Lateral Distribution Function Research Articles

Model-independent approach to deducing the mass composition of primary cosmic rays on the basis of the scale invariance in the radial distribution of electrons in extensive air showers

A new approach to deducing the mass composition of primary cosmic rays is proposed using the air showers universality and the scaling property of the electron lateral distribution function. Experimental data from the KASCADE, MSU, and KASCADE-Grande arrays have been analyzed, allowing conclusions as to the variations of mass composition above the knee to be drawn independently of the hadron-nucleus interaction model.

Restoring the azimuthal symmetry of lateral distributions of charged particles in the range of the KASCADE-Grande experiment

The reconstruction of Extensive Air Showers (EAS) observed by particle detectors at the ground is based on the characteristics of observables like the lateral particle density and the arrival times. The lateral densities, inferred for different EAS components from detector data, are usually parameterised by applying various lateral distribution functions (LDFs). The LDFs are used in turn for evaluating quantities like the total number of particles or the density at particular radial distances. Typical expressions for LDFs anticipate azimuthal symmetry of the density around the shower axis. The deviations of the lateral particle density from this assumption arising from various reasons are smoothed out in the case of compact arrays like KASCADE, but not in the case of arrays like Grande, which only sample a smaller part of the azimuthal variation. KASCADE-Grande, an extension of the former KASCADE experiment, is a multi-component Extensive Air Shower (EAS) experiment located at the Karlsruhe Institute of Technology (Campus North), Germany. The lateral distributions of charged particles are deduced from the basic information provided by the Grande scintillators – the energy deposits – first in the observation plane, then in the intrinsic shower plane. In all steps azimuthal dependences should be taken into account. As the energy deposit in the scintillators is dependent on the angles of incidence of the particles, azimuthal dependences are already involved in the first step: the conversion from the energy deposits to the charged particle density. This is done by using the Lateral Energy Correction Function (LECF) that evaluates the mean energy deposited by a charged particle taking into account the contribution of other particles (e.g. photons) to the energy deposit. By using a very fast procedure for the evaluation of the energy deposited by various particles we prepared realistic LECFs depending on the angle of incidence of the shower and on the radial and azimuthal coordinates of the location of the detector. Mapping the lateral density from the observation plane onto the intrinsic shower plane does not remove the azimuthal dependences arising from geometric and attenuation effects, in particular for inclined showers. Realistic procedures for applying correction factors are developed. Specific examples of the bias due to neglecting the azimuthal asymmetries in the conversion from the energy deposit in the Grande detectors to the lateral density of charged particles in the intrinsic shower plane are given.

A NEW METHOD FOR FINDING CORE LOCATIONS OF EXTENSIVE AIR SHOWERS

Analysis of an extensive air shower (EAS) detected by surface arrays highly depends on the determination of core locations. Here we present a new method to find the core location of an EAS that, unlike the common methods, does not depend on the lateral distribution function and uses arrival times of secondary particles. This method improves the accuracy of finding the core location of a low-energy EAS in the internal parts of an array, in comparison with common methods.

Macroscopic geo-magnetic radiation model; polarization effects and finite volume calculations

An ultra-high-energy cosmic ray (UHECR) colliding with the Earth's atmosphere gives rise to an Extensive Air Shower (EAS). Due to different charge separation mechanisms within the thin shower front coherent electromagnetic radiation will be emitted within the radio frequency range. A small deviation of the index of refraction from unity will give rise to Cherenkov radiation up to distances of 100 m from the shower core and therefore has to be included in a complete description of the radio emission from an EAS. Interference between the different radiation mechanisms, in combination with different polarization behavior will reflect in a lateral distribution function (LDF) depending on the orientation of the observer and a non-trivial fall-off of the radio signal as function of distance to the shower core.

The lateral distribution function of coherent radio emission from extensive air showers: Determining the chemical composition of cosmic rays

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 different scaling of the LDF at small and at large distances. As a first application we calculate the LDF for proton- and iron-induced showers and we show that this offers a very sensitive measure to discriminate between these two. We show that due to interference between the geo-magnetic and the charge-excess contributions the intensity pattern of the radiation is not circular symmetric.

