Radio detection of cosmic ray air showers in the digital era TimHuegea aInstitutfu¨rKernphysik,KarlsruherInstitutfu¨rTechnologie-CampusNord,Postfach3640,76021Karlsruhe,Germany Abstract 6 In1965itwasdiscoveredthatcosmicrayairshowersemitimpulsiveradiosignalsatfrequenciesbelow100MHz. 1 Afteraperiodofintenseresearchinthe1960sand1970s,however,interestinthedetectiontechniquefadedalmost 0 completely. Withtheavailabilityofpowerfuldigitalsignalprocessingtechniques,newattemptsatmeasuringcosmic 2 rayairshowersviatheirradioemissionwerestartedatthebeginningofthenewmillennium. Startingwithmodest, n small-scale digital prototype setups, the field has evolved, matured and grown very significantly in the past decade. a Today’s second-generation digital radio detection experiments consist of up to hundreds of radio antennas or cover J areas of up to 17 km2. We understand the physics of the radio emission in extensive air showers in detail and have 6 developedanalysisstrategiestoaccuratelyderivefromradiosignalsparameterswhicharerelatedtotheastrophysics 2 oftheprimarycosmicrayparticles,inparticulartheirenergy,arrivaldirectionandestimatorsfortheirmass.Inparallel ] tothesesuccesses,limitationsinherentinthephysicsoftheradiosignalshavealsobecomeincreasinglyclear. Inthis M article, we review the progress of the past decade and the current state of the field, discuss the current paradigm of I theradioemissionphysicsandpresenttheexperimentalevidencesupportingit. Finally,wediscussthepotentialfor . h futureapplicationsoftheradiodetectiontechniquetoadvancethefieldofcosmicrayphysics. p - Keywords: o high-energycosmicrays,radioemission,extensiveairshowers r t s a [ 1. Introduction cles initiated by the primary cosmic ray in the atmo- sphere[3]. However,theestablisheddetectionmethods 1 Even though more than 100 years have passed since all have their drawbacks, and the community is con- v the discovery of cosmic rays, many questions about 6 stantly looking for ways to improve on the established 2 their origin, the physics of their acceleration and their techniques. Aprimeexampleofsuchanendeavoristhe 4 hadronic interactions in the atmosphere are still unan- proposed AugerPrime [4] upgrade of the Pierre Auger 7 swered [1]. To tackle the complexity of the problem, Observatory, which strives to achieve sensitivity to the 0 two ingredients are very important: First, cosmic rays masscompositionofcosmicraysatthehighestenergies 1. have to be measured with sufficient statistics, a diffi- via separate measurements of the electromagnetic and 0 cult task at the highest energies where the particle flux muonicairshowercomponentsusinganadditionallayer 6 becomes as small as one particle per km2 per century, 1 of scintillators deployed on top of the existing water- see Fig. 1. Second, the measurement quality has to be : Cherenkovdetectors. v as good as possible to provide enough information, in i Inthepastdecade,thefieldofradiodetectionofcos- X particular,toidentifythemassoftheprimaryparticles, mic ray air showers has undergone an impressive re- an essential piece of information in testing hypotheses r naissance. Building on the knowledge gathered from a for particle acceleration and propagation. Techniques historicalradiodetectionexperimentsinthe1960sand suchaslarge-scaleparticledetectionwithground-based 1970s, innovative projects were started in the early arrays and fluorescence detection of air showers with 2000s, driven by high expectations [5]. The goal of optical telescopes have been employed with great suc- these projects was to first provide a proof of princi- cess over many decades [2]. These approaches detect ple for the detection of air showers using digital radio “extensive air showers”, cascades of secondary parti- techniques, and then to evolve these approaches into a new technology for large-scale air shower measure- ∗Email:[email protected] ments. Having met with great success, these activities PreprintsubmittedtoPhysicsReports January28,2016 Equivalentc.m.energy s (GeV) pp 102 103 104 105 106 5) 1019 1. V 1e RHIC(p-p) Tevatron(p-p) 7TeV14TeV HiRes-MIA -sr 1018 HERA(-p) LHC(p-p) HiResI -1s HiResII 2 AugerICRC2013 -m ( 1017 TASD2013 ) E ( J 2.5 1016 Radio E x u fl 1015 d e al c S 1014 ATIC KASCADE(SIBYLL2.1) PROTON KASCADE-Grande2012 RUNJOB TibetASg(SIBYLL2.1) 1013 IceTopICRC2013 1013 1014 1015 1016 1017 1018 1019 1020 1021 Energy (eV/particle) Figure1:Theenergyspectrumofthehighestenergycosmicraysmeasuredbyvariousexperiments.Theenergyrangeaccessibletoradiomeasure- mentsisindicated.Atlowparticleenergies,radiosignalsbecomeweakandareoverwhelmedbybackground.Athighenergies,conceptstocover verylargeeffectivedetectionareashaveyettobedeveloped.Diagramupdatedandadaptedfrom[3]. steadily gained in momentum, as is illustrated in Fig. and the most important characteristics of the emission. 