Final results of the LOPES radio interferometer for cosmic-ray air showers
W.D. Apel, J.C. Arteaga-Velázquez, L. Bähren, K. Bekk, M. Bertaina, P.L. Biermann, J. Blümer, H. Bozdog, E. Cantoni, A. Chiavassa, K. Daumiller, V. de Souza, F. Di Pierro, P. Doll, R. Engel, H. Falcke, B. Fuchs, H. Gemmeke, C. Grupen, A. Haungs, D. Heck, J.R. Hörandel, A. Horneffer, D. Huber, T. Huege, P.G. Isar, K.-H. Kampert, D. Kang, O. Krömer, J. Kuijpers, K. Link, P. Luczak, M. Ludwig, H.J. Mathes, M. Melissas, C. Morello, S. Nehls, J. Oehlschläger, N. Palmieri, T. Pierog, J. Rautenberg, H. Rebel, M. Roth, C. Rühle, A. Saftoiu, H. Schieler, A. Schmidt, S. Schoo, F.G. Schröder, O. Sima, G. Toma, G.C. Trinchero, A. Weindl, J. Wochele, J. Zabierowski, J.A. Zensus, LOPES Collaboration
aa r X i v : . [ a s t r o - ph . H E ] F e b Eur. Phys. J. C manuscript No. (will be inserted by the editor)
Final results of the LOPES radio interferometer forcosmic-ray air showers
W.D. Apel , J.C. Arteaga-Vel´azquez , L. B¨ahren , K. Bekk , M. Bertaina ,P.L. Biermann , J. Bl¨umer , H. Bozdog , E. Cantoni , A. Chiavassa ,K. Daumiller , V. de Souza , F. Di Pierro , P. Doll , R. Engel ,H. Falcke , B. Fuchs , H. Gemmeke , C. Grupen , A. Haungs ,D. Heck , J.R. H¨orandel , A. Horneffer , D. Huber , T. Huege ,P.G. Isar , K.-H. Kampert , D. Kang , O. Kr¨omer , J. Kuijpers ,K. Link *, 1 , P. Luczak , M. Ludwig , H.J. Mathes , M. Melissas ,C. Morello , S. Nehls , J. Oehlschl¨ager , N. Palmieri , T. Pierog ,J. Rautenberg , H. Rebel , M. Roth , C. R¨uhle , A. Saftoiu ,H. Schieler , A. Schmidt , S. Schoo , F.G. Schr¨oder *, 1, 17 , O. Sima ,G. Toma , G.C. Trinchero , A. Weindl , J. Wochele , J. Zabierowski ,J.A. Zensus - LOPES Collaboration Institute for Astroparticle Physics (IAP) [formerly, Institute for Nuclear Physics (IKP)], Karlsruhe Institute of Technology(KIT), Karlsruhe, Germany Instituto de F´ısica y Matem´aticas, Universidad Michoacana, Morelia, Michoac´an, Mexico ASTRON, Dwingeloo, The Netherlands Dipartimento di Fisica, Universit`a degli Studi di Torino, Torino, Italy Max-Planck-Institut f¨ur Radioastronomie, Bonn, Germany Institute for Experimental Particle Physics (ETP), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania Osservatorio Astrofisico di Torino, INAF Torino, Torino, Italy Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, S˜ao Carlos, Brasil Department of Astrophysics, Radboud University Nijmegen, AJ Nijmegen, The Netherlands Department of Physics, Bergische Universit¨at Wuppertal, Wuppertal, Germany Institut f¨ur Prozessdatenverarbeitung und Elektronik, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany Faculty of Natural Sciences and Engineering, Universit¨at Siegen, Siegen, Germany Institute of Space Science, Bucharest-Magurele, Romania Department of Astrophysics, National Centre for Nuclear Research, L´od´z, Poland Studsvik Scandpower GmbH, Hamburg, Germany Bartol Research Institute, Department of Physics and Astronomy, University of Delaware, Newark DE, USA Department of Physics, University of Bucharest, Bucharest, Romania now at: European Commission, Joint Research Centre (JRC), Karlsruhe, Germany preprint; accepted by EPJ C for publication Abstract
LOPES, the LOFAR prototype station, wasan antenna array for cosmic-ray air showers operatingfrom 2003 - 2013 within the KASCADE-Grande exper-iment. Meanwhile, the analysis is finished and the dataof air-shower events measured by LOPES are availablewith open access in the KASCADE Cosmic Ray DataCenter (KCDC). This article intends to provide a sum-mary of the achievements, results, and lessons learnedfrom LOPES. By digital, interferometric beamformingthe detection of air showers became possible in theradio-loud environment of the Karlsruhe Institute ofTechnology (KIT). As a prototype experiment, LOPEStested several antenna types, array configurations and * e-mail: [email protected] ; [email protected] calibration techniques, and pioneered analysis methodsfor the reconstruction of the most important showerparameters, i.e., the arrival direction, the energy, andmass-dependent observables such as the position of theshower maximum. In addition to a review and updateof previously published results, we also present newresults based on end-to-end simulations including allknown instrumental properties. For this, we applied thedetector response to radio signals simulated with theCoREAS extension of CORSIKA, and analyzed themin the same way as measured data. Thus, we were ableto study the detector performance more accurately thanbefore, including some previously inaccessible featuressuch as the impact of noise on the interferometric cross- correlation beam. These results led to several improve-ments, which are documented in this paper and canprovide useful input for the design of future cosmic-rayexperiments based on the digital radio-detection tech-nique. Keywords
Cosmic rays · extensive air showers · radioemission · LOPES (LOFAR PrototypE Station)
What is the potential of the digital radio detection tech-nique for high-energy astroparticle physics? To answerthis question, LOPES (the LO
FAR
PrototypE Station)was deployed in the early 2000’s and operated for aboutone decade. Meanwhile the experiment is concluded anddata analysis finished. Therefore, it is time to summa-rize: What is the answer to the original question? Whathas been achieved? What else have we learned, whatnew questions emerged, and how is the field continu-ing?Thanks to prototype experiments such as LOPES,digital radio detection has been established as an addi-tional technique for the measurement of cosmic-ray airshowers. First measurements of the radio emission wereperformed with analog detectors more than fifty yearsago [1,2,3]. However, their accuracy for the cosmic-rayenergy and the position of the shower maximum waslimited by the analog technology used and by the in-complete theoretical understanding of the radio emis-sion of air showers. Nevertheless, the community main-tained a certain level of interest in the technique andcontinued experimental efforts regarding the radio de-tection of air showers [4,5]. A technical breakthroughwas achieved in the 2000’s with the digital antenna ar-rays LOPES [6] and CODALEMA [7] because the dig-itally saved data enabled sophisticated post-processingand computing-extensive analyses of the measurements.In parallel, progress was made on a variety of simulationand calculation tools [8,9,10,11], whose latest genera-tions are generally able to reproduce measured radiosignals. Together with the second generation of digi-tal antenna arrays such as AERA [12], LOFAR [13],TREND [14], and Tunka-Rex [15], the measurementsof LOPES and CODALEMA were critical to improvethe understanding of the emission processes, in partic-ular by comparing the measured radio signals with thepredictions of Monte Carlo simulations of extensive airshowers and to the data of the co-located particle de-tector arrays.Because LOPES was triggered by the co-locatedparticle-detector array KASCADE-Grande, a compari-son of radio and particle measurements of the same air showers demonstrated that radio detection provides anaccuracy for the shower direction [16] and energy [17]approximately equal to that of the particle-detector ar-ray. As prototype station in the radio-loud environmentof the Karlsruhe Institute of Technology, the precisionof LOPES was, however, limited [17]. With improvedmethods and at more radio-quiet sites, the successorarrays LOFAR in the Netherlands [18], the Auger En-gineering Radio Array (AERA) of the Pierre Auger Ob-servatory in Argentina [19], and Tunka-Rex in Siberia[20] have meanwhile achieved an accuracy comparableto the leading optical techniques for air showers evenfor the position of the shower maximum.In general, radio detection combines several advan-tages of the classical detection techniques for air show-ers. Like the air-fluorescence and air-Cherenkov lightof air showers, also the radio emission depends on therelatively well-understood electromagnetic shower com-ponent, i.e., the radio signal has an intrinsic sensitivityto the energy of the electromagnetic component and theposition of the shower maximum. The radio techniqueis not restricted to clear nights, but works under al-most any weather conditions. LOPES showed that onlythunderclouds directly over the antenna array have asignificant impact on the radio signal [21], which low-ers the available measurement time by only a few per-cent. Radio detectors share their advantage of avail-ability around the clock with the classical technique ofsecondary-particle detection at the ground. Thus, an-tennas arrays are the ideal companion to particle de-tectors, in particular to muon detectors that yield com-plementary information to the electromagnetic showercomponent measured via the radio signal. Moreover,as it was done at LOPES, a particle detector arraycan provide a trigger to the radio antennas, which fa-cilitates the discrimination of air-shower radio signalagainst background.Digital radio experiments [22,23,24] also revealedsome complications of the radio technique: Due to theinterplay of two different emission mechanisms, the ra-dio footprint on ground has a two-dimensional, asym-metric shape. The two proven emission mechanisms arethe geomagnetic deflection of the electrons and positrons[25],[26], which is the dominant effect for most air-showergeometries, and the weaker Askaryan effect, i.e., ra-dio emission due to the variation of the net charge ofthe shower front during the shower development [27].Several radio arrays in radio-quiet environments haveexperimentally confirmed the coexistence of these twoemission mechanisms [28,29,30]. At LOPES, this com-plication was neglected against the typical measure-ment uncertainties, i.e., the LOPES measurements wereinterpreted as if the radio emission were purely geomag- netic. The resulting inaccuracy was small compared toother uncertainties, e.g., resulting from the high radiobackground at the site. Another complication of the ra-dio technique regards self-triggering, which turned outto be possible, but difficult, and is unnecessary when ra-dio arrays are operated as extension to particle-detectorarrays. Finally, we learned that fully efficient detec-tion for all arrival directions requires a relatively denseantenna spacing below 100 m, but sparse arrays withkilometer-wide spacing still qualify for the detection ofinclined air showers. Despite these complications, theprinciple advantage of a precise all-day sensitivity tothe electromagnetic shower component make the ra-dio technique a suitable extension to existing particle-detector arrays, and potentially even for stand-aloneneutrino detection.Given these prospects of the radio technique, wehave decided to provide this review of previous LOPESresults starting with a summary of the main results,followed by a description of the LOPES setup and itsvarious configurations. The focus is on the latest re-sults using end-to-end simulations based on CoREAS,which are published in detail in the last PhD thesis re-lated to LOPES [31], and have partly been shown onconferences [32,33,34]. We also include an overview oflessons learned, in the hope that some mistakes mightbe avoided by future radio experiments.
