Radio detection of cosmic ray air showers in the digital era

22.1 MB·

by  T. Huege

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
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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
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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