2. Today’s experiments have matured well beyond the Next, we will discuss the evolution of modelling ef- prototyping phase. They are aimed either at covering forts which, in conjunction with results from various large areas with a minimum number of antennas or at experiments,ledtothisparadigm. Afterwards,wewill measuring individual air showers with hundreds of ra- describe the experimental projects which were devel- dioantennasatatime. Radiosignalsareexpectedtobe opedoverthepastdecadeandhighlighttheirgoalsand measurable above background at energies (cid:46) 1017 eV, technologicalchoices,beforediscussingsomeanalysis- and probably down to energies as low as (cid:38) 1016 eV relatedaspectsandthenmovingontoadetaileddescrip- whenapplyinginterferometricanalysistechniques, see tion of the important experimental results achieved to Fig.1. date and how they compare to theoretical predictions. In parallel to the experimental activities, models for Finally,weclosewithanoutlooktopossiblefuturedi- the physics of the radio emission emanating from ex- rectionsofthefieldofairshowerradiodetection. tensive air showers have matured to a degree that the emissionmechanismsarenowgenerallyassumedtobe 2. The starting point for digital radio detection of well-understood. Asitturnsout,thereisalargeoverlap airshowers betweenthephysicsofradioemissionfromairshowers andthephysicsofradioemissionfromparticleshowers Modernradioexperimentsbuiltonknowledgegained indensemedia. Wewillmentiontheseparallelswhere 50yearsago,whichprovidedavaluablestartingpoint. appropriate.However,wedeliberatelyfocusthisreview Here,wequicklydiscussthemostrelevantinformation on the case of air showers and the methods to detect availablefromthehistoricalworksandthenoutlinethe themwithradiotechniques. promises of the radio detection technique which led to Afterashortintroductionofthestartingpointforthe renewedinterestandsparkedthenewprojects. modern-dayexperiments, includinganoverviewofthe 2.1. Theknowledgefromhistoricalexperiments meritswarrantingtheinvestigationofradiodetectionof cosmicrays, wewillsetthescenewithareviewofthe Radio detection of cosmic rays per se is not a new current paradigm of air shower radio emission physics technique. Infact,theexperimentalproofthatairshow- 2 50 n ctio 45 e 40 et o d 35 di 30 a n r 25 o s 20 n o uti 15 ontrib 1 50 C 0 57913579135701357913579135 66677777888899999900000111 99999999999999999900000000 11111111111111111122222222 London Calgary Budapest Hobart Denver Muechen Plovdiv Kyoto Paris Bangalore La Jolla Moscow Adelaide Dublin Calgary Rome Durban alt Lake C. Hamburg Tsukuba Pune Merida Lodz Beijing Rio de Jan. The Hague S Figure2: Numberofcontributionsrelatedtoradiodetectionofcosmicraysorneutrinosatthebi-yearlyInternationalCosmicRayConferences. Dataupto2007weretakenfrom[6]. ers emit impulsive radio signals was made as early as the geomagnetic field axis. Due to the geomag- 1965[7]. Asaconsequence,severalgroupsengagedin netic nature of the emission, the signal is gener- experimental and theoretical work to study the details ally expected to be strongest in antennas measur- oftheradioemission. Itisnotthegoalofthisarticleto ing the polarisation component aligned with the review these historical works, and we kindly refer the Lorentz force. For detection sites at geographic readertotheexcellentarticleofAllan[8]forsuchare- mid-latitudes,thiscorrespondstotheeast-westpo- view. larisationcomponent. However, let us briefly discuss the most relevant • The signal strength measured by an antenna de- piecesofinformationwhichwereavailablefromthehis- pends on the lateral distance from the air shower torical works at the time that the community rediscov- axis and can be fitted with an exponential lateral ereditsinterestinradiodetectionofcosmicrays. These distributionfunction(LDF).1 were: Thegistofthisknowledgecanbesummarizedinone • Air showers initiated by cosmic rays emit impul- formula, often referred to as the “Allan-formula” (eq. sive radio emission. The emission was originally (84)inRef.