the Askaryan effect, is presented. The time-domain calculation developed in this article is based on a form factor to account for the lateral dimensions of the shower. It is computationally efficient and able to reproduce the results of detailed particle shower simulations with high fidelity in most regions of practical interest including Fresnel effects due to the longitudinal development of the shower. In addition, an intuitive interpretation of the characteristics …
Cosmic rays with energies up to $10^{11}\,\mathrm{GeV}$ enter the atmosphere and produce showers of secondary particles. Inside these showers muons with high transverse momentum ($p_\mathrm{T} \gtrsim 2\,\mathrm{GeV}$) are produced from the decay of heavy hadrons, or from high $p_\mathrm{T}$ pions and kaons very early in the shower development. These isolated muons can have large transverse separations from the shower core up to several hundred meters, together with the muon bundle forming a double or triple track signature in IceCube. The separation from the core is a measure of the transvers…