The following list provides a quick overview of impor-tant results obtained by LOPES. Some of them are re-viewed in more detail in the later sections. – LOPES was the first digital radio array which un-ambiguously proved that the detection technique issuitable to study air showers generated by high-energy cosmic rays [6]. – LOPES confirmed earlier results [2] that the domi-nant emission mechanism is due to the Lorentz force.The amplitude of the radio signal is correlated withthe geomagnetic angle [6], and the ratio of the signalof differently aligned antennas is consistent with thepolarization pattern expected by geomagnetic emis-sion [35],[36]. – Several very inclined events were detected by LOPES[37]. The slope of the lateral distribution was ob-served to become flatter with increasing shower in-clination [38], i.e. the more inclined the shower thelarger the radio footprint. This is in line with laterresults by ANITA [39] and by the Auger Engineer-ing Radio Array [40]. – Closeby thunderstorm clouds with high atmosphericelectric fields can significantly change the radio emis-sion of air showers and can cause much higher radio-signal amplitudes than during normal weather con-ditions [41,21]. – Digital interferometry, in particular cross-correlationbeamforming, is an effective way of lowering the de-tection threshold and identifying air-shower pulsesagainst background [42]. – LOPES pioneered methods for the calibration ofthe absolute amplitude using an external referencesource [43],[44] , and for the continuous calibrationof the relative timing by a reference beacon emittingsine-wave signals [45]. The nanosecond relative tim-ing accuracy was essential for digital interferometry. – Thanks to its absolute calibration, LOPES was ableto test the radio-signal amplitudes predicted by theREAS [46] and CoREAS [8] radio extensions of theCORSIKA Monte-Carlo simulation code on an ab-solute level. Applying the improved amplitude cali-bration showed that not REAS, but the newer CoREASis fully compatible to LOPES within its measure-ment uncertainties [44]. – The lateral distribution of the radio signal falls lesssteeply than indicated by the historic results fromthe analog era [2]. A Gaussian lateral distributionfunction [17] describes LOPES data best, but a sim-ple exponential LDF turned out to be sufficient formany applications [47,38]. In the latter case, the av-erage exponential decay constant observed by LOPESis approximately R = 180 m. – The wavefront of the radio emission by air show-ers was found to be of hyperbolic shape [48], whichsubsequently was confirmed by LOFAR with moreprecise measurements [49]. – The frequency spectrum observed with LOPES canbe described by a power law or exponential functionfalling towards higher frequencies [50]. – LOPES provided an experimental proof that the ra-dio signal depends on the longitudinal shower de-velopment [51], and was able to measure the depthof the shower maximum for individual events. Al-though the measurement uncertainties were too largefor an interpretation in terms of mass composition,LOPES showed that the lateral distribution [17] andthe wavefront [48] can each be used to reconstructthe position of the shower maximum. Due to the better insight and update of the absolute calibra-tion, numerical values for amplitude measurements reportedin publications prior to 2015 need to be corrected by a factorof 2 . ± . Fig. 1
Photo of an inverted v-shape dipole antenna of theLOPES-30 setup in the KASCADE particle-detector array. – Despite the high radio background at the LOPESsite, LOPES achieved a competitive accuracy of bet-ter than 20 % for the energy of the primary particleand of better than 0 . ◦ for the arrival direction (de-tails in this article). This section describes the technical setup of the LOPESexperiments and its data acquisition, the procedure fordata analysis and end-to-end Monte Carlo simulationsreproducing measured events. The section concludeswith a description of the data set used for the resultspresented in this article and its public access via KCDC.3.1 Retrospective view on different experimentalstagesLOPES started in 2003 by deploying ten dipole-likeLOFAR prototype antennas at the KASCADE arrayfor cosmic-ray air showers (Fig. 1). Triggered by theparticle-detector arrays KASCADE [52] and KASCADE-Grande [53], LOPES soon detected the radio emissionof air showers with energies above 10 eV [6], and sub-sequently was extended to 30 antennas (Fig. 2). At thebeginning, all LOPES antennas were aligned in east-west direction because, due to its dominant geomag-netic origin, the radio signal is on average strongest inthe east-west direction.End of 2006, half of the then 30 antennas were ro-tated to align them in north-south direction. The simul-taneous measurements of the north-south and east-westaligned antennas provided additional evidence for thedominantly geomagnetic nature of the radio emission[35]. Five antenna positions were equipped with both polarization directions, but due to restrictions in thecabling infrastructure the remaining ten east-west andten north-south aligned antennas were placed at dif-ferent positions (Fig. 3). Since the radio signal and itspolarization changes significantly on the scale of the an-tenna spacing (26 −
37 m between adjacent antennas)[54], this special separation of differently aligned an-tennas turned out to hamper a reconstruction of thesignal polarization. At LOPES, we therefore decided toanalyze the east-west and north-south aligned antennasseparately. Because of the longer measurement time andthe stronger signals, the event statistics was higher forthe east-west aligned antennas [38], and most resultsare based on these east-west measurements – includingthe new results presented in the following sections.In the winter of 2009/2010, the configuration of LOPESwas changed again, i.e, the antennas were exchanged toten ’tripole’ stations, each consisting of three orthogo-nal dipole antennas aligned in east-west, north-south,and vertical direction [55]. This setup was operatinguntil 2013 when the whole KASCADE experiment wasstopped and subsequently dismantled. Due to a new re-search facility close to the LOPES site, the backgroundlevel increased substantially during the last phase ofLOPES limiting the statistics of events above thresh-old. Nonetheless, statistical analyses and a few individ-ual events with detectable signal in all three polariza-tion directions again confirmed the general picture ofthe dominant geomagnetic emission [36]. In addition tothe overall increase of the background level, we notedthat the background rises towards the horizon, as is ex-pected for anthropogenic radio background. Thus, nofinal conclusion was drawn whether such a more expen-sive setup with three polarization directions per stationwould have an advantage over a setup with two anten-nas per station.3.2 Data-Acquisition SystemWhile the setup of the antennas was changed severaltimes over the operation period of LOPES, the hard-ware of the data-acquisition remained the same. Tech-nical details can be found, e.g., in reference [55] and[56], and only the main features are described here.The voltage measured at each antenna was contin-uously digitized and stored in a ring buffer, where thedigitization of all antenna signals was synchronized bya common clock distributed via cables. Upon receivinga trigger from KASCADE or KASCADE-Grande, thebuffers of all antennas were read out and combined toone event containing the coincident traces of all 30 an-tennas. Each event was stored on disk and combinedduring later analysis with the coincident KASCADE or
April 2003 February 2005 December 2006 February 2010LOPES 10 LOPES 30 LOPES 30 pol LOPES 3D January 2013
Fig. 2
Timeline of the LOPES experiment: Starting with 10 east-west aligned antennas of the inverted v-shape dipole type(LOPES 10), LOPES was soon extended to 30 such antennas (LOPES 30). End of 2006, half of these antennas were rotatedby 90 ◦ to north-south alignment (LOPES 30 pol). Finally, all antennas were dismantled and 10 tripole antennas connected tothe existing cables and DAQ infrastructure (LOPES 3D). The results presented in this article are based on data acquired withthe LOPES 30 and LOPES 30 pol setups. B BB - B
200 m m
13 m
Central Detector Array Cluster Detector Station Electronic Station Muon Tracking Detector Grande Station Radio Antenna (LOPES)
Fig. 3
Map of the LOPES and KASCADE arrays: east-westaligned antennas are marked with upward triangles, north-south aligned antennas with downward triangles (i.e., starsare antenna stations equipped with both polarizations), cir-cles mark the positions of the tripole stations deployed in2009/2010, and dashed triangles mark those antennas dis-mantled in 2006 when deploying north-south aligned anten-nas.
KASCADE-Grande event providing the trigger, i.e, theradio signal measured by LOPES could be compareddirectly to the particle measurements of the same airshower.Due to limitations of analog-to-digital converters(ADCs) available at this time for a reasonable budget, afrequency band of a maximum width of 40 MHz had tobe selected for LOPES. The radio signal is strongest atfrequencies below 100 MHz, because at these frequen-cies the wavelengths exceed the typical thickness of the particle front of air showers (today we know that thesignal-to-noise ratio can be better at higher frequenciesunder some circumstances, and at the Cherenkov anglethe radio emission extents even up to GHz frequenciesas shown by the CROME experiment at the same site[57]; see Appendix H). Taking into account the knowl-edge when LOPES was built, the location of the fre-quency band of LOPES had been chosen to 40 −
80 MHzas a compromise between the Galactic background in-creasing towards lower frequencies and avoiding the FMband.The radio signals received by the LOPES anten-nas were sampled in the second Nyquist domain with anominal depth of 12 bits at a rate of 80 MHz (see Fig. 4).Analog filters in the signal chain strongly suppressedthe frequency range outside of the nominal band of 40 −
80 MHz. This band was further reduced during analysisby digital filters to an effective band of 43 −
74 MHz toavoid systematic uncertainties because of slightly differ-ent cut-off frequencies of the individual filters. As thesampling conditions fulfill the Nyquist theorem, the ra-dio signal between the samples in this band could laterbe retrieved by upsampling.Because the time synchronization of LOPES hadglitches causing occasional offsets up to a few samplesbetween antennas, we applied a dedicated method toimprove the relative timing. First, the carrier signals ofTV transmitters in the measurement band were usedand later a dedicated reference beacon emitting con-tinuous sine waves [45]. This external reference beaconensured that the relative timing between different an-tennas was accurate to about 1 ns, which correspondsto a phase error of less than 30 ◦ at 80 MHz. Togetherwith an accurate measurement of the antenna positionsby differential GPS this enabled the use of LOPES asa digital interferometer.The complete antenna array was calibrated by anexternal reference source several times per year startingin 2005 [43], achieving an absolute accuracy of the mea-sured radio amplitude of about 16 % [44]. Since the di-rectional pattern of the antennas was not measured, thedirectional gain dependence of the antennas was takenfrom simulations which, however, came with some defi-ciencies (cf. section 4). Regarding the phase response of DA frontendPC RAMmodule active antenna (including LNA) dig.data opticaltransmit.