[8]),asfollows: discovered at a frequency of 44 MHz, but suc- (cid:32) (cid:33) cessful detections from as low as 2 MHz up to E (cid:15) = 20µVm−1MHz−1 p 500MHzfollowed. ν 1017eV (cid:32) (cid:33) • The radio signal, at least at frequencies below × sinα cosθ exp − R , (1) 100MHz,iscoherent. Inotherwords,thereceived R0(ν,θ) powergenerallyscalesquadraticallywiththenum- inwhich(cid:15) denotesthepeaktotalamplitude(modulus) ν berofemittingparticles,andthuswiththeenergy oftheelectricfieldvectordividedbytheeffectiveband- of the primary cosmic ray (with the exception of width of the measurement, E is the energy of the pri- p showersbeingtruncatedwhenhittingtheground). mary cosmic ray, α is the so-called “geomagnetic an- • The emission is dominated by a geomagnetic ef- gle”, i.e.theanglebetweentheairshoweraxisandthe fect, since a clear correlation of the radio signal strength is seen with the angle between the air 1Keepinmind,however,thatthehistoricalexperimentsonlymea- shower axis (the axis determined by the arrival suredtheradioLDFaveragedovermanydifferentairshowers,notthe direction of the primary cosmic ray particle) and radioLDFofanindividualairshoweritself. 3 geomagnetic field axis, θ is the “zenith angle”, i.e. the detectiontorenew. Wewilldiscussthereasonsforthis anglewrt.verticalincidenceofthecosmicrayprimary, renewalinthenextsubsection. and R denotes the lateral distance perpendicular from theairshoweraxis,oftendenoted“axisdistance”. The 2.2. Thepromisesofradiodetection scalefactorR dependsonfrequencyandzenithangle, 0 buttherewerenoparticularlyquantitativeresultsavail- Asmentionedintheintroduction,existingtechniques ableatthetime. using particle detector arrays and optical fluorescence In spite of this significant knowledge, a number of detectors (or optical Cherenkov light detectors) have importantquestionswereopen: beenverysuccessfulinstudyingcosmicraysoveravery wide range of energies. However, they do have their • Severalsecondaryemissionmechanismshadbeen shortcomings. investigated on a theoretical basis, and there were All detection techniques at energies beyond (cid:38) some experimental results suggesting that the ge- 1014 eV rely on the measurement of the extensive air omagnetic emission was not the only mechanism. shower cascade initiated by a primary cosmic ray in However, these were indications at best, and they the atmosphere. This air shower is dominated by the were far from being accepted in the community. electromagnetic component (electrons, positrons and The relevance of the atmospheric refractive in- photons) and has a characteristic evolution with atmo- dexgradienthadalsobeenstudiedtosomeextent sphericdepth,showninFig.3. Theshowerfirstgrows, [9,10]. thenreachesamaximum,andafterwardsdiesout. • There were theoretical investigations on the sen- 7e+09 sitivity of the radio signal, in particular its LDF, proton on the longitudinal evolution of the air shower 6e+09 iron [c9le,,1b0u]t,naondextpheursimthenetamlatessstsoforthqeuapnrtiimtaatirvyepsaturtdi-- nd e- 5e+09 a ieswereavailable. + 4e+09 e • Theabsolutestrengthoftheradioemissionwasre- er of 3e+09 b portedverydifferently,uptofactorsof100inam- um 2e+09 n plitude, by different groups [11]. The assumption 1e+09 wasthatthiswasduetodifficultiesinprovidingan 0 absolutecalibrationforthemeasurements. 0 100 200 300 400 500 600 700 800 900 1000 atmospheric depth X [g cm-2] • Itwasunclearhowimportanttheinfluenceofelec- tricfieldsintheatmosphere(sayinthunderclouds Figure3:Longitudinalevolutionprofilesoftheelectromagneticcom- [12]) could be and whether an effect on the radio ponentsofextensiveairshowersinitiatedbyprotonandironprimaries signalwastobeexpectedevenforfairweather. If withanenergyof1019 eV,assimulatedwithCORSIKA[14]. The the latter were true, it would make the technique depthofthemaximumoftheairshowerevolution, Xmax, provides valuableinformationaboutthemassoftheprimaryparticle. More unreliable for any quantitative measurements, as massiveparticlesonaveragehavealowerdepthofshowermaximum, theatmosphericelectricfieldataltitudesofseveral andtheirdistributionofXmaxvaluesscatterslessthanforlighterpar- kilometersishardtomonitor. ticles. In the mid-1970s, the activities on radio detection