A prototype system for detecting the radio-frequency pulse associated with cosmic ray air showers

Nuclear Instruments and Methods in Physics Research A 498 (2003) 256–288

A prototype system for detecting the radio-frequency pulseassociated with cosmic ray air showers

Kevin Greena,1, Jonathan L. Rosnera,*, Denis A. Supruna, J.F. Wilkersonb

aDepartment of Physics, Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USAbCenter for Experimental Nuclear Physics and Astrophysics, Department of Physics, University of Washington, Seattle, WA 98195, USA

Received 3 June 2002; received in revised form 20 October 2002; accepted 11 November 2002

Abstract

The development of a system to detect the radio-frequency (RF) pulse associated with extensive air showers of cosmic

rays is described. This work was performed at the CASA/MIA array in Utah, with the intention of designing equipment

that can be used in conjunction with the Auger Giant Array. A small subset of data (less than 40 out of a total of 600 h

of running time), taken under low-noise conditions, permitted upper limits to be placed on the rate and strength of

pulses accompanying showers with energies around 1017 eV:r 2002 Elsevier Science B.V. All rights reserved.

PACS: 96.40.Pq; 29.40.�n; 95.55Vj; 95.30.Gv

Keywords: Extensive air showers; Radiation detectors; Cosmic ray detectors; Radiation mechanics; Auger array

1. Motivation

As a result of work in the 1960s and 1970s [1–4],some of which continued beyond then (see, e.g.,Refs. [5–8]), it appears that air showers of energy1017 eV are accompanied by radio-frequency (RF)pulses [9], whose properties suggest that they aredue mainly to the separation of positive andnegative charges of the shower in the Earth’smagnetic field [10,11]. The most convincing datawere accumulated in the 30–100 MHz frequency

range. However, opinions differ regarding thestrength of the pulses, and atmospheric andionospheric effects have led to irreproducibilityof results. In particular, there may also be pulsesassociated with cosmic-ray-induced atmosphericdischarges [12,13]. There are reports of detection atMHz or sub-MHz frequencies [5–7], which couldbe associated with such a mechanism. Signalsabove 100 MHz have also been reported [8].

A study was undertaken of the feasibility ofequipping the Auger array [14] with the ability todetect such pulses. The higher energy of theshowers to which the array would be sensitivecould change the parameters of detection. Before adesign for large-scale RF pulse detection could beproduced, it was necessary to retrace some of thesteps of the past 30 years by searching for the

*Corresponding author. Tel.: +1-773-702-7694; fax: +1-

773-703-8038.

E-mail address: [email protected] (J.L. Rosner).1Present address: Louis Dreyfus Corporation, Wilton, CT

06897, USA.

0168-9002/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved.

doi:10.1016/S0168-9002(02)01995-2

pulses accompanying 1017 eV showers, and bystudying some of the factors which led to theirirreproducibility in the past. RF pulses may beable to provide auxiliary information aboutprimary composition and shower height [3].

In this article we describe the prototype activityat the CASA/MIA site and draw some conclusionsfrom it regarding plans for the Auger project. Wehave not been able to demonstrate the presence ofRF pulses at CASA/MIA, and could only setupper limits for their intensity. The upper limits onthe rates of events in which the North–South (orEast–West) projection of the signal pulse wasgreater than some value were established atRupðEnNS > E0

nÞ ¼ 0:555=ðE0nÞ

2 h�1 and RupðEnEW >E0nÞ ¼ 0:889=ðE0

nÞ2 h�1; respectively, with En being

the electric field strength per unit of frequency,measured in mV=m=MHz: More concrete plans forRF detection at Auger must await a prototype atthe Auger site which utilizes some of the lessonslearned from the present work. A preliminarydescription of this work was presented in Ref. [15].

In Sections 2 and 3 we discuss expectations forRF signals and previous claims of their observa-tion. Section 4 is devoted to details of the setup atCASA/MIA, including some of the reasons forchoosing the specific configuration utilized. Ourpreliminary results are given in Section 5, whileSection 6 deals with issues specific to a giant arraysuch as Auger. We summarize in Section 7.Appendix A gives details of the sensitivity calcula-tion, Appendix B establishes some properties ofsimulated pulses, while Appendix C summarizescost estimates for an installation at the Auger site.

2. Expectations

We briefly summarize some expectations [3] forthe characteristic of the RF signal associated withcosmic ray air showers.