80 MSp/s40−80 MHz RF dig.data PCIbusopticalreceiver Memory Buffer (TIM−Module)
Clock Card vetotime−stamp
Master ClockModule & distributionclock generationsync signaldistribution distributionsync signaldistributionclock
Slave Clock Module sync signal from KASCADE sync signal
RML (Receiver Module LOPES) coax cable
10 x per station
3x 3x
Fig. 4
Data-acquisition system (DAQ) of LOPES organized in three stations of 10 channels, each. The signal of all antennaswas digitized continuously in ring buffers. After receiving an external trigger, the signal of all 30 antennas were read outsimultaneously and stored on one of nine local computers. Then, the data were combined to one event in a central computerand stored on a hard disk and as backup additionally on tape.
Table 1
Properties of the LOPES experiment.Location 49 ◦ ′ N, 8 ◦ ′ EAltitude 110 m above sea levelSize approx. 0 .
04 km Geomagnetic field B = 48 . µ T, θ B = 25 . ◦ Number of antennas up to 30Nominal band 40 −
80 MHzEffective band 43 −
74 MHzTrigger by co-located KASCADE(-Grande) the LOPES signal chain, the largest effect was by thefilters whose phase response was measured in the labo-ratory and was corrected for during analysis. However,we did not need to correct for the gain of the individualcomponents, because LOPES features the end-to-endcalibration of the absolute gain by the external refer-ence source.In summary, the data-acquisition system of LOPESwas fully appropriate and fulfilled its purpose of pro-viding reliable radio measurements of every triggeredKASCADE(-Grande) event. 3.3 Analysis pipelineData analysis was performed by an open-source soft-ware ’CR-Tools’ written in C++. The software as wellas calibration and instrumental data of LOPES weremade publicly accessible in a repository shared withLOFAR [58]. The LOPES software comes with differ-ent applications, e.g, for instrumental tests, calibra-tion measurements, and a standard analysis pipelinefor cosmic-ray air showers used for the results presentedhere. The individual steps of this pipeline are describedin detail in various references [31,59,60].In the first step of the pipeline, the measurementswere corrected for known instrumental properties suchas the phase response of the filters, the simulated di-rectional antenna pattern, and the total absolute gainobtained from end-to-end calibration measurements. Inthe second step of the pipeline, the data quality was en-hanced by upsampling and by digitally removing narrow-band interferences: the frequency spectrum measuredat each antenna was obtained by a fast Fourier trans-form (FFT) of the recorded traces. Narrow-band lines inthe frequency spectrum generally are of anthropogenicorigin. Consequently, they were suppressed. This en-hanced the signal-to-noise ratio and left the broad-band air-shower signal almost unchanged. Three of these sup-pressed lines in the frequency spectrum corresponded tothe sine waves emitted by the dedicated reference bea-con of LOPES [45], whose phasing was used to correctthe relative timing between the individual antennas toan accuracy of about 1 ns.Upsampling was performed by the zero-padding methodin the frequency domain: after a Fast Fourier Trans-form (FFT), zeroes were added to the frequency spec-trum for the frequencies below the nominal band, i.e.,for 0 −
40 MHz, for an upsampling factor of two, andalso at higher frequencies until n ×
40 MHz for an up-sampling factor of n >
2. Several cross-checks, e.g.,with calibration pulses, had shown that high upsam-pling factors enabled a timing precision of better than1 ns although the original samples were 12 . n = 8, and for timing-sensitive analyses at an upsampling factor of at least n = 16.The interferometric method used at LOPES wascross-correlation (CC) beamforming, which was the nextstep in the pipeline: The traces of the individual anten-nas were shifted according to the arrival time of theradio wavefront. This time shift depended on the ar-rival direction of the signal and on the shape of theradio wavefront. For the latter we used an hyperboloidcentered around the shower axis with a variable angle ρ between the shower plane and the asymptotic cone ofthe hyperboloid [48]. After the time shift of the individ-ual traces, the CC beam CC ( t ) was calculated as thesum of all pair-wise cross-correlations of shifted traces(details in Refs. [50,42]): CC ( t ) = sgn( S ( t )) s | S ( t ) | N p with S ( t ) = N X i = j s i ( t ) s j ( t )(1)with N the number of antennas, N p the number of pairs(all combinations of two different antennas), and s ( t )the time-shifted signal in an individual antenna.Because the CC beam features rapid oscillations, itwas smoothed by block averaging over consecutive sam-ples over 37 . n × n ). A Gaussian was fitted to this smoothedCC-beam trace and the height of this Gaussian wasused as measure for the amplitude of the CC beam.This smoothing made the reconstruction more robust,but lowered the amplitude of the CC beam. Therefore, the CC-beam amplitudes depend on the reconstructionprocedure and are difficult to compare to other experi-ments.In an iterative fit procedure we searched for themaximum CC-beam amplitude by varying the cone an-gle ρ of the wavefront and the arrival direction. Tospeed up the reconstruction procedure, we used theKASCADE(-Grande) reconstruction as initial value forthe shower axis and search for the maximum in a rangeof 2 . ◦ around this initial value. This range is morethan five times larger than the direction accuracy ofboth arrays, KASCADE(-Grande) and LOPES, and wechecked that the search range was large enough to avoida bias due to the selection of the initial value. Hence,the maximization procedure yielded a reconstruction ofthe arrival direction as well as of the steepness of theradio wavefront.Using the arrival direction and cone angle found bymaximizing the cross-correlation beam, we also form apower beam: p ( t ) = vuut N N X i s i ( t ) (2)The fraction of the power and the CC-beam, the so-called excess beam, is a measure for the coherence of thesignal [62]. Assuming that the air-shower pulse is mostlycoherent in the individual antennas, incoherent contri-butions by background increase the value of the powerbeam, but not of the CC beam. Thus, the fraction ofthe total power contained in the CC beam is one of thequality criteria applied to the data set (cf. Sec. 3.5).Furthermore, by the time shift of the indiviudaltraces that maximizes the CC beam, we knew the ar-rival time of the signal in each antenna. Thus, we couldsubsequently measure the signal amplitude at each in-dividual antenna even very close to the noise level andwithout the need of applying additional quality cutsat the level of single antennas. Then, these amplitudemeasurements at the individual antennas were used forfurther analyses.The amplitude measurements at the individual an-tennas are given in field strength per effective band- In an earlier version of the LOPES pipeline we used a spher-ical wavefront which corresponds to the approximating of astatic point source. The maximization procedure of the CC-beam was similar, varying the arrival direction and the dis-tance to the assumed point source (= radius of curvature)instead of the arrival direction and the cone angle. Such amethod of searching for the point in the sky maximizing aninterferometric beam was recently re-suggested in [61]. AtLOPES, however, we switched to the hyberbolic wavefrontmodel because it describes the measured and simulated eventsslightly better than a spherical wavefront model and also en-abled a more precise X max reconstruction [48]. width, using an effective bandwidth of LOPES of 31 MHz(this means that values stated here need to be multi-plied by 31 MHz to obtain the field strength in µ V/min the effective band.) With some remaining limitations(see below), these amplitudes are easier to interpretthan the CC beam and were used for the final step ofthe pipeline, which was the reconstruction of the lateraldistribution. Although an exponential lateral distribu-tion function (LDF) features an unphysical singularityat the shower axis, it turns out to provide a sufficientand simple empirical description of the LOPES mea-surements - given the significant uncertainties of typi-cally 4 − ǫ , over dis-tance to the shower axis, d axis : ǫ ( d axis ) = ǫ exp( − η ( d axis −
100 m)) (3)where the amplitude at 100 m axis distance, ǫ , is agood energy estimator, and the slope parameter η issensitive to the longitudinal shower development [51],as was predicted on the basis of simulations [64].The lateral distribution was even better describedby a Gaussian LDF which contains an additional freeparameter. We used the Gaussian LDF for the recon-struction of the energy and the position of the showermaximum [17]. However, for the energy precision, theGaussian LDF provided no significant improvement com-pared to the simpler exponential LDF [31]. We there-fore use the simpler exponential LDF (Eq. 3) for theanalysis presented here.3.4 End-to-end simulationsThe latest feature implemented in the analysis soft-ware is the treatment of air-shower simulations in thesame way as measured data. The radio signal of air-showers was calculated by the CoREAS extension ofthe CORSIKA Monte Carlo code [8]. Afterwards, allknown instrumental effects were applied on simulatedelectric-field vectors at each antenna position, in par-ticular the gain pattern of the antennas, the amplitudeand phase characteristics of the signal chain, and thequantization of the signal implied by the resolution ofthe 12-bit ADC. The simulated signals were stored astraces with the LOPES sampling rate of 80 MHz in thesame data format as real events (see Fig. 5 for a typi-cal example event). Subsequently, the simulations wereanalyzed using the same standard analysis pipeline asfor the measurements.Optionally measured noise was added to the simu-lated events. For this purpose, we used real background measured by the LOPES antennas. Thus, the perfor-mance of the LOPES experiment could be assessed us-ing these end-to-end simulations. In particular the cross-correlation beamforming was studied with the simula-tions, and the measurements of the hard to interpretCC beam were compared quantitatively to the predic-tions of the CoREAS simulations.With the new end-to-end simulations, we were ableto check the effect of a simplification made when com-paring REAS and CoREAS simulations to LOPES mea-surements in earlier publications [38]: when processingthe simulations, we simply filtered the east-west andnorth-south polarization components of the simulatedelectric field to the effective band of LOPES, but ig-nored that LOPES was unable to measure these electricfield components directly. Due to the inverted v-shapeof the LOPES antennas the east-west and north-southaligned antennas are also partially sensitive to verticallypolarized signals. In contrast to other experiments fea-turing two orthogonally aligned antennas at each sta-tion, the three components of the electric field vectorcould not be reconstructed at LOPES. Since at mostantenna positions only one antenna was available, e.g.,east-west aligned, necessarily a simplifying assumptionhad to be made in the reconstruction of the radio signal.Therefore, we used a simplified treatment of the decon-volution of the direction-dependent antenna pattern,which is described in detail in reference [31]. Neverthe-less, with the new end-to-end simulations