Particle detectors only measure a momentary snap- of cosmic rays ceased almost completely, as is evident shot of the secondary particles in an air shower reach- alsofromFig.2. Thiswasduetoanumberofreasons, ingtheground,andtypicallyonlysampleasmallfrac- for example there were problems in associating the ra- tion of these particles due to their limited area cover- diomeasurementsreliablywiththerelevantairshower age. This yields very indirect information about the characteristics, which was sometimes attributed to the original primary cosmic ray particle. In particular, un- effectsofunknownatmosphericelectricfields.Also,the certainties in the hadronic interactions at energies well fluorescence imaging technique pioneered in the Fly’s beyond those accessible in collider experiments intro- Eyeexperiment[13]seemedmorepromisingandmade duce significant systematic uncertainties in the recon- goodprogress, whichshiftedtheinterestofthecosmic struction of the characteristics of the primary particle raycommunity. Ittook30yearsfortheinterestinradio from the ground-based particle detector measurements 4 [3]. An important problem unsolved to date is the dis- tection technique re-emerged in the early 2000s; for a crepancy in the number of muons predicted by simu- reviewofthefieldatthattimesee[5]. Radiodetection lations, which at 1019 eV is at least 30% lower than wasexpectedtohavethefollowingadvantages: the one derived from hybrid measurements with fluo- • The radio emission is caused by the electromag- rescence telescopes and particle detectors at the Pierre netic component of the air shower. As such it Auger Observatory [15]. The most likely explanation does not suffer strongly from uncertainties in the for this discrepancy is in the extrapolation of hadronic hadronicinteractionmodels. interaction physics well beyond the scale probed with measurementsatparticleaccelerators,whichalsomea- • Theradiosignalisintegratedoverthefullshower sureinaverydifferentregimethantheextremeforward evolution. (Thereisnorelevantdampingintheat- interactionsinairshowers. Whileparticledetectorscan mosphere at VHF frequencies.) It thus represents be seen as the “work-horse” of cosmic ray detection, acalorimetricenergymeasurement. since in particular they can measure with 100% duty cycle, information from other detectors is thus needed • Radiomeasurementscanbeperformedwithessen- toexploitthemtotheirfullpotential,especiallywithre- tially100%dutycycle.2 gardtoareliablereconstructionoftheabsoluteenergy • Theradiosignalshouldbesensitivetothelongitu- scaleofcosmic-rays. ThePierreAugerObservatoryin dinalshowerevolutionandthusX . particularhascommittedtosucha“hybridapproach”by max combining particle detectors with optical fluorescence • Radio antennas can be built comparably cheaply. telescopes which are used to calibrate the energy scale Possibly, very large areas could be instrumented oftheparticledetectors. Itremainsverydifficult,how- economicallywithradiodetectorstodetectcosmic ever,todeterminethemassoftheprimaryparticlefrom raysatthehighestenergies. ground-based particle detectors. This requires at least the separate measurement of the electromagnetic and • Incontrasttothe1960sand1970s,powerfuldigi- muoniccomponentsoftheairshower,asisthegoalof tal signal processing is available today. (No more theAugerPrimeupgrade[4],andstillmightsufferfrom photographingofoscilloscopetraces!) Whiledig- systematicuncertaintiesinhadronicinteractionmodels. italelectronicsdocomewithapricetag,radiode- The most-used optical detection technique is the tectionsdirectlyprofitsfromMoore’slaw. Digital detection of ultraviolet light emitted by excited air electronicsgetexponentiallycheaperintime. moleculesintheairshower. UsingpixelatedUVcam- Intheearly2000s,theideaarosetoapplydigitalra- eras, the longitudinal evolution of an air shower as diodetectiontotheproblemofcosmicrayphysics[17]. shown in Fig. 3 can be imaged. The integral of the One vision driving these activities was the hope that longitudinal evolution profile yields a calorimetric en- a combination of particle detectors and radio antennas ergy measurement of the air shower. As the emission could yield similar information as the combination of offluorescencelightisvastlydominatedbytheelectro- particle and fluorescence detectors — but with 100% magnetic component of the air shower, it is much