2.1. Mechanisms of pulse generation

In the 1950s, Wilson [12] proposed that cosmicrays could induce the atmosphere to act as a giantspark chamber, triggering discharges of theambient field gradient. This gradient, normally

around 100 V=m; can attain values as high as10 kV=m during intense thunderstorm activity [3].Thus, the mechanism would lead to pulses ofgreatly varying intensity, whose correlation withair showers would be difficult to establish unlessfield gradients could be monitored over the wholepath of the discharge.

Another mechanism of pulse generation isassociated with the asymmetry in electron andpositron yields in showers as a result of Comptonand knock-on processes. By the end of the shower,electrons outnumber positrons by about 10–25%,leading to a transient of vertically moving negativecharge [9]. This is thought to be the mainmechanism for generation of radio-frequencysignals from showers in solid material such aspolar ice [16] or sand [17], but is probably not thedominant mechanism in the atmosphere.

Still another source of electromagnetic radiationin a cosmic ray shower involves the separation ofpositive and negative electric charges in the Earth’smagnetic field. This is thought to be the dominantmechanism accounting for atmospheric pulseswith frequencies in the 30–100 MHz range, andwill be taken as the model for the signal for whichthe search was undertaken.

2.2. Characteristic pulse

The time profile of a pulse due to charge-separation in the Earth’s magnetic field can bemodelled [3] by assuming that the bulk of theshower giving rise to the pulse is concentratedbetween an altitude of 10 and 5 km (for a showerof energy 1017 eV) and calculating the pulseduration by comparing the total path lengthsbetween the antenna and the beginning and theend of the shower. The rise time of a pulse from ashower with zero zenith angle observed 200 mfrom its axis is expected to be about 5 ns; followedby a longer decay time and a still longer recoverytime with opposite amplitude (about 100 ns) suchthat the total DC component is zero.

The radiation from any stage of the showerwhich is traveling directly towards the antenna isexpected to arrive to the antenna about the sametime as the shower itself. The difference isaccounted for by the refraction index of air. Such

K. Green et al. / Nuclear Instruments and Methods in Physics Research A 498 (2003) 256–288 257

an essentially d-function pulse has the highest-frequency components in its spectrum. Showersfor which the impact parameters of the coresare farther from the antenna will have reducedhigh-frequency components since the total pulseduration will be longer, approaching severalmicroseconds for vertically incident showersviewed from the side.

The pulse is expected to grow linearly inamplitude with shower energy as a result of theincreased number of particles emitting RF energy.This linear growth assumes coherence of theemitting particles, which is probably a goodassumption for RF wavelengths of several meters.The greater penetration of the atmosphere by moreenergetic showers also leads to an increased RFsignal since the radiating particles are closer to thereceiver. This should make the pulse amplitudeincrease more rapidly than linearly with primaryenergy. However, this effect is largely offset by thefact that a greater fraction of such deeply penetrat-ing showers will have reduced high-frequencycomponents in their pulses, as a result of thegreater apparent time taken by the pulse to build upto its maximum amplitude at the receiver. Thecombination of the above three effects is expectedto lead fortuitously to an overall linear dependenceof pulse amplitude on primary energy [3].

At extremely high energies, shower particles willeven be lost by collision with the Earth. This maygive rise to a different type of RF signal but willnot be effective in the context of the charge-separation mechanism considered here. The pulsesassociated with charge separation in the Earth’smagnetic field should correspond to radio signalswith approximately horizontal polarization. (Forshowers not arriving vertically from directly over-head there will also be a small vertical polarizationcomponent.)

2.3. RF backgrounds

Discharges of atmospheric electricity constitutean important source of background pulses. Thesewill be detected at random intervals at a rate whichdepends strongly on local weather conditions aswell as on ionospheric reflections. Man-made RFsources include television and radio stations,

police and other communications services, broad-band sources (such as ignition noise), and sourceswithin the experiment itself. (We shall discuss suchsources for the CASA/MIA array presently.) Thepropagation of distant noise sources to the receiveris a strong function of frequency. During years ofsunspot minima (e.g., 1995–6), ionospheric propa-gation on frequencies above 25 MHz is rare exceptfor ‘‘sporadic-E’’ propagation, which can permitsignals to arrive from distances of up to 2000 kmvia a single reflection from the ionosphere. Assolar activity increases (e.g., subsequently to 1996),consistent daytime propagation over even greaterdistances can occur on frequencies up to andbeyond 30 MHz:

Galactic noise can be the dominant signal inexceptionally radio-quiet environments for fre-quencies in the low VHF (30–100 MHz) range [3].For higher frequencies in such environments,thermal receiver noise becomes the dominant effect.We shall see that the CASA/MIA site is far fromquiet enough that these effects become limiting.