we treatedsimulations and measurements in the same way andwere able to fully compare them with each other.Furthermore, with the end-to-end simulations wewere able to study the error made by the simplification.Since both, the polarization of the radio signal emittedby an air shower as well as the antenna gain, dependon the arrival direction, the size of the error is stronglyarrival-direction dependent. While for individual eventsthe error can be as large as a factor of 2, on average thereconstructed values of the field strengths are only fewpercent lower than the true values of the simulated airshowers. Figure 6 shows the dependence of this bias onthe azimuth and zenith angle: each point correspondsto the arrival direction of a real air shower measured byLOPES (the distribution is nonuniform because the am-plitude of the radio signal and the detection thresholdof LOPES depended strongly on the arrival directionof the air shower relative to the geomagnetic field). Forthe large majority of events, the error by the simplifi-cation is smaller than 10 % and well within systematicuncertainties quoted in earlier publications.In addition to the bias for the reconstructed fieldstrength in individual antennas, we also studied the av-erage effect of the simplified treatment of the antenna -2.0 -1.9 -1.8 -1.70.00.51.01.52.0 time (µs) s m oo t hed bea m / band w i d t h ( µ V / m / M H z ) -2.0 -1.9 -1.8 -1.7-505 CoREAS Proton Simulation time (µs) f i e l d s t r eng t h / band w i d t h ( µ V / m / M H z ) -2.0 -1.9 -1.8 -1.7-505 LOPES Measurement time (µs) f i e l d s t r eng t h / band w i d t h ( µ V / m / M H z ) -2.0 -1.9 -1.8 -1.70.00.51.01.5 time (µs) s m oo t hed bea m / band w i d t h ( µ V / m / M H z ) cross-correlation (CC) beamGaussian fit to CC beampower beam cross-correlation (CC) beamGaussian fit to CC beampower beamindividual antennasindividual antennasdistance to shower axis d (m)50 100 150 200 250 3001100.1 m a x i m u m a m p li t ude ( µ V / m / M H z ) distance to shower axis d (m)50 100 150 200 250 3001100.1 m a x i m u m a m p li t ude ( µ V / m / M H z ) Result of reconstruction: θ = 45.2 ° φ = 7.2 ° ε = 19.5 ± 2.5 µV/m/MHz η = 11.8 ± 1.0 km -1 ( ) )m 100(exp)( −⋅−= d η d εε Lateral Distribution Function (LDF): Result of reconstruction: θ = 44.3 ° φ = 8.9 ° ε = 16.9 ± 1.9 µV/m/MHz η = 11.5 ± 1.0 km -1 ( ) )m 100(exp)( −⋅−= d η d εε Lateral Distribution Function (LDF):
Fig. 5
Example event measured by LOPES and simulated with CoREAS using the KASCADE-Grande reconstruction asinput: energy E = 3 . · eV, azimuth φ = 8 . ◦ , zenith θ = 44 . ◦ . This event is a best case example with high signal-to-noiseratio. Therefore, the signal is easily visible in all antennas. Left:
LOPES measurement.
Right:
CoREAS end-to-end simulationincluding the detector response.
Top:
Time series of the signal in the individual antennas (after the time shift for the hyperbolicbeamforming in the shower direction).
Middle:
Cross-correlation beam and power beam after block-averaging over 37 . Bottom:
Lateral distribution of the maximum instantaneous amplitude (peak of Hilbert envelope) in each antennaand the fitted LDF (figure from Ref. [34]).0 s i m p , E W / E t r u e , E W E zenith angle θ e l e c t r i c fi e l d realistic simulation seteast-west
0 50 100 150 200 250 300 350 azimuth angle φ (°)
0 50 100 150 200 250 300 350 s i m p , N S / E t r u e , N S E azimuth angle φ (°) zenith angle θ e l e c t r i c fi e l d realistic simulation setnorth-south Fig. 6
Ratio between the true polarization components in individual antennas and the values reconstructed by the standardanalysis pipeline of LOPES for end-to-end CoREAS simulations including all known detector effects for the east-west (EW)and north-south (NS) aligned antennas. While for individual events the deviation can be as large as a factor of 2, in most casesthe reconstructed values are only slightly smaller than the true ones. The average bias is only (4 . ± .
5) % for the east-westcomponent and (7 . ± .
6) % for the north-south component.
Table 2
Average bias due to noise determined by comparing the end-to-end simulations with and without noise for the east-west (EW) and north-south (NS) polarization components, respectively. The stated values were calculated as (1 - withoutnoise / with noise) for values given in % and as (without noise - with noise) for the slope parameter η . For the parameters ofthe lateral distribution, ǫ and η , also the biases due to the simplified reconstruction method of the electric field used byLOPES are stated: (1- true / reconstructed) and (true - reconstructed), respectively. Such a bias cannot be determined forparameters of the cross-correlation beamforming, since it implicitly includes the reconstruction simplifications and, thus, no’true’ values without bias are available from the CoREAS simulations. The ± indicates the standard deviation, which for thebias due to noise can be interpreted as average statistical uncertainty of the corresponding quantity due to noise.bias due to reconstruction bias due to noise net biasCC-beam amplitude EW − (1 . ± .
9) %NS − (3 . ± .
5) %cone angle ρ CC EW +(0 . ± .
0) %NS (0 . ± .
1) %lateral amplitude ǫ EW +(1 . ± .
1) % − (1 . ± .
3) % +(1 . ± .
6) %NS +(6 . ± .
3) % − (1 . ± .
3) % +(3 . ± .
4) %lateral slope η EW − (1 . ± .
64) km − +(1 . ± .
80) km − +(0 . ± .
72) km − NS − (1 . ± .
85) km − +(0 . ± .
70) km − +(0 . ± .
35) km − gain on the reconstructed lateral distribution (see Fig. 7for an example). By comparing the true values of thesimulations with the result of the end-to-end simula-tions with and without noise, we discovered that noiseintroduces an additional bias on the amplitude andslope parameters, ǫ and η , respectively. This biasis on top of a bias due to noise in individual anten-nas, which we had already corrected for in our stan-dard analysis [63]. For the amplitude parameter ǫ ,the size of each effect (noise bias and antenna-gain-simplification bias) is small relative to the dominating16 % scale uncertainty of the amplitude calibration. Forthe slope parameter η , the size of the individual biasesare comparable to the measurement uncertainties, but the biases by noise and by the simplified treatment ofthe antenna gain partly compensate each other. Over-all, the mean net biases are small, but there is a rel-atively large spread, which reflects an event-by-eventsystematic uncertainty (see Table 2). This implies thatthe measurements of individual events have to be in-terpreted with care while average values over dozens tohundreds of events should be affected only marginally.Consequently, LOPES results published prior to thispaper can be considered reliable. f i e l d s t r eng t h ( µ V / m / M H z ) axis distance d (m)
20 40 60 80 100 120 140 160 1800.1110
Fig. 7
Lateral distribution of a typical example event mea-sured by LOPES and simulated with CoREAS. The appli-cation of the detector response (= end-to-end) impacts theCoREAS simulations only marginally. Generally, a differentslope for the simulated and measured lateral distribution isexpected for individual events because the position of theshower maximum is subject to shower-to-shower fluctuation. west-east (m)600 - - - - - - s o u t h - n o r t h ( m ) - - - - - - east-west alignedLOPES antennaGrande stationshower cores of LOPES events Fig. 8
Impact point of the shower axis (core) of the eventspassing the quality cuts described in the text. In addition tothe KASCADE array (Fig. 3) also the detector locations ofthe larger KASCADE-Grande array are shown. & . eV, whichwas significantly lower than the detection threshold ofLOPES around 10 eV. We removed those events fromthe analysis which had a zenith angle larger than 45 ◦ or which had their shower cores outside of the fidu- Table 3
Statistics of LOPES events used in this paper. Thetwo subsets of LOPES events triggered and well reconstructedby KASCADE and KASCADE-Grande, respectively, overlapby a few events which is why the total number of events isless than the sum. For those measured events remaining afterall quality cuts, also the statistics of corresponding showerssimulated by CoREAS are shown that pass all quality cuts forboth cases of a proton and iron nucleus as primary particle.Cumulative Quality Cuts KASCADE Grande Total
E > eV 951 3042 3974signal-to-noise ratio 415 310 715power in CC-beam 345 245 582exclude thunderstorms 339 239 simulated events 302 162 464sim. events with noise 258 122 cial areas of the KASCADE or KASCADE-Grande ar-ray, respectively. After applying these cuts, both arrayswere fully efficient for all types of primary cosmic rayswell below the relevant energy range, and we can safelyassume that all events that had a radio signal pass-ing the LOPES reconstruction were triggered. However,LOPES itself was not fully efficient, i.e., only a fractionof the triggered events passed the LOPES reconstruc-tion (see Table 3 and Fig. 9) . Corresponding to the twoparticle-detector arrays providing the trigger, there aretwo data sets of LOPES events, KASCADE and Grandeevents, which have only little overlap (Fig. 8). Depend-ing on the analysis, we either use both data sets com-bined, or only the KASCADE data set because thoseevents have their core contained inside of the LOPESantenna array which allows for a higher quality of theevent reconstruction.For the present analysis we used data recorded bythe east-west aligned v-shape dipole antennas from De-cember 2005 to October 2009, because starting Decem-ber 2005 LOPES featured an absolute amplitude cali-bration [43]. During this time almost 4000 well-reconstructedKASCADE and KASCADE-Grande events with an en-ergy of at least 10 eV triggered LOPES and werepropagated through the LOPES analysis pipeline. Tothose events which passed the analysis pipeline with-out error, which implies, e.g., that the reconstructionof the arrival direction converged, we applied furtherquality cuts: – The signal-to-noise ratio of the CC-beam must begreater than 14 · p N ant /
30, with N ant the numberof antennas contributing to the measurement of theevent. Because the biases related to the partial efficiency of LOPESare difficult to estimate, we refrain from determining the ab-solute flux, energy spectrum, or mass composition.2 lg (energy / eV) f r a c t i on nu m be r o f e v en t s triggered by KASCADE detected by LOPES Fig. 9