less affectedbyhadronicinteractionuncertainties. Also,the dutycycleinsteadof10%dutycycle. We will discuss in the course of this review which atmospheric depth at which the air shower reaches its of these promises can be kept and which cannot. Be- maximum particle number, the “shower maximum” or X (in g cm−2) can be read off from the profile and fore wego into any moredetail of the evolutionof the max radio emission experiments, let us set the scene with a yields precious information about the mass of the pri- summaryofwhatweknowaboutthenatureoftheradio mary particles, again visible in Fig. 3. Fluorescence emissionfromairshowerstoday. detectorsthusyieldveryhighqualitydata—however, they do it effectively in less than 10-15% of the time. Their“dutycycle”islimitedtosuchsmallnumbersbe- 3. The physics of radio emission from extensive air cause the technique relies on clear, moon-less nights. showers Fiducial volume cuts further limit the fraction of data Before reviewing the progress of the last decade on usableforanalyses. Attheveryhighenergies,theloss boththetheoreticalandtheexperimentalsideindetail, instatisticsofmorethanafactorof10isanimportant drawback.Also,theairqualityatthesitehastobegood andhastobemonitoredveryclosely[16]. 2Aswewillsee,onlythunderstormslowerthisvalue,butittypi- In light of these limitations, interest in the radio de- callyremainsatalevelofmorethan95%atmostsites. 5 let us first go through a concise summary of the radio 100m 3 emission physics as we understand it today. We will 200m keepthediscussionmostlynon-technical,readersinter- 2] 300m estedinthedetailsareencouragedtostudytheoriginal m 500m publicationsreferencedinthetext. x m 700m V/ 2 900m 3.1. Geomagneticemission 2 [ e c Themainemissionmechanismforradiopulsesfrom n a cosmic ray showers is associated with the geomag- st netic field: Secondary electrons and positrons in the s di 1 air shower are accelerated in the magnetic field. One xi a ideathatwasfollowedwasthatthisaccelerationdirectly x leadstotheradioemissionasinsynchrotronemission, d el h[1e7n]c.e Hthoewteervmer,“gtheiossyvniecwhrodtoroesnneomtiscsoirorne”ctwlyasdecsocirnibede c fi 0 ri theemissionphysicsinairshowers. Thereasonisthat ct e electronsandpositronsdonotpropagateunimpededon El long, let alone periodic orbits. Instead, they interact continuouslywithairmolecules. Thesituationiscom- -1 parabletotheoneofelectronsinaconductortowhicha 0 20 40 60 80 voltageisapplied. Intheequilibriumofaccelerationby time x speed of light [m] themagneticfieldanddecelerationininteractionswith 5 air molecules a net drift of the electrons and positrons z] H arisesinoppositedirectionsasgovernedbytheLorentz M 2 force m/ -5 10 V/ F(cid:126) =q(cid:126)v×B(cid:126). (2) d [ 5 el whereqdenotestheparticlecharge,(cid:126)visitsvelocityvec- c fi 2 ri torandB(cid:126)isthemagneticfieldvector.Forparticlesorig- ct -6 100m e 10 inallymovingalongtheshoweraxis, theresultingcur- el 200m rentwillbeperpendiculartotheshoweraxis,i.e.wecan al 5 300m r refertothemas“transversecurrents”. ct 500m e 2 p Thereisonemoreimportantingredient: Thesetrans- S 700m -7 verse currents vary as the air shower evolves and the 10 2 numberofsecondaryparticlesfirstgrows,thenreaches 1 2 5 10 2 5 10 2 a maximum, and then declines as the shower dies out frequency [MHz] (cf. Fig. 3). It is this time-variation of the transverse currentswhichleadstoelectromagneticradiation. Due Figure4:Radiopulses(top)arisingfromthetime-variationofthege- to the relativistic speed of the emitting particles, the omagneticallyinducedtransversecurrentsina1017eVairshoweras observedatvariousobserverdistancesfromtheshoweraxisandtheir emission is compressed in short pulses in the forward correspondingfrequencyspectra(bottom). Refractiveindexeffects direction, along the shower axis (Fig. 4, top). Cor- arenotincluded.Adaptedfrom[18]. respondingly, the emission has broad-band frequency spectra (Fig. 4, bottom). For geometrical reasons, the pulses get broader and the frequency spectra cut off at lowerfrequenciesastheobservermovesawayfromthe Thepolarisationoftheradiationbythetime-varying showeraxis.Interpretedinamicroscopicway,thetime- transverse currents is linear with the electric field vec- variation of the transverse currents can be associated tor aligned with the Lorentz force, i.e. along the(cid:126)v× B(cid:126) withaccelerationofindividualparticles,i.e.,itisinfact direction, where the propagation direction of the parti- accelerationofchargedparticlesthatproducestheradi- cles(cid:126)vcanbeapproximatedwiththeshoweraxis. This ation. isillustratedintheleftpanelofFig.5. 