3. Some previous observations

An early proposal involved detection of theionization produced by air showers via radar[18,19]. The first claim for detection of thecharge-separation mechanism utilized relativelynarrow-band techniques at 44 and 70 MHz [1]. ASoviet group reported signals at 30 MHz [20],while a University of Michigan group at theBASJE Cosmic Ray Station on Mt. Chacaltaya,Bolivia [2] studied pulses in the 40–90 MHz range.The collaboration of Allan at Haverah Park inEngland [3] studied the dependence of signals onprimary energy Ep; perpendicular distance R ofclosest approach of the shower core, zenith angley; and angle a between the shower axis and themagnetic field vector. Their results indicate thatthe electric field strength per unit of frequency, En;could be expressed as

En ¼ 20Ep

1017 eVsin a cos y

� exp �R

R0ðn; yÞ

� �mV=m=MHz; ð1Þ

K. Green et al. / Nuclear Instruments and Methods in Physics Research A 498 (2003) 256–288258

where R0 is an increasing function of y; equal (forexample) to ð110710Þ m for n ¼ 55 MHz andyo351:

The Haverah Park observations are consistentwith the model mentioned in Section 2.2 in whichthe pulse’s onset is generated by the start of theshower at an elevation of about 10 km abovesea level, while its end is associated with thegreater total path length (shower þ signal propa-gation distance) associated with the shower’sabsorption about 5 km above sea level. (Theelevation at the CASA/MIA site is about 1450 mabove sea level; the average atmospheric depth is870 g=cm2 [21].)

The Haverah Park observations were subse-quently updated to yield field strengths approxi-mately 12 times weaker than Eq. (1) [4], whileobservations in the USSR gave field strengthsapproximately 2.2 times weaker than (1). Thus,some question persists about the magnitude of theeffect, serving as an impetus to further measure-ments if the RF detection technique is to beemployed as part of a new giant array.

More recent pulse detections include claims forpulses with components below 500 kHz seen byobservers at the AGASA array in Akeno, Japan [5]and a group working at Yakutsk in Siberia [7], andclaims for pulses at VHF frequencies seen bygroups at the Gran Sasso in Italy [6] and atGauhati University in India [8]. There seems to beno unanimity regarding the time duration, genera-tion mechanism, or intensity of these pulses.Related methods have been used to study light-ning-induced pulses [22].

4. CASA/MIA prototype setup

4.1. Description of the CASA/MIA detector

The Chicago Air Shower Array (CASA) [21]was originally constituted as a rectangular grid of33� 33 stations on the surface of the desert atDugway Proving Ground, Dugway, Utah. Theinter-station spacing is 15 m: A station has four61 cm� 61 cm� 1:27 cm sheets of plastic scintil-lator each viewed by its own photomultiplier tube(PMT). When a signal appears on 3 of 4 PMTs in a

station, a ‘‘trigger request pulse’’ of 5 mA with5 ms duration is sent to a central trailer, where adecision is made on whether to interrogate allstations for a possible event. Details of this triggerare described in Ref. [21].

For future reference, we shall denote thecoordinates of each box by ðnx; nyÞ; where�16pðnx; nyÞp16; nx ¼ ðx=15 mÞ; ny ¼ ðy=15 mÞ;and ðx; yÞ denotes the position of the center of thebox to the (East, North) of the center of the array.When this experiment was begun the CASA arrayhad already been reconfigured to remove boxeswith �16pnxp� 13; i.e., the 4 westernmost‘‘ribs’’ of the array. For runs performed in 1998,boxes with nx ¼ 16 had also been removed fromthe array.

The University of Michigan collaborators de-signed and built a muon detection array (MIA) tooperate in conjunction with CASA. It consists ofsixteen ‘‘patches’’, each having 64 muon counters,buried 3 m below ground at various locations inthe CASA array. (See Fig. 1.) Each counter haslateral dimensions 1:9 m� 1:3 m: Four of thepatches, each about 45 m from the center of thearray, lie on the corners of a skewed rectangle;four, each about 110 m from the center of thearray, lie on a quadrangle with slightly differentskewed orientation, and eight lie on the sides andcorners of a rectangle with sides xC7180 m andyC7185 m:

In April of 1991, the CASA/MIA array waspartially disabled by a lightning strike which hitone of the few trees on the site. The array wasrepaired, and an extensive lightning-protectiongrid installed. The grid consisted of wires strungon poles about 15 feet above the array, traveling inthe x; y; and x7y directions. This grid turned outto have significant effect on our choice ofparameters for the RF studies.