Top: Number of events triggered by the KASCADEarray with a reconstructed energy above 10 eV (no eventhad an energy above 10 eV); and the number of events inthe subset passing all LOPES quality cuts. Bottom: Fractionof the two event numbers which is a measure for the efficiencyof LOPES. – The CC beam must contain at least 80 % of thetotal power, which excluded events contaminated bybackground. – To reject thunderstorm events, events with an at-mospheric electric field of at least 3 kV/m were ex-cluded. This cut was applied to events recorded af-ter the installation of a local electric field mill on 24August 2006.After the quality cuts, 570 measured LOPES eventsremain in the analysis.Using the KASCADE dataset, we were able to es-timate the efficiency because the shower cores of theseevents were contained or very close to the LOPES an-tenna array (Fig. 9). For energies above 2 · eV, morethan half of the LOPES events passed all of the qualitycuts mentioned above. For most of the Grande events,the shower cores were too distant from the LOPES ar-ray for a detectable radio signal. More detailed discus-sions on the dependencies of the amplitude of the radiosignal, e.g,. on the energy, the geomagnetic angle, andthe distance to the shower axis can be found in manyof the references cited in the introduction.We also produced a library of CoREAS simulationsusing the energy, arrival direction, and shower core re-constructed by KASCADE(-Grande) as input. Using ’KASCADE(-Grande)’ refers to both, the KASCADE andthe KASCADE-Grande data sets, at the same time. CORSIKA 7.3 with the hadronic interaction model QGSJetII.03, two simulations were created per LOPES event,one with a proton and one with an iron nucleus as pri-mary particle. Because different LOPES analyses useddifferent selection criteria, versions of the analysis pipeline,and subsequent quality cuts, the exact data sets variedslightly over time and LOPES publication, and someshowers were not included in the simulation library.Still, there is significant overlap between all selections,and for about 90 % of the measured events used herethere are corresponding CoREAS simulations. Each sim-ulation was processed twice through the standard anal-ysis pipeline, once the pure simulated radio traces andonce the simulated radio traces after adding randomlyselected noise samples measured by LOPES.After the analysis pipeline, the simulated events weresubject to the same quality cuts as the measured events.Since many of the measured events are close to thedetection threshold, only a part of the correspondingsimulated showers passed the quality cuts (the vice-versa situation does not happen because those showersmissing the cuts for the measurements, were simply notsimulated). In case of pure simulations without addingnoise, 464 events passed all quality cuts for both, pro-ton and iron, as primary particle (after removing 3 sim-ulated events for which the fit of the lateral distributionfailed). In case of the simulations with measured noiseadded, 380 events passed all quality cuts for both, pro-ton and iron, as primary particle. These common eventswith both measured and simulated results available arethe data set used for the results shown here.The LOPES events were made available to the pub-lic in the
KASCADE Cosmic Ray Data Center (KCDC) [65] in November 2019 as part of the ’Oceanus’ release. .In addition to the reconstructed parameters of theseLOPES events (up to 20 parameters per event and 4parameters per antenna in an event), also the corre-sponding KASCADE-Grande data can be downloadedfrom KCDC as detailed in the user manual available onthe KCDC website. The LOPES data can be found assubset of the KASCADE data in the KCDC data shop: https://kcdc.ikp.kit.edu/ Using the end-to-end simulations, we first checked forthe consistency of measurements and simulations. Gen-erally, the CoREAS simulations describe the measured Due to different versions of the KASCADE reconstructionsoftware ’KRETA’, the values available in KCDC may differslightly from the ones used in the analysis presented in thispaper.3 events well. Therefore, in a second step we used the sim-ulations to study several features of our analysis proce-dure, in particular the relation between the amplitudeat a specific lateral distance and the CC-beam ampli-tude. Finally, we provide an update on earlier resultsregarding the direction and energy accuracy of LOPESand the sensitivity to the shower maximum.4.1 Consistency of Measurements and end-to-endSimulationsDo CoREAS simulations agree with the measurements?In earlier publications, we had compared the amplitudepredicted by CoREAS with the amplitudes measuredby LOPES, but were not able to assess the systematicuncertainties due to the simplified treatment of the an-tenna gain described above. With the new end-to-endprocessing of the simulations, we solved this problemand could compare simulations and measurements in an“apples-to-apples” way. The remaining significant un-certainties are the scale uncertainty of the amplitudecalibration of 16 % and the 20 % uncertainty on theenergy reconstructed by KASCADE-Grande that wasused as input for the simulations.We confirmed that CoREAS describes the absoluteamplitude well, both for the CC-beam amplitude andfor the amplitude ǫ at 100 m obtained from the LDFfit. Determining the offset between simulations and dataas a factor k of a line fitted to the event-by-event cor-relation (Fig. 10) and as the mean of a histogram ofthe deviations (Fig. 11) yielded consistent results. Alsothe offsets between simulations and measurements forthe CC-beam amplitude and for the amplitude ǫ at100 m axis distance are consistent within statistical un-certainties. The difference of about 11 % to 12 % be-tween proton and iron showers can be explained by thedifferent fraction of the energy in the electromagneticcomponent emitting the radio signal. In all cases, themean offset between LOPES and CoREAS is lower thanthe calibration scale uncertainty.Hence, except for a few outliers, the CoREAS sim-ulations are generally consistent with the LOPES mea-surements. These outliers were observed in earlier anal-yses, too [38]. For all outliers, the measured amplitudeis significantly higher than the simulated one (in thevice-versa situation, an event was likely not detectedat all). Such upward fluctuation of the measured am-plitude could be caused, e.g., by undetected thunder-storms (however, only one of the outliers is an eventdetected before the thunderstorm monitoring was in-stalled), man-made radio noise overlapping with theair-shower signal, or systematic issues in the instrumentresponse or reconstruction procedure. A closer investigation of the comparison of the CoREASsimulations and the measurements revealed that thereis a trend in the ratio of measured versus simulated am-plitudes with zenith angle (Fig. 12). This trend mightbe due to deficits in the simulated antenna patternused for the interpretation of the measurements (reg-ular calibration measurements were only done for thezenith, and cannot be repeated for other directions sinceLOPES is dismantled). This unknown reliability of theantenna pattern is a major systematic uncertainty forthe interpretation of amplitudes of individual events,but only a smaller uncertainty for average values of thefull data set which has its mean at < cos θ > = 0 . < cos θ KASCADE > = 0 .
86 and < cos θ Grande > =0 . η of the LDF and the cone angle ρ , i.e, the an-gle between the shower plane and the asymptotic coneof the hyperbolic wavefront determined by maximiz-ing the CC-beam amplitude, the measured distribu-tions are slightly wider than the simulated ones. Sucha wider distribution is expected if there are additionalmeasurement uncertainties not considered in the end-to-end simulations. Indeed, there are such uncertainties:the weather-dependent uncertainty on the antenna gainincreases the uncertainty on the lateral slope; and occa-sional glitches and jitters in the time synchronization,though corrected mostly by the beacon, increase theuncertainty on the wavefront reconstruction. Thus, aslightly wider distribution of the measured parametersthan in the end-to-end simulations was expected, anddoes not mean that CoREAS would not describe thedistributions correctly.Regarding the mean values of the distribution, thereis a small inconsistency, which may reflect unknown sys-tematic uncertainties. The measured distributions of η and ρ are each individually compatible with CoREAS.However, given that both distributions originate fromthe same measured events, there is an interesting diver- V/m/MHz)µ(
LOPES CC V / m / M H z ) µ ( s i m p CC kproton = 1.095 ± 0.005 V/m/MHz)(µ
LOPES CC V / m / M H z )( µ s i m F e CC kiron = 0.972 ± 0.005 Fig. 10
Event-by-event comparison of the cross-correlation-beam amplitude of the LOPES measurements and the end-to-endCoREAS proton and iron simulations (including noise; for east-west antennas). The k values are the offsets of the fitted dashedlines to the one-to-one correlation (solid lines), which is in both cases smaller than the calibration scale uncertainty of 16 %.The outliers are mostly the same events as in Fig. 12. nu m be r o f e v en t s (%) LOPES )/CC sim -CC
LOPES (CC
CC-beam deviation:
IronMean 2.6 ± 1.5 %Std.dev. 25.0 ± 1.3 %ProtonMean -8.4 ± 1.7 %Std.dev. 23.1 ± 1.3 %end-to-end simulations with noise nu m be r o f e v en t s (%) ) / LOPES - CoREAS (LOPES IronMean 3.9 ± 1.6 %Std.dev. 25.5 ± 1.3 %ProtonMean -7.7 ± 1.6 %Std.dev. 27.8 ± 1.3 %end-to-end simulations with noise
Fig. 11
Comparison of LOPES measurements and end-to-end simulations including noise for the cross-correlation amplitude(i.e., the histograms to Fig. 10) and the amplitude ǫ at 100 m distance from the shower axis as determined by a fit of thelateral distribution (for east-west antennas). The stated values are from a Gaussian fitted to the histograms. gence: For the slope parameter η , the measured distri-bution is close to the proton distribution. For the coneangle ρ , the measured distribution is closer to the irondistribution. This discrepancy was reported earlier byus [34]. In order to make a conclusion whether there wasan unknown systematic effect at LOPES, or whetherthis discrepancy originates from the simulations, fur-ther investigation will be necessary at more accurateinterferometric antenna arrays, such as LOFAR [13] orthe SKA [66]. 4.2 Relation of the Cross-Correlation Beam and theLateral DistributionThe end-to-end simulations finally enabled us to bet-ter study the interpretation of the CC-beam ampli-tude. With the first LOPES data we had already shownthat the CC-beam amplitude was approximately lin-early correlated with the energy of the primary particleafter correction for the geomagnetic angle α , i.e., the an-gle between the Earth’s magnetic field and the showeraxis [6]. While the absolute amplitude ǫ measured inindividual antennas is easy to understand, the absolute ) q cos( L O PES d i v i ded b y C o R EAS a m p li t ude ) q cos( L O PES d i v i ded b y C o R EAS a m p li t ude Fig. 12
Ratio of the measured amplitude ǫ at 100 m axis distance and the simulated amplitude of the CoREAS end-to-endsimulations including noise for 380 events passing all quality cuts (left). In the profile (right) 11 outliers with ratios larger than2.5 are excluded (see text for discussion). Deficiencies of the antenna model cannot be excluded and might be the reason forthe trend in the ratio versus zenith angle. slope parameter h of lateral distribution ( km -1 )
10- 5- 0 10 15 20
CoREAS p
CoREAS Fe
MeanStd. dev. 5.33.8MeanStd. dev. 3.63.1
LOPES
MeanStd. dev. 5.64.15 nu m be r o f e v en t s cone angle of hyperbolic cross-correlation beam r CC (°) nu m be r o f e v en t s CoREAS p
CoREAS Fe
MeanStd. dev. 1.260.29MeanStd. dev. 1.150.26
LOPES
MeanStd. dev. 1.200.330 0.5 1.0 1.5 2.52.0 hyperbolic wavefront and asymptotic cone r plane perpendicular to shower axiscone angle Fig. 13
Comparison of LOPES measurements and the end-to-end CoREAS simulations for KASCADE(-Grande) events: theslope of the lateral distribution η , and the cone angle of the wavefront ρ CC determined by cross-correlation beamforming. amplitude of the CC-beam lacked interpretation and itwas not clear how the CC-beam amplitude related tothe amplitudes in individual antennas.We now investigated this by comparing the ampli-tude ǫ determined by the LDF with the CC-beamamplitude (Fig. 14).We find a linear correlation which has a mean ratioof < ǫ /CC > = 1 . ± .