6 Inprinciple,anychargedparticleundergoesthepro- asymmetries in the radio signal arise, as depending on cesses described here. However, only electrons and the observer location, the two contributions can add positrons contribute significantly to the radio signal as constructivelyordestructively. Thearisingasymmetry, theyhavebyfarthehighestcharge/massratio. Already specificallyalongthedirectiondenotedby(cid:126)v×B(cid:126) (east- muonsaremuchtooheavytomakeasignificantcontri- westforverticalairshowers)isillustratedbythevisual- bution. ization of the “radio footprint” (two-dimensional radio Thisemissionphysicshasalreadybeendescribedby LDF)depictedinFig.6. Thedegreeofasymmetryde- Kahn&Lerche[19]. Amodernformulationwasdevel- pends on the relative strength of the geomagnetic and opedbyScholten,WernerandRusydi[18]. charge excess contributions, and thus in particular on thegeomagneticangleofagivenairshoweraswellas 3.2. Chargeexcessemission(Askaryaneffect) thestrengthofthelocalgeomagneticfield. Inadditiontothedominatinggeomagneticcontribu- tion3 a secondary effect exists. It is well known that there is a negative charge excess of ≈ 10−20% in air 90 showers, which is caused mostly by the fact that the 90 ambient medium is ionized by the air shower particles m] andtheionizationelectronsaresweptwiththecascade, 70 70 µV/ [ whilethemuchheavierpositiveionsstaybehind.Asthe 50 50 gth n e showerevolves,theabsolutenegativechargepresentin 30 30 str themovingcascadegrows,reachesamaximumandfi- eld nallydecreaseswhentheshowerdiesout. Hence,again 10 10 fi there is a time-varying charge excess, and this leads to pulsesofelectromagneticradiation. Thisradiationalsohaslinearpolarisation. However, theelectricfieldvectorisorientedradiallywithrespect 200 200 to the shower axis. In other words, the orientation of 100 100 0 0 the electric field vector depends on the location of an north[m] -100 -100 east[m] observer(radioantenna)withrespecttotheshoweraxis, -200 -200 asisillustratedintherightpanelofFig.5. Figure6: Simulationofthetotalelectricfieldamplitudeinthe40- The mechanism described here, together with 80MHzbandforaverticalcosmicrayairshoweratthesiteofthe Cherenkov-likeeffectsthatwillbedescribedinthenext LOPESexperiment. Theasymmetryarisesfromthesuperpositionof section, is essentially the Askaryan-effect [22, 23]. It thegeomagneticandcharge-excessemissioncontributions. Refrac- usuallyplaysasub-dominantroleinairshowerphysics, tiveindexeffectsareincluded.Adaptedfrom[25]. however it is the sole relevant emission mechanism in particle showers in dense media and has been investi- gated in considerable depth in the context of neutrino While the footprint shown in Fig. 6 illustrates the detection via radio emission in ice and the lunar re- peakamplitudemeasuredatvariousobserverlocations, golith(see,e.g.,[24]).Sincethelengthscalesofparticle acloserlookatthetime-evolutionoftheimpulsiveradio showersindensemediaaremuchsmaller,theresulting emissionisshowninFig.7. Thepulsesassociatedwith radiationisstrongestatGHzfrequencies. Theunderly- thetwoemissionmechanismsarenotperfectlysynchro- ingphysics,however,isthesameasinair. nized, a sign that the time-variation of the transverse currents induced by geomagnetic effects and the time- 3.3. Superposition of the contributions and signal variationofthenetchargeexcessareslightlyoffsetover asymmetries the course of the longitudinal evolution of the exten- When the electric field vectors associated with the siveairshower. Therefore,theelectricfieldvectordoes two emission mechanisms are superposed, complex not generally trace a line in the plane perpendicular to the shower axis; instead, it generally traces an ellipse. Inotherwords, theradioemissionfromcosmicrayair 3Obviously,thegeomagneticcontributionvanishesforairshowers showersisgenerallyofellipticalpolarisation,i.e.anad- arrivingparalleltothemagneticfield.Forairshowerswithasmallge- mixture of linear and circular polarisation. This effect omagneticanglethusthechargeexcessemissioncanactuallybecome dominant. remainstobeprovenexperimentally. 