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ICRC 2007 Proceedings - Pre-Conference Edition 30TH INTERNATIONAL COSMIC RAY CONFERENCE ICRC 2007 Proceedings - Pre-Conference Edition Calculation of radio emission from high-energy air showers N. N. KALMYKOV1, A. A. KONSTANTINOV1, R. ENGEL2. 1 Scobeltsyn Institute of Nuclear Physics, Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia 2 Institut fur¨ Kernphysik, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany [email protected] Abstract: Results of the simulation of radio signals from 1017 eV extensive air showers are reported. The simulations are based on a track-by-track electric field calculation using the EGSnrc Monte Carlo shower code. The lateral distribution of the predicted radio emission is compatible with the recent LOPES-10 experimental data at distances < 300 m. Perspectives of extending EAS radio emission calculations to the ultra-high energy range (up to 1020 eV) are also discussed. Introduction particle trajectories using the Monte Carlo (MC) technique. In such an approach, shower properties Radio emission accompanying extensive air show- can be included in the most accurate and simple ers (EAS) is considered as a promising alterna- way, which, however, requires very large comput- tive to traditional methods of high energy cosmic ing time at primary energies above 1015 eV. ray detection. Recently, first measurements from Using the MC approach, EAS radio emission a new generation of radio antenna arrays, LOPES has been theoretically investigated most inten- [1], which is co-located with the KASCADE air sively within the framework of the “geosyn- shower array [2], and CODALEMA [3], were pub- chrotron emission” model [5] proposed by Falcke lished. The experimentally found, good correla- and Gorham in 2003 [6]. In this model, it is as- tion of the signal with the shower energy has also sumed that the overall radio signal of air showers is renewed the interest in theoretical predictions [1]. dominated by the radio emission due to the deflec- In general, there are two approaches of calculating tion of particle trajectories in the magnetic field of the radio signal of an air shower. the Earth. In the geosynchroton model, simulations The starting point of Askaryan’s predictions in are performed in the time domain, i.e. the elec- 1961 was the model of the motion of effective tric field contributions produced by shower parti- charges in EAS [4]. In [4] both electron excess cles are summed as function of the detection time and charge separation in the Earth’s magnetic field [5, 7]. The refractive index of air is taken as unity. were proposed as responsible for the EAS radio In this paper, we follow a more general approach emission. In this picture a shower is considered as that does not explicitly distinguish between the a continuous system of charges and currents. Evi- geosynchroton or Cherenkov radio signal. We dently, the approach of calculating the radio emis- calculate the radio signal of each shower parti- sion for a system of charges and currents rather cle in Fourier space (frequency domain). Signal than individual particles has the potential of being contributions due to start and end points of parti- numerically very efficient. cle trajectories and localized momentum changes On the other hand, parametrizations of the overall in Coulomb scattering and bremsstrahlung are in- charges and currents in EAS have not yet been de- cluded as well as the continuous deflection in the veloped. Therefore it is very useful to start with Earth’s magnetic field. The refractive index of air an approach that is based on following individual is naturally accounted for in the simulation. CALCULATION OF RADIO EMISSION Electric field calculation In the EAS case, particle trajectories are mainly governed by elementary interactions with air and ICRC 2007 Proceedings - Pre-Conference Edition also the deflection of the particles in the Earth’s magnetic field. The problem then is to calculate the radiation from a charged particle having a tra- jectory which cannot be described by an analytic function. An important constraint is that the sum over all particles should result in an expression similar to that of the continuous charges and cur- rents approach. As MC simulation is a linear procedure employ- Figure 1: Illustration of the individual trajectory ing a “straight-step-by-straight-step” particle trans- contributions considered in the calculation. portation, it is natural to calculate the electric field ~ ~ from a charged particle by considering the tra- βs⊥ βs+1⊥ jectory as a sum of many leaps of the velocity × − . (2) 1 − n~e · β~ 1 − n~e · β~ β~ = ~u/c: Rs s Rs s+1 Here ε is the permittivity of vacuum, c is the light ~ ~ ~ ~ 0 Eω ΣN = Eω 0 → β1 + ... speed in vacuum, k = nω/c, n is the refractive | {z } birth of the particle index of air, R is the distance between electron lo- ~ ~ ~ ~ ~ ~ cation and the observation point, ~eR is the unit vec- + Eω βs → βs+1 + ... + Eω βN → 0 . (1) ~ tor in the direction of observation, ξ0 is the radius- | {z } | {z } ~ deflection of the particle death of the particle vector of electron at the time t0 and β⊥ is the trans- ~ verse component of β with respect to ~eR. Here N is the total number of adjoining individ- In comparison, in the geosynchrotron model only ual trajectory segments at which the velocities β~ s the terms in the series (1) which are due to the par- are being constant vectors, Fig.1. Internal terms ticle deflections in the Earth’s magnetic field are in the series (1) may describe both discrete in- taken into account. teractions of charged particles in air (including multiple Coulomb scattering and secondary parti- cle creation below the simulation threshold) and Modelling their “smooth” deflection in the Earth’s magnetic or electric fields. Calculations of the EAS radio emission are carried In the case of discrete interactions, the electric field out in the “particle-by-particle” manner in a spe- can be estimated within classical radiation theory cial program written for this purpose. A photon rather than quantum theory due to ω∆t 1, is used as primary particle and MC shower mod- where ω is the observation frequency and ∆t is the elling is performed just for the electromagnetic time of interaction. part of the shower using the EGSnrc code [9]. The In the framework of the Fraunhofer approximation, density and optical properties of the Earth’s atmo- the Fourier-component E~ω of the electric field at a sphere are taken to be uniform within slices of 9.5 given frequency ω = 2πν produced by a sudden g/cm2. The strength and declination of the Earth’s ~ ~ leap βs → βs+1 of an electron velocity at the time magnetic field correspond to those for the LOPES (s+1) experiment. The radiation field is calculated via moment t0 is given by (2) for all particle energies above the threshold ~ ~ E~ω βs → βs+1 = 100 keV. The upper limit on step size of particle straight transport is equal to 1 m. ikRs e e iω(t(s+1)−n~e ·ξ~ (s+1)/c) = e 0 Rs 0 × A straight-forward MC simulation of the full 8π2ε c R 0 s shower development is limited to energies up to 30TH INTERNATIONAL COSMIC RAY CONFERENCE ' 1015 eV. The situation may be improved by ap- plying the “thinning” method [10], which is char- acterized by the parameter εth = Eth/E0, where Eth is the energy at which the thinning process is ICRC 2007 Proceedings - Pre-Conference Edition started, E0 is the energy of primary particle. The influence of thinning on the radio emission calcu- lation quality has been studied in the 1012 − 1014 eV range. Unfortunately, the general conclusion is that thinning does not allow to increase the pri- mary energy as much as would be needed to sim- ulate showers at ultra-high energy. Namely, at the LOPES frequency range (40-80 MHz), the accept- able level εth reduces computing time by a factor of only 10-20 for a range of observation distances up to 200-300 m from a shower axis. The reason is that for radio emission the low energy particles (having energies much less than the critical energy of 81 MeV) are extremely important. Figure 2: Number of charged particles of a 1017 eV photon-initiated vertical shower as a function of −7 atmospheric depth. Thinning level εth = 2 · 10 Results or Eth = 20 GeV. The model results are compared to Greisen’s parameterization for a radiation length In Fig.2 the longitudinal profile of one 1017 eV of 36.8 g/cm2 and an critical energy of 81 MeV. photon-initiated vertical shower is presented. The initial photon was injected at 30 km above the sea level. The simulated profile is similar to the aver- age cascade curve at 1017 eV. Therefore it is rea- sonable to assume that the given shower is rep- resentative for a comparison of the predicted ra- dio emission with experimental data at energies of about 1017 eV that is averaged over many showers. The comparison with LOPES-10 experimental data is plotted on Fig.3, where the simulated ra- dio emission has been averaged over north, south, west and east directions. A correlation of radio sig- nals with distance is found for the group of events selected out of 5 months of LOPES-10 measure- ments [8]. All selected showers have energies in 16 17 the range E0 ' 5 · 10 − 6 · 10 eV and zenith angles < 50◦. In the comparison, it has been taken into ac- count that experimentally measured and theoreti- cally calculated field strengths are not absolutely Figure 3: Lateral distribution of EAS radio emis- identical.
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