22 for the LOPES mea-surements, 1 . ± .
19 for the proton simulations, and1 . ± .
14 for the iron simulations. The stated ratiosare the mean and standard deviations of a Gaussian fit-ted to the ratio of ǫ and the (normalized) CC-beamamplitude. The outliers are mainly the more distantevents, with a core in the Grande array, which show asignificantly lower CC-beam amplitude. Since the CCbeam represents a non-trivial way of averaging over theindividual antenna signals, this was expected due tothe steeply falling lateral distribution of the radio sig- nal. While the CC beam itself does not contain anycorrection for the lateral distribution and is expectedto depend on the mean distance of the antennas fromthe shower axis, ǫ should be independent of the dis-tance by construction. The fact that the outliers areconsistent in the measurements and end-to-end simula-tions, indicates that they are not an artifact, but havea physical explanation in the lateral distribution of theradio signal.One would expect that a normalization of the CC-beam amplitude by the average exponential falloff ofthe radio amplitude with axis distance would fix theissue. Therefore we multiplied all CC-beam amplitudesby exp( d mean /
180 m), where 180 m corresponds to theaverage lateral slope parameter η = 5 . − measuredwith the LDF. This normalization improves the corre-lation and changes the average ratio to 1 . ± .
11 forthe LOPES measurements, 1 . ± .
19 for the proton simulations, and 1 . ± .
11 for the iron simulations.However, for some distant events this correction was in-sufficient which is visible by the few remaining outliersin the middle plot of Fig. 14). Multiplying the CC-beamamplitude instead by the square of this normalizationfactor, exp( d mean /
180 m) , yielded a linear correlationbetween the CC-beam amplitude and ǫ with a ratioof 1 . ± .
16 for the LOPES measurements, 1 . ± . . ± .
14 for the ironsimulations. Note that there is no reason to expect a ra-tio of 1; since the amplitude ǫ d depends on the referencedistance d to the shower axis, choosing a different refer-ence distance will automatically lead to a different valuefor the ratio. Nonetheless, the measurement of this ratiois useful, e.g., for comparing earlier publications usingeither the CC-beam or the lateral distribution. Regard-ing the relative standard deviation, there is no majordifference between both normalizations, but there is re-garding the outliers which are Grande events at largerdistances. Although the squared normalization is dif-ficult to explain from simple principles, we point outthat we observe the improvement regarding the outliersby this normalization consistently in the measurementsand simulations. This means that albeit empirical, thechoice of the normalization is not arbitrary. It is likelyrelated to the complex interplay of the physics of theradio emission and the detector response, since both areincluded in the end-to-end simulations. The consistenteffects of these normalizations in the measurements andsimulations also show that the CC-beam amplitude canbe well studied on an absolute level using the end-to-end simulations.4.3 Reconstruction of Shower ParametersAt LOPES we used the cross-correlation beam as wellas the pulse time and amplitude in individual anten-nas to reconstruct the most important shower param-eters, which are the arrival direction, the energy, andthe depth of the shower maximum ( X max ). Apart fromthe improved calibration [44], the reconstruction proce-dure used for the final results presented here had notchanged significantly compared to earlier publications.However, for the CC beam the reconstruction proce-dure evolved over time, since we meanwhile used themore accurate hyperbolic wavefront for the beamform-ing instead of the spherical wavefront used in the earlyyears of LOPES [48]. Moreover, due to the end-to-endsimulations, we were able to update the formula forthe reconstruction of the primary energy using the CC-beam amplitude.The arrival direction was reconstructed by maximiz-ing the CC-beam amplitude (cf. Sec. 3.3). With the end- to-end simulations, we checked the intrinsic accuracyby comparing the true and reconstructed directions foreach event. In simulations without noise, the accuracyis 0 . ◦ and in simulations with noise the accuracy is0 . ◦ (Fig. 15). In contrast to particle detectors, Poissonstatistics do not limit the accuracy of arrival time mea-surements of a radio array, which explains why radio de-tection can easily provide for a high angular resolution.This high accuracy also shows the importance of anadequate wavefront model, since the deviation betweenthe plane wavefront and the used hyperbolic wavefrontis already an order of magnitude larger (the averagecone angle measured by LOPES is 1 . ◦ ; see Fig. 13).Thus, the use of an inadequate wavefront could other-wise dominate the uncertainty of the arrival direction.For the LOPES measurements, we can only givean upper limit for the achieved direction accuracy bycomparing the directions reconstructed with LOPESand with KASCADE-(Grande). Doing so, the averageaccuracy of LOPES was estimated to be better than0 . ◦ . This value includes the uncertainty of KASCADE-(Grande), which is not known accurately enough tomake a reliable estimation of the stand-alone accuracyof LOPES. It is plausible that the direction accuracy ofLOPES was worse than in the simulations because thesimulations did not include uncertainties in the relativetiming between the antennas and in the core positiontaken from the KASCADE(-Grande) reconstruction. Inany case, the resulting upper limit for the accuracyof 0 . ◦ is better than needed for most applications incosmic-ray physics. This demonstrates that even with alimited size and number of detectors, a radio array canprovide for an excellent angular resolution.For the reconstruction of the energy of the primaryparticle, we had already shown that in addition to theamplitude of the lateral distribution at a specific dis-tance [17] also the CC-beam amplitude provides an en-ergy estimator [6]. Our new results confirm that the CC-beam method features a measurement accuracy approx-imately equal to the lateral-distribution method. Withthe end-to-end simulations, we determined an indepen-dent absolute calibration for the energy reconstructedusing the CC beam. Furthermore, we updated the wayhow we normalize to the angle between the geomagneticfield and the shower axis and to the mean axis distanceof the antennas contributing to the CC-beam - result-ing in the following formula for the reconstruction ofthe energy E of the primary particle: E = κ · CC · exp ( d mean /
180 m) | ~v × ~B | EW (4) a m p li t ude a t m e ( µ V / m / M H z ) CC beam amplitude (µV/m/MHz) no normalization with axis distance CoREAS p CoREAS Fe LOPES KASCADE / events/// a m p li t ude a t m e ( µ V / m / M H z ) normalized CC beam amplitude (µV/m/MHz) normalization with mean axis distance CoREAS p CoREAS Fe LOPES KASCADE / events/// a m p li t ude a t m e ( µ V / m / M H z ) normalized CC beam amplitude (µV/m/MHz) normalization with mean axis distance squared CoREAS p CoREAS Fe LOPES KASCADE / events///
Fig. 14
Event-by-event comparison of the amplitude at 100 m axis distance and the amplitude of the cross-correlation beam.While for KASCADE events there always is a good correlation, this is not the case for several Grande events (outliers in leftand middle plots are Grande events), which have a larger axis distance to the LOPES antennas. Normalizing the CC-beamamplitude by the mean lateral distance improves the correlation significantly.
CoREAS p CoREAS FeMean 0.1 °Mean 0.1 ° LOPES Mean 0.5 ° nu m be r o f e v en t s angular deviation to KASCADE(-Grande) direction (°) Fig. 15
Angular deviation between the arrival direction re-constructed by KASCADE or KASCADE-Grande, respec-tively, for the LOPES measurements and the CoREAS end-to-end simulations including noise. Simulations without noise(not shown, see Ref. [31]) have a mean deviation of 0 . ◦ . Thevariable bin size accounts for a constant solid angle coveredby each bin. with CC the amplitude of the cross-correlation beam, d mean the mean axis distance of the antennas contribut-ing to the measurement of the event, and ~v × ~B theunit vector of the geomagnetic Lorentz force, i.e., wenormalized the CC-beam amplitude by the size of itseast-west component, and κ a proportionality factor de-termined by the average of the proton and iron simula-tions [31]: for the 258 KASCADE events the used pro-portionality factor is κ = 41 . µ V/m/MHz) andfor the 122 Grande events κ = 36 . µ V/m/MHz).In both cases the values were determined as mean of theproton and iron simulations because showers initiatedby heavy primaries have a slightly lower radio ampli- tude on ground than those initiated by light particles(cf. Fig. 11). By this choice of the mean value, the maxi-mum energy bias for an individual event is ± d mean /
180 m) instead of exp( d mean /
180 m)deteriorated the correlation of the CC-beam amplitudewith the energy instead of improving it (this again is anempirical observation which is consistent in the LOPESmeasurements and the CoREAS end-to-end simulations).We have investigated possible reasons for the need oftwo different proportionality factors κ for the KASCADEand Grande events: A possible explanation is that KASCADEevents are mostly contained in the array, while the coreof Grande events generally is outside the LOPES ar-ray. Moreover, there might be a selection bias, sinceonly a small fraction of the triggered Grande eventsis detected by LOPES. However, neither simple up-ward fluctuations nor systematic measurement uncer-tainties are possible causes of the effect because thefactors κ have been derived from the end-to-end simu-lations. Nonetheless, also the LOPES measurement ofthe energy is systematically higher for Grande eventsthan for KASCADE events when using an equal pro-portionality factor as a cross-check. The effect seems tobe even stronger in the measurements, probably due tosystematic uncertainties or selection biases not presentin the simulations, such as upward fluctuations of theCC beam increasing the detection probability. However,a solid quantitative investigation is not possible becausemost LOPES events do not fulfill the minimum qualitycriteria for the KASCADE and Grande energy mea-surements simultaneously. Consequently, while a firmconclusion is difficult due to the limitations of the ex-perimental setup, it appears that simulations and mea- energy reconstructed by CC-beam (eV) KAS C A D E (- G r ande ) ene r g y ( e V ) CoREAS p CoREAS Fe LOPES nu m be r o f e v en t s CoREAS p
CoREAS Fe
MeanStd. dev. - 4.813.9MeanStd. dev. 6.813.0
LOPES
MeanStd. dev. 3.623.0 (Energy
KASCADE(-Grande) - Energy reconstructed, CC-beam )Energy
KASCADE(-Grande) (%)
Fig. 16
Comparison of the energy reconstructed by the amplitude of the cross-correlation beam to the KASCADE(-Grande)energy for LOPES measurements and CoREAS simulations including noise. Left: Per-event comparison. The outliers in theupper-right corner visible also in the simulations have a small east-west component of the geomagnetic Lorentz vector of p EW ≤ .