7 v x v x B v x v x B v x B v x B Figure5:Left:Illustrationofthegeomagneticradiationmechanism.Thearrowsdenotethedirectionoflinearpolarisationintheplaneperpendic- ulartotheairshoweraxis. Irrespectiveoftheobserverposition,theemissionislinearlypolarisedalongthedirectiongivenbytheLorentzforce, (cid:126)v×B(cid:126)(east-westforverticalairshowers).Right:Illustrationofthechargeexcess(Askaryan)emission.Thearrowsillustratethelinearpolarisation withelectricfieldvectorsorientedradiallywithrespecttotheshoweraxis.Diagramshavebeenadaptedfrom[20]and[21]. 60 60 60 0 0 0 -60 -60 -60 -60 0 60 -60 0 60 -60 0 60 60 90 m] 60 80 V/ µ [ 70 h gt 60 n 0 0 e 0 50 str d 40 el -60 2300 otal fi -60 -60 0 60 t -60 0 60 m] 0 60 60 60 V/ µ [ B x v 0 0 x 0 v g n alo -60 -60 d -60 0 60 -60 -60 0 60 fiel field along v x B [µV/m] -60 0 60 Figure7:Illustrationofthetime-evolutionoftheelectricfieldvectorinthe40-80MHzfrequencybandforantennasat100mlateraldistancetothe north,north-east,east,south-east,south,south-west,west,andnorth-west(countingclockwisefromthetoppanel)oftheimpactpointofavertical 1017eVairshowerattheLOPESsite. ThefieldisdecomposedincomponentsalongthedirectionoftheLorentzforceandperpendiculartothat. Themapinthecenterillustratesthetotalamplitudefootprint.Refractiveindexeffectsareincluded.Adaptedfrom[25]. 3.4. Forward beaming, coherence and Cherenkov-like effects Animportantfactorintheemissionphysicsiscoher- ence.Aslongasradiationatagivenfrequencyfromdif- 8 40 ferentparticlesacquiresnegligiblerelativephaseshifts duringitspropagationtotheobserver,thevectorialelec- 20 tricfieldsaddupcoherently. Thismeansthattheelec- tric field amplitude scales linearly with particle num- m] berandthus(approximately)withtheenergyofthepri- V/ 0 m musaerfyulpfaeratitculree.fTohreenlienregayrimtyeoasfuthreismdeenptsenwdiethncreadisioatveecrhy- gth [ -20 n niques.Equivalently,thereceivedpowerscalesquadrat- e r icallywiththeenergyoftheprimaryparticle. d st -40 Obviously, coherence is frequency-dependent and el more pronounced at low frequencies. Coherence is in- c fi -60 ri fluencedbythespatialparticledistribution(mainlythe ct thickness of the air shower disk, but for observers at ele -80 n=1 large lateral distances also its lateral extent) as well as n=1.0003 geometricaleffectsandpropagationphysics. -100 n=n(z) Due to the relativistic motion of the radiating parti- clesalongtheairshoweraxis, theradiationisstrongly 0 2 4 6 8 10 12 14 16 18 20 forward-beamed, requiring antennas placed within a time [ns] constrained“illuminatedarea”.Furthermore,therefrac- tiveindexoftheatmosphereisnotunity. Atsealevela Figure 9: Simulated radio pulses for an air shower with a primary typicalvalueisn = 1.000292,anditscalesproportion- energy of 5×1017 eV. The observer is located at an axis distance of100m.Therefractiveindexnhasbeenadoptedasunity(vacuum), allywiththeairdensitytohigheraltitudes. 1.0003(sealevel)andarealisticgradientintheatmospheren(z),illus- tratingtheensuingtimecompressionoftheradiopulses.Theparticle distributionisapproximatedtohavenolateralextent. Adaptedfrom ×106 [27]. 1 n=1.0 70 n=1.0002 ns/m] 10-1 nn==1n.(0h0)03 60 es compressedintimeandcanthusbecomeveryshort,as ssion factor [ 1100--32 profile 345000 mberofparticl ieocsmanlsiah1sso0“iw1Co7nnheeuVirnpenaFtkioriogsvGsh.Hroi8wnzgeaf”rnrsedwqoi9uft.heonrtTcdyiheperiissc1afc0ola0rrniomnlbge,saraedasrdvitiesoirssfcoholroohwvceaenretretinind-t e u ompr 10-4 20 n Fig.10. c At lateral distances which fall inside the Cherenkov 10 10-5 ring,thepulsesarestretchedbytherefractiveindexef- 0 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 fects and the transition frequency from coherent to in- height [m] coherentemissionisdecreased. Also,thetime-ordering Figure 8: For different models of the atmospheric refractive index ofsignalsisreversed:signalsemittedintheearlystages n, emissionemanatingfromcertainheightshcanbestronglycom- of the air shower arrive later than those emitted in late pressedintime,asindicatedbythecompressionfactorontheleftver- stages. ticalaxis. Ifthestronglycompressedemissionregioncoincideswith Atlargelateraldistances,outsidetheCherenkovring, thosepartsofthelongitudinalshowerevolutionprofile(blacklineand rightverticalaxis)atwhichtheshowerchangesrapidly,strongcom- the refractiveindex effects arenegligible, asthe pulse- pressedradiopulsesoccur.Adaptedfrom[26]. widthsaredominatedbygeometricaleffects. Thelarger thelateraldistance,thebroaderthereceivedpulsesand