Surface studies by reversed-flow inverse gas chromatography: A review

In the present work, the application of reversed-flow inverse gas chromatography (RF-IGC) to adsorption studies related to heterogeneous catalytic processes on noble metal supported catalysts is reviewed. RF-IGC methodologies are technically simple and they are combined with suitable mathematical treatments which give the possibility for studying the kinetics of catalyzed surface reactions, as well as the topography and the nature of the active sites of solid catalysts. Adsorption parameters, such as rate constants, adsorption energies, adsorption entropies, local isotherms, surface diffusion coefficients, lateral interaction energies and energy distribution functions, are simultaneously determined by RF-IGC. The potential of the novel methodologies has been evaluated by utilising as model systems CO adsorption/oxidation over well-studied Pt–Rh/SiO 2 and nanosized-Au/γ-Al 2O 3 catalysts. The main findings are presented and future goals are also discussed.

The lateral distribution function of high energy muons in EAS around the knee

The lateral distribution function of high energy muons in EAS around the knee ( 5.9 ≤ lg N e ≤ 7.1 ) has been measured for near vertical showers ( θ ≤ 20 ° , 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 the EAS size spectrum is found to be at lg N e ≈ 6.3 . The experimental results are compared with Monte Carlo simulations.

Model-insensitive approach to the cosmic ray primary mass composition deduction

We present new results for radial scale factors, R 0 , of the lateral distribution function of extensive air shower electrons. It is shown that difficulties in the direct experimental estimation of R 0 are no bar to primary mass composition deduction with weak sensitivity to hadronic interaction model implemented in calculations. Possibilities for more effective primary particles separation based on multi-component analysis are discussed.

Energy determination of cosmic ray showers in surface arrays using signal inference at a single distance from the core

In most high energy cosmic ray surface arrays, the primary energy is currently determined from the value of the lateral distribution function at a fixed distance from the shower core, r 0 . The value of r 0 is mainly related to the geometry of the array and is, therefore, considered as fixed independently of the shower energy or direction. We argue, however, that the dependence of r 0 on energy and zenith angle is not negligible. Therefore, in the present work we propose a new characteristic distance, which we call r opt , specifically determined for each individual shower, with the objective of optimizing the energy reconstruction. This parameter may not only improve the energy determination, but also allow a more reliable reconstruction of the shape and position of rapidly varying spectral features. We show that the use of a specific r opt determined on a shower-to-shower basis, instead of using a fixed characteristic value, is of particular benefit in dealing with the energy reconstruction of events with saturated detectors, which are in general a large fraction of all the events detected by an array as energy increases. Furthermore, the r opt approach has the additional advantage of applying the same unified treatment for all detected events, regardless of whether they have saturated detectors or not.

Observation of radio signals from air showers at the Pierre Auger Observatory

Radio detection of cosmic ray induced air showers has been demonstrated in dedicated setups in the past. Currently, radio detector setups are being tested at the Pierre Auger Observatory, in Malargüe, Argentina, for the detection of ultra high energy cosmic rays. These efforts have been rewarded with promising results. Radio signals from air showers have been measured in coincidence with the Auger surface detector array. One of the current data sets consists of 313 triggered radio events in coincidence with the surface detector of the observatory. These events have been used to make first analyses, which focus on the lateral distribution function of the radio signals and on the reconstruction of the arrival direction of cosmic rays. Furthermore, the radio background data have been studied. A periodic variation corresponding to the apparent motion of the galactic center has been observed. New, stand-alone, radio detectors have been developed and the next phase of testing at the Auger Observatory has started in May 2008. The aim is to show that an independent radio detector at the Auger Observatory with an area of about 20 km 2 is feasible.

ENERGY ESTIMATION OF ULTRA HIGH ENERGY COSMIC PARTICLES BY LATERAL DISTRIBUTION FUNCTIONS OF EXTENSIVE AIR SHOWERS

Energy is among the characteristics of Ultra High Energy Cosmic Rays (E > 5 ×1019 eV ) which could be estimated experimentally based on simulations. This paper attempts to estimate the energy of an UHECR proton by applying a Monte Carlo simulation code. A number of extensive air showers, vertical and inclined, are simulated to derive the lateral distribution functions of the shower particles. The scenario of simulations is adapted to the P. Auger Observatory site.

Calculating lateral distribution functions of the Cherenkov light from extensive atmospheric showers in terms of a multilevel scheme

A new technique for calculating the lateral distribution function of the Cherenkov light in very-high-energy extensive atmospheric showers is proposed. It is shown that the calculation results are in good agreement with the experimental data.