1; for two of them the corresponding LOPES points are at energies about three times higher than the plotted range;for the other outliers see the discussion related to Figs. 10 and 12. Right: Histogram of the relative deviation, where thestandard deviation provides a measure of the energy precision. surements are at least qualitatively consistent regardingthe need of different proportionality factors.We checked the accuracy of the energy reconstruc-tion by Eq. 4 by comparing the true and reconstructedvalues for the end-to-end simulations with noise, andby comparing the LOPES and KASCADE-Grande re-construction for the measured events (Fig. 16). Accord-ing to the simulations, the energy precision could be asgood as 13 % to 14 %, with an additional bias of theorder of ± showermaximum . The two methods used by LOPES are basedon the slope of the lateral distribution [17] and on theopening angle of the asymptotic cone of the hyperbolicwavefront [48]. The more distant the shower maximumfrom the array, the flatter is the lateral distributionand the flatter is the wavefront. With the end-to-endsimulations we confirm our earlier results that both pa-rameters are statistically correlated with the distanceto the shower maximum (Fig. 17). In earlier publica- slope parameter h of lateral distribution ( km -1 )
5- 0 10 15 205 geo m e t r i c a l d i s t an c e t o X ( k m ) m a x CoREAS-p CoREAS-Fe CoREAS-p CoREAS-Fe cone angle of hyperbolic cross-correlation beam r CC (°) geo m e t r i c a l d i s t an c e t o X ( k m ) m a x Fig. 17
Correlation of the lateral slope parameter η (left) and of the wavefront cone angle ρ (right) of the CoREAS end-to-endsimulations (with noise) with the geometrical distance to the shower maximum for the contained KASCADE events. Theprofile in black denotes the mean and standard deviation in each bin. tions [34], we had used these dependencies to determinethe mean atmospheric depth of the shower maximum, X max , though with limited precision. As at the time ofthe original publications, we are unable to quantify theadditional systematic uncertainties, e.g., the wavefrontreconstruction seems to be sensitive to the uncertaintyof the core position. The wavefront method might there-fore be useful primarily for dense arrays with a goodresolution of the shower core, such as LOFAR or theSKA.As noted earlier [48,34], there is a difference in theabsolute scale of X max resulting from the wavefront andthe lateral slope methods. While both methods show asensitivity to X max , i.e,. are suitable to measure X max ofan individual event with a certain precision, there seemsto be an additional uncertainty on the absolute scaledepending on the method. Understanding and quan-tifying these scale uncertainties will be crucial for anaccurate interpretation of X max in terms of mass com-position. For this purpose, we suggest that also otherexperiments could compare their X max reconstructionsof an amplitude-based (e.g., lateral slope) and a timing-based (e.g., wavefront) method. This will be most im-portant for those experiments using radio as only tech-nique for X max , but will only be a minor issue for hy-brid arrays also featuring optical detectors available forcross-calibration of the scale [15,19]. Moreover, bettermethods for the estimation of the efficiency and aper-ture are needed to avoid a bias caused by the partialefficiency of a radio array close to its threshold [67]. LOPES was a successful pathfinder for the radio detec-tion of air showers in the digital era. It was a driver and initiator of the meanwhile matured detection tech-nique for ultra-high-energy cosmic rays, and providedessential contributions to the understanding of the radioemission and the potential of the detection technique.While today there is a general agreement in the commu-nity on the principles of the radio emission, this was notthe case when LOPES started, and its measurementshelped to understand deficits in earlier models and sim-ulation codes. Now CoREAS simulations and LOPESmeasurements are compatible within uncertainties forall tested parameters, which shows that the physicalprocesses of the radio emission are well understood.Even so, the question remains why the wavefront andlateral slope methods result in a slightly different X max scale although both methods were calibrated using thesame CoREAS simulations. Further investigations atother experiments will help to investigate whether thisis due limitations of our understanding of the LOPESdetector or due to the simulations.Independent of the simulations, the comparison ofthe LOPES and KASCADE-(Grande) measurementsprovided the proof-of-principle that the radio techniquecan be used for accurate measurements of the arrival di-rection and energy of cosmic rays – even in a noisy envi-ronment. Using the full potential of the radio technique,including an accurate reconstruction of X max , however,requires a location more radio-quiet than the LOPESsite. This has meanwhile been demonstrated by sev-eral second-generation experiments following LOPES[68,20,19].LOPES also pioneered many methods regarding theradio technique which have been used by other experi-ments, such as LOFAR, AERA, and Tunka-Rex. Exam-ples are the continuous monitoring of the atmosphericelectric field and the calibration methods used by LOPES,in particular the monitoring of the relative timing with a beacon [69,70] and the end-to-end amplitude calibra-tion using an absolutely calibrated external referencesource [71,72,73]. The latter also enabled the compari-son of the absolute energy scales of different air-showerarrays using radio measurements [74]. Finally, the pub-lic availability of the data on the KCDC platform sus-tains the LOPES measurements for future analyses.So what questions remain? The most important oneis about the relevance of the technique for the progressof the general field. Can the radio technique alone or incombination with particle-detector arrays provide newknowledge on cosmic-ray physics or the particle physicsof air-showers?As stand-alone technique, radio antennas can beused to instrument huge areas for a reasonable price,as planned for the GRAND array aiming at ultra-high-energy cosmic rays and neutrinos [75]. For the solutionof many of the open questions in high-energy astropar-ticle physics, a major increase in measurement accuracyfor the properties of the primary particle is required, inparticular for its mass [76,77]. The radio technique nowseems to deliver a measurement accuracy mostly equalto the established techniques, but can it also enhancethe total accuracy over the state-of-the-art?The results of LOPES and other experiments al-ready provided hints that antenna arrays can improvethe energy and direction accuracy, and possibly alsothe accuracy of X max providing access to the elemen-tal composition of cosmic rays. These gradual improve-ments of the state-of-the-art are important. Yet, thereare two ideas under investigation that go beyond andmay provide for major breakthroughs with the nextgeneration of antenna arrays: – Can a significant increase in antenna density in-crease the overall accuracy for air showers and possi-bly reveal substructures in the shower development?This remains to be shown by LOFAR or the SKA[66]. – An alternative idea is to combine radio and muondetectors in hybrid arrays because the radio andmuon signals contain complementary informationon the shower development [6]. As supported by arecent simulation study [78], the combination of ra-dio and muon detectors can indeed provide for anincrease of the accuracy for the mass compositionof cosmic rays. This idea still needs deeper inves-tigation and experimental demonstration at appro-priate air-showers arrays, such as the planned en-hancement of IceTop [79,80] and the AugerPrimeupgrade of the Pierre Auger Observatory [81,82].In summary, the LOPES results, experiences, andlessons learned remain a valuable resource for the cur-rent and next generation of digital antenna arrays for air-shower detection. These are now dedicated to allkinds of cosmic messengers – high-energy cosmic rays,photons, neutrinos – and it becomes likely that radioarrays will play a major role in high-energy astroparti-cle physics during the coming decades.
Acknowledgements
We thank the reviewers for carefullychecking the manuscript. Their suggestions helped to improvethe paper. LOPES and KASCADE-Grande were supportedby the German Federal Ministry of Education and Research.KASCADE-Grande was partly supported by the MIUR andINAF of Italy, the Polish Ministry of Science and Higher Ed-ucation and by the Romanian Authority for Scientific Re-search UEFISCDI (PN19060102 and PN19150201/16N/2019grants). The present study was also supported by grant VH-NG-413 of the Helmholtz association and by the ’HelmholtzAlliance for Astroparticle Physics - HAP’ funded by the Ini-tiative and Networking Fund of the Helmholtz Association,Germany.
Appendix - Lessons Learned
LOPES being among the first digital radio arrays forair showers, we also used it as a test facility for variousnew technologies and ideas related to radio detection ofcosmic rays. Not all of them were published in refereedjournals and not all of them were successful. Nonethe-less, there are lessons learned form these approachesand the design and data analysis of future experimentsmay profit from the experience made. For these rea-sons, we give a summary of these approaches and theirresults and other lessons learned.