This refractive index gradient has important conse- the lower is the transition frequency from coherent to quencesfortheresultingradiationpattern.Ifforagiven incoherentemission. emission region along the shower axis an observer is Westressherethattherefractiveindexgradientinflu- located at the corresponding Cherenkov angle4, radia- ences the radiation emitted by the time-varying trans- tion emitted from all along this region arrives simul- versecurrentsandtime-varyingchargeexcessbycom- taneously at the observer. In other words, pulses are pressing(orstretching)itintime. Itisvalidtotermthis 4Duetotherefractiveindexgradientintheatmosphere,thereisof “Cherenkov-like” effects. However, the reader should coursestrictlyspeakingnowell-defined,uniqueCherenkovangle. notconfusethiswith“Cherenkovradiation”inthesense 9 200 600 electric field amplitude is lower (the radiated power is distributed over a larger area), but also the LDF is less 150 500 steep. Thismakesinclinedairshowersmorefavourable 100 fordetectionwithasparseantennagrid[29]. north position [m] -55000 234000000 fieldstrength[V/m]µ floqtthhfuueeaFethmnpnoetrcroiiitmmasnytgaafiuixrmxntyihemdpdepeouarrzggmrteetaoinonceoimltstfehoe.asbttnaCarsniteihcginrsaalvdtneliai,cgvbsaaeioldlnseuusflorianctutholecXeatdrduieriaitsmstetiharopamonnrowcesiren,teaaebrlin,ssuttXohttfemhiraseamecxflot.adoensTercespthieoontihdsff- max -100 in the geometrical distance between radio source and 100 observer, and thus can be exploited to determine X -150 max from radio measurements. The most obvious way to -200 0 access this information is the LDF, as discussed above -200 -150 -100 -50 0 50 100 150 200 andillustratedinthecomparisonbetweenFig.6foran east position [m] iron-induced air shower (small X ) and Fig. 12 for a max Figure 10: Radio-emission footprint of the total field strength of a proton-inducedairshower(largeXmax)(notethediffer- vertical1017eVairshowerinducedbyanironprimaryattheLOPES entscales). Forthesamegeometricalreasons,thegeo- siteasseeninthefrequencyrangefrom300to1,200MHz. Adapted metricalsourcedistancealsoinfluencestheshapeofthe from[25]. radio wavefront, which can be determined by precise timing measurements, and the pulse shape (or spectral of a (constant) net charge moving through a medium index of the frequency spectrum) measured at a given withavelocitywhichishigherthanthemedium-speed- lateral distance. We will discuss the sensitivity of the of-light [28]. Such a contributionby “Cherenkov radi- radiosignaltothemassoftheprimaryparticleinmore ation” must certainly be present, but to our knowledge depthinthechapteronexperimentalresults. itiscompletelynegligibleforthecaseofairshowersat 250 radiofrequencies. 250 m] 200 200 V/ 3.5. Sourcedistanceeffects 150 150 h[µ gt As the radio emission is strongly forward-beamed, 100 100 en str intoaconeofafewdegreesopeningangle,thedistance 50 50 eld of the radio source from the observer has a strong in- 0 fi 0 fluence on the size of the illuminated area. It should be noted that for the radio emission, geometrical dis- tance scales, in particular the distance from source to observer, matters. This is in contrast to the air shower evolution which is governed by the amount of matter 200 200 100 100 traversed(atmosphericdepth). 0 0 A particularly important effect is the dependence of north position [m] -100 -100 east position [m] -200 -200 the radio emission on the air shower zenith angle. As the zenith angle increases, the traversed atmospheric Figure 12: Radio-emission footprint of the 40-80 MHz total field depth grows as5 cos−1(θ). The air shower reaches its strengthofavertical1017eVairshowerinducedbyaprotonprimary attheLOPESsite.Adaptedfrom[25]. maximum at a given atmospheric depth, thus for more inclinedshowersthismaximumwillbeatsignificantly largergeometricaldistancesfromtheobserverthanfor vertical air showers. As a consequence, the forward- 4. Modernmodelsandsimulationsofairshowerra- beamed radio emission illuminates a much larger area, dioemission as is illustrated impressively in Fig. 11. The average In parallel with the modern experimental efforts, modellingeffortsfortheradioemissionfromextensive 5Thisisanapproximationforaplanaratmospherewhichisvalid air showers werestarted. We give anoverview here of uptozenithanglesof≈70◦. approaches that have been tried out, but will focus on 10