Underground muon counters as a tool for composition analyses

The transition energy from galactic to extragalactic cosmic ray sources is still uncertain, but it should be associated either with the region of the spectrum known as the second knee or with the ankle. The baseline design of the Pierre Auger Observatory was optimized for the highest energies. The surface array is fully efficient above 3 × 10 18 eV and, even if the hybrid mode can extend this range below 10 18 eV, the second knee and a considerable portion of the wide ankle structure are left outside its operating range. Therefore, in order to encompass these spectral features and gain further insight into the cosmic ray composition variation along the transition region, enhancements to the surface and fluorescence components of the baseline design are being implemented that will lower the full efficiency regime of the Observatory down to ∼10 17 eV. The surface enhancements consist of a graded infilled area of standard Auger water Cherenkov detectors deployed in two triangular grids of 433 m and 750 m of spacing. Each surface station inside this area will have an associated muon counter detector. The fluorescence enhancement, on the other hand, consists of three additional fluorescence telescopes with higher elevation angle (30°–58°) than the ones in operation at present. The aim of this paper is threefold. We study the effect of the segmentation of the muon counters and find an analytical expression to correct for the under counting due to muon pile-up. We also present a detailed method to reconstruct the muon lateral distribution function for the 750 m spacing array. Finally, we study the mass discrimination potential of a new parameter, the number of muons at 600 m from the shower axis, obtained by fitting the muon data with the above mentioned reconstruction method.

The implication of charged particle lateral distribution function for extensive air shower studies

The knowledge of charged particle lateral distribution function (LDF) is of prime importance in extensive air shower (EAS) investigations. This function is necessary for the determination of the total number of particles as well as some other classification parameters. The Nishimura-Kamata-Greisen (NKG) function is being actively employed by many researchers in spite of the fact that it was derived under rather crude assumptions (in so-called B Approximation of the electromagnetic cascade theory). Our paper discusses the dependence of the EAS size spectrum on the LDF form adopted and compares two LDFs: the traditional NKG-function and the scaling function suggested recently. Prominence is given to the EAS MSU data but the results of other EAS arrays (AGASA, Yakutsk and KASCADE) are also considered.

Structure-transport analysis for particulate packings in trapezoidal microchip separation channels

This article investigates the efficiency of particulate beds confined in quadrilateral microchannels by analyzing the three-dimensional fluid flow velocity field and accompanying hydrodynamic dispersion with quantitative numerical simulation methods. Random-close packings of uniform, solid (impermeable), spherical particles of diameter d(p) were generated by a modified Jodrey-Tory algorithm in eighteen different conduits with quadratic, rectangular, or trapezoidal cross-section at an average bed porosity (interparticle void fraction) of epsilon = 0.48. Velocity fields were calculated by the lattice Boltzmann method, and axial hydrodynamic dispersion of an inert tracer was simulated at Péclet numbers Pe = u(av)d(p)/D(m) (where u(av) is the average fluid flow velocity through a packing and D(m) the bulk molecular diffusion coefficient) from Pe = 5 to Pe = 30 by a Lagrangian particle-tracking method. All conduits had a cross-sectional area of 100d(p)(2) and a length of 1200d(p), translating to around 10(5) particles per packing. We present lateral porosity distribution functions and analyze fluid flow profiles and velocity distribution functions with respect to the base angle and the aspect ratio of the lateral dimensions of the different conduits. We demonstrate significant differences between the top and bottom parts of trapezoidal packings in their lateral porosity and velocity distribution functions, and show that these differences increase with decreasing base angle and increasing base-aspect ratio of a trapezoidal conduit, i.e., with increasing deviation from regular rectangular geometry. Efficiencies are investigated in terms of the axial hydrodynamic dispersion coefficients as a function of the base angle and base-aspect ratio of the conduits. The presented data support the conclusion that the efficiency of particulate beds in trapezoidal microchannels strongly depends on the lateral dimensions of the conduit and that cross-sectional designs based on large side-aspect-ratio rectangles with limited deviations from orthogonality are favorable.