Appendix A: Self-trigger
LOPES was successful due to its external trigger byKASCADE(-Grande). While a self-trigger might be ben-eficial for some science cases, it is not critical when radiois added as additional technique to a hybrid array fea-turing particle detectors for the purpose of increasingthe overall measurement accuracy for cosmic rays. How-ever, for very inclined showers in addition to the radiosignal only muons arrive at ground, and the low parti-cle density provides a challenge for particle detectors.Thus, there are other experimental approaches such asANITA [39] and GRAND [75] which require stand-aloneradio detection with a self-trigger.At LOPES we developed hardware and algorithmsfor self-triggering at the LOPES
STAR setup [83], whichconsisted of 10 additional logarithmic periodic dipoleantennas in the KASCADE-Grande array. These effortsled to effective techniques for filtering RFI and reject-ing background pulses. Although the algorithms weresuccessful to identify air-shower pulses in previously recorded test samples, we were not successful in self-triggering events with the deployed hardware. One ofthe problems was that also anthropogenic backgroundpulses often led to coincident signals in several anten-nas. Nonetheless, several experiments have meanwhilesuccessfully demonstrated self-triggering at more radioquiet sites [39,84,85,86,87,14]. Appendix B: Measurements at 50 −
500 kHz
Motivated by historic measurements, we also tried todetect air showers at much lower frequencies in theband of 50 −
500 kHz. Using the standard KASCADEtrigger provided for LOPES, we did not detect any airshower in this band in 13 days of measurements al-though more than 70 of the triggering showers had en-ergies above 10 eV. The sensitivity was likely limitedby the radio-loud environment of LOPES. Hence, wederived an upper limit of 136 +48 − mV m − MHz − forthe field strength of the vertical component of the ra-dio signal emitted by the air showers in this frequencyband [88]. Appendix C: Tripole Antennas
In the last stage of LOPES, called LOPES-3D, ten’tripole’ antennas were deployed, each consisting of threeorthogonally aligned dipoles in east-west, north-south,and vertical direction [55]. Due to the very high back-ground level for the vertical polarization, only few eventswith signal in all three polarization channels were de-tected [36]. The measured polarization of these eventsconfirmed the prediction for geomagnetic emission.One of the motivations of deploying a third po-larization channel was that the signal would be over-determined if the arrival direction was known. Thismeans that in theory the arrival direction of the radiosignal could be reconstructed from the measurement ofa single tripole antenna. Due to the specific polariza-tion pattern of the radio emission on ground caused bythe interplay of the Askaryan and geomagnetic emissionmechanisms, a sufficiently accurate measurement of theelectric field vector at each antenna position can also beutilized for many other purposes, such as refining theposition of the shower core or rejecting RFI [89]. An-other motivation was to test whether the threshold forvery inclined events could be lowered by the verticalchannel, since by simple geometry considerations theradio emission of inclined air showers features a signif-icant vertical polarization component. At LOPES-3Dwe were not able to demonstrate either of this, and it is not clear whether the level of vertically polarized back-ground would be low enough at other locations to suc-cessfully apply one or both ideas. If measurements withthree polarization were repeated elsewhere, we suggestconsidering to rotate the whole tripole setup by 45 ◦ to-wards the horizontal plane as already done by others[90,91]. This would avoid one explicit vertical polar-ization channel, and make the antenna setup easier tounderstand due to the rotational symmetry around thepole where the antenna is mounted. Appendix D: Interferometry of Air Showers
At LOPES we successfully applied cross-correlation beam-forming as an interferometric method to lower the de-tection threshold in a radio-loud environment. The rea-soning behind CC beamforming is that the signal hasthe same time structure in all antennas, while any back-ground or noise have not. Hence, CC beamforming en-hances the signal-to-noise ratio with increasing numberof antennas. This technique is widely used in radio as-tronomy: a signal arriving as plane wave from distantsources can be assumed to be the same in all antennas.For air showers the radio signal changes significantlyfrom antenna to antenna, and it is a priori not clear thatcross-correlation beamforming is useful. Nevertheless,cross-correlation beamforming turned out to be a keyasset of LOPES for identifying air-shower pulses againstthe background. Probably because the measured pulseshape was primarily determined by the filter responseand not by the original pulse shape emitted by the airshowers, the signal structure was similar enough in theindividual antennas, and the signal-to-noise ratio wasenhanced even though the signal was not equal in allantennas.Nonetheless, these complications make the absolutevalue of the CC amplitude difficult to interpret and tocompare between experiments. For the same radio foot-print at ground, a different antenna array might mea-sure different CC-beam amplitudes. Consequently, theapplication of CC beamforming or other interferomet-ric methods needs to be re-investigated before applyingit to a different array configuration such as a differentantenna spacing or frequency band. For the comparisonof experiments, more universal quantities, such as theelectric field strength or the total radiation energy in agiven frequency band [92] should be used.
Appendix E: Imaging of Air Showers
LOPES provided the first successful radio images of airshowers (Fig.18, [6]). For a few 10 ns, the air shower is Fig. 18
Image of the radio emission of an air-shower detectedby LOPES (as originally published in [6]). The bright spot inthe center indicates the arrival direction of the air shower. the brightest source in the sky. The image clearly marksthe arrival direction of the air showers. The brightnessis correlated to the size of the electromagnetic showercomponent and, thus, to the energy of the primary par-ticle. Moreover, the wavefront shape used to producethe image via beamforming contains information on thedistance of the emission. However, the radio images ofshowers were insufficient to reveal any of the substruc-ture of the detected air showers.Unlike images of extended sources in astronomy andunlike the air-shower images produced by the incoher-ent air-fluorescence technique, the radio images of theair showers observed by LOPES were just bright pointswith no sub-structure. Since the shower front and theradio signal both propagate with approximately thespeed of light, the radio signal detected by LOPES istime compressed to a single pulse containing the emis-sion from the whole shower development. This is alsotrue for air-Cherenkov light emitted by air showers, butsince the optical wavelengths are small, at least lateralsubstructure is visible in Cherenkov-light images of airshowers. The radio emission, however, originates mostlyfrom a region around the shower axis smaller than onewavelength. Therefore, it is not surprising that no sub-structures were visible in the radio images - at least atthe LOPES frequency band of 40 −
80 MHz and at smallviewing angles corresponding to the small axis distanceswhere LOPES observed the showers (at larger viewingangles corresponding to larger axis distances it mightbe easier to resolve the structure of the shower, but the signal is significantly weaker). On top of these in-trinsic difficulties in radio imaging of air showers, thereare side lobes of the instrument and secondary maximaof the cross-correlation beam which lead to apparentstructure in the image. These difficulties still need tobe resolved before radio imaging can be applied to theopen questions in air-shower and cosmic-ray physics.
Appendix F: Observation of Thunderstorms
LOPES featured a special mode for the observation ofthunderstorms making utilizing the long buffer timeof several ms in the transient buffer boards used fordata acquisition. In addition to the radio signals ofthe air showers, that were altered by the atmosphericelectric fields of the thunderclouds [41], also the di-rect radio emission of lightning was observed [21]. Dueto the limited statistics and small size of the LOPESand KASCADE-Grande arrays, no conclusion could bemade whether air-showers initiate lightning. Nonethe-less, the idea of studying thunderclouds by the radiosignals detected from air showers was developed fur-ther and successfully applied with higher accuracy atLOFAR [93]. Recently the enhancement of radio sig-nals of air-showers during thunderstorm conditions wasalso confirmed at lower frequencies of a few MHz [94].
Appendix G: Analysis Software
To our knowledge, LOPES was the first radio arrayfor air showers whose analysis software was made avail-able with open access. Some components of the softwarewere shared between LOPES and LOFAR, which waseasy because both software resides in the same reposi-tory. However, we do not know about any external usersof the LOPES software. There are at least two reasonswhy our software was difficult to transfer to other ex-periments. First, the LOPES analysis pipeline was de-signed specifically for the needs of digital radio inter-ferometry, and other antenna arrays mostly use non-interferometric approaches. Second, and most impor-tantly, the LOPES software was hard to maintain andhard to compile on new systems. The software makesuse of several external libraries which were not wellmaintained and did not compile easily on more modernsystems. The examples of the Offline software of thePierre Auger Collaboration [95] and of the newer Nu-RadioReco software [96] show that a different softwaredesign and strict coding rules greatly facilitate the useof the software for other experiments - to the benefitof the community. Consequently, we recommend thatnew software developed for future experiments should follow a modular approach and restrict the use of ex-ternal libraries to those widely used and likely to bemaintained for a long time. Appendix H: Frequency Band
The frequency band of LOPES of 40 −
80 MHz waschosen for technical considerations and taking into ac-count the limited knowledge of the radio emission ofair showers that was available when LOPES was de-signed. It was not yet known that the coherence con-ditions lead to strong emission up to a few GHz at theCherenkov angle [57] despite the radio emission not be-ing Cherenkov light [97]. Since the Cherenkov ring hasa diameter of about 100 −
150 m around the shower axisfor the zenith angle range until 45 ◦ and the altitude of110 m of LOPES, a higher frequency band would likelyhave had improved the signal-to-noise ratio.Meanwhile, the progress in high-fidelity simulationsof the radio emission enabled dedicated design stud-ies for future experiments. Therefore, we have learnedthat depending on the science case, the instrumentedarea and the antenna spacing, other frequency bandsmight be better. In particular, higher frequency bandsup to several 100 MHz can improve the signal-to-noiseratio and lower the detection threshold [98]. This is nowtaken into account in the design of future radio arrays[80,75]. Appendix I: Practical Advice
Last but not least, we learned several practical lessonsin operating the experiment, which we list here in thehope that others may benefit from our experience: – A graphical user interface helps to understand ex-perimental issues quickly. – A monitoring website providing a quick overview ofthe experimental status is very helpful. – It occasionally happened that during maintenanceor deployment the polarization channels of an an-tenna were accidentally swapped. Therefore, aftereach maintenance operation, this should be checkedby appropriate monitoring tools, e.g., by the relativestrengths of RFI or beacon lines in the frequencyspectra recorded by the antenna channels. – Most difficult to detect were polarity flips of chan-nels (corresponding to an accidental rotation of 180 ◦ of the antenna). Although an antenna looks sym-metrical, polarity flips can degrade the performanceof the array, in particular when combining antennasin an interferometric analysis. – All cables should be deployed on or preferably un-der ground, but not in the air. Otherwise, electricalground loops may impact the measurements. – RFI emitted by other electronics or detectors is diffi-cult to mitigate by shielding alone because Faradaycages only help to a limited extent. For LOPES, itwas critical that the distance between the anten-nas and the closest KASCADE particle detectorswas larger than one wavelength. This enabled us todistinguish the radio signals emitted by air showersand the RFI ’signals’ by the particle detectors bytiming.
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