Study of extensive air showers and primary energy spectra by MAKET-ANI detector on mountain Aragats

Small and middle size surface detectors measuring extensive air showers (EAS) initiated by primary cosmic rays (PCR) incident on terrestrial atmosphere have been in operation for the last 50 years. Their main goal is to explore the “knee” in all particle spectrum to solve the problem of cosmic ray (CR) origin and acceleration. The recent achievements of atmospheric Cherenkov telescopes and X-ray space laboratories, establishing the supernova remnants (SNRs) as a source of hadronic cosmic rays, pose stringent conditions on the quality of EAS evidence. After establishing the existence of the “knee” itself, the most pronounced result from EAS studies is the rigidity dependent shift of the knee position to the highest energies. This feature was first observed by separation of the primary flux in different mass groups in MAKET-ANI, EAS-TOP and KASCADE experiments. The MAKET-ANI detector is placed on Mt. Aragats (Armenia) at 3200 m above the sea level (40°25′N, 44°15′E). More than 1.3 × 10 6 showers with size greater than 10 5 particles were registered in 1997–2004. The detector effectively collected the cores of EAS, initiated by primaries with energies of 10 14–10 17 eV. After proving that the quality of the EAS size and shape reconstruction was reasonably high, we present the lateral distribution function (LDF) for distances from 10 to 120 m from EAS core and EAS size spectra in 5 zenith angle intervals. We use CORSIKA simulations to present the energy spectra. The results from the MAKET-ANI experiment on the energy spectra of the “light”(p + He) and “heavy” (O + Si + Fe) nuclear groups are compared to the spectra obtained by balloon experiments and to other available spectra.

On the choice of the lateral distribution function for EAS charged particles

Knowledge of the lateral distribution function (LDF) of charged particles in extensive air showers (EASs) is necessary for adequate determination of both the total number Ne of particles and other parameters used to classify the showers selected for analysis. Many researchers continue to actively use the Nishimura-Kamata-Greisen LDF despite that fact that it was obtained theoretically within a fairly rough approximation of electromagnetic cascade theory. In this study, the dependence of the shape of the EAS spectrum over the number of particles on the type of LDF used to treat experimental data is investigated. The Nishimura-Kamata-Greisen function and the scaling function are analyzed [5]. Major attention is given to the data obtained at the Moscow State University EAS array.

Diblock Polyampholytes Grafted onto Spherical Particles: Effect of Stiffness, Charge Density, and Grafting Density

The structure of spherical brushes formed by symmetric diblock polyampholytes end-grafted onto small spherical particles in aqueous solution is examined within the framework of the so-called primitive model using Monte Carlo simulations. The properties of the two blocks are identical except for the sign of their charges. Three different chain flexibilities corresponding to flexible, semiflexible, and stiff blocks are considered at various polyampholyte linear charge densities and grafting densities. The link between the two blocks is flexible at all conditions, and the grafted segments are laterally mobile. Radial and lateral spatial distribution functions of different types and single-chain properties are analyzed. The brush structure strongly depends on the chain flexibility. With flexible chains, a disordered polyelectrolyte complex is formed at the surface of the particle, the complex becoming more compact at increasing linear charge density. With stiff blocks, the inner blocks are radially oriented. At low linear charged density, the outer blocks are orientationally disordered, whereas at increasing electrostatic interaction the two blocks of a polyampholyte are parallel and close to each other, leading to an ordered structure referred to as a polyampholyte star. As the grafting density is increased, the brush thickness responds differently for flexible and nonflexible chains, depending on a different balance between electrostatic interactions and excluded volume effects.

The optimum distance at which to determine the size of a giant air shower

To determine the size of an extensive air shower it is not necessary to have knowledge of the function that describes the fall-off of signal size from the shower core (the lateral distribution function). In this paper an analysis with a simple Monte Carlo model is used to show that an optimum ground parameter can be identified for each individual shower. At this optimal core distance, r opt, the fluctuations in the expected signal, S( r opt), due to a lack of knowledge of the lateral distribution function are minimised. Furthermore it is shown that the optimum ground parameter is determined primarily by the array geometry, with little dependence on the energy or zenith angle of the shower or choice of lateral distribution function. For an array such as the Pierre Auger Southern Observatory, with detectors separated by 1500 m in a triangular configuration, the optimum distance at which to measure this characteristic signal is close to 1000 m.

On the composition of cosmic rays with E 0 ≥ 1017 eV according to the Yakutsk EAS array data

The energy spectrum and anisotropy of primary cosmic rays, as well as the lateral distribution functions of electrons and muons in extensive air showers (EASs) with E 0 ≥ 1017 eV, are presented according to the Yakutsk EAS array data. It has been shown that the spectrum and lateral distribution functions in some energy ranges have different shapes for the particles that arrive from the disc of the Supergalaxy (Local Supercluster of galaxies) and from the other part of the celestial sphere. This is interpreted as the manifestation of the interaction of extragalactic primary cosmic rays with the gas of the Supergalaxy that possibly leads to the production of new ultra-high-energy particles.