During the operation of the present experiment,144 surface Cherenkov detectors [23] were dis-tributed throughout the array. Other additions tothe array, which shall not concern us, included astereographic atmospheric Cherenkov detector(DICE) [24] and an optical facility for commu-nicating with a high-resolution atmospheric fluor-escence detector (HiRes) [25] located on a hilltopseveral miles away.


4.2. Initial RF surveys at CASA/MIA site

In order to determine whether RF pulse detec-tion was feasible at the CASA site, a spectrumanalyzer was used to make a broad survey of theRF noise at the CASA site in various frequencyranges and at various locations. It was determinedthat in the central trailer, the broad-band noiseassociated with various computers, switchingpower supplies, and other electronics was sointense that no RF searches could be undertaken.The same was true to a great extent at any positionwithin the perimeter of the lightning-protection

grid. Moreover, it was deemed unsafe to erect anantenna above that grid within the perimeter of thearray, since any projecting object would defeat thepurpose of the grid.

Surveys just outside the array indicated a muchquieter RF environment. An antenna was placedabout 24 m east of box (16,0), corresponding tox ¼ 263:8 m; y ¼ 0 m; and its signal fed into atrailer located about 10 m closer to the array. Allfurther studies were performed using this config-uration. (See Fig. 1.) Nonetheless, there stillremained a number of identifiable noise sources,which we now describe.

Fig. 1. Geometry of the CASA/MIA array. Small squares denote CASA stations; cross-hatched rectangles denote muon patches.

Large rectangle near center is the central trailer; rectangle to right (east) of the array is RF trailer; symbol ‘‘A’’ denotes placement of

antenna.


4.2.1. Television and FM broadcast stations

The CASA/MIA site is about 100 km southwestof Salt Lake City, at first sight affording areasonably quiet RF environment. However, manytelevision and FM stations in Salt Lake Citybroadcast from a high mountain about 35 kmsouthwest of Salt Lake City, or 65 km northeast ofDugway. These are responsible for a majorcomponent of the RF signal in the range whichis of greatest interest to us. As an example, wesummarize the VHF television stations broad-casting from the above site [26] in Table 1. Thevideo and audio frequencies shown are carrierfrequencies. Video signals are modulated withvestigial-sideband modulation, occupying therange from 1:25 MHz below the carrier frequencyto about 3:5 MHz above it. A color subcarrier lies3:58 MHz above the video carrier. Audio signalsare frequency modulated with deviation notexceeding 250 kHz so as to remain within thetotal allotted bandwidth of 6 MHz for eachchannel. The FM broadcast band, extending from88 to 108 MHz; is packed with strong signals, withthe strongest typically spaced by the 0:8 MHzinterval characteristic of inter-station spacing in alarge urban area.

4.2.2. CASA noise

The CASA boards contain crystals oscillating atvarious frequencies, including 16, 20, and 50 MHz:The behavior of a single CASA board wasinvestigated at the University of Chicago. Thevarious clock signals were detected at shortdistances ðo1 mÞ from the board, but a much

more intense set of harmonics of 78 kHz ema-nated from the switching power supplies. Theseharmonics persisted well above 100 MHz. At144–148 MHz (monitored using an amateur radiotransceiver), they overlapped, leading to intensebroad-band noise.

The above signals were considerably less pro-blematic at the RF trailer. During CASA opera-tion the boards’ clock frequencies and some oftheir harmonics (including 32, 40, and 48 MHz)were detectable. However, noise from the switch-ing power supplies seemed to be at an acceptablylow level.

The CASA boards emit powerful RF pulseswhen digitizing and transmitting data. Thesepulses constituted a major background to ourRF search, and will be discussed in Section 5. Thenoise arrived through the antenna system and notthrough the trigger cable or antenna feed cable, aswas determined by acquiring data with a dummyload in place of the antenna.

4.2.3. Intermittent narrow-band interference

In addition to persistent RF carriers from TVand FM broadcast stations, intermittent signalswould appear from time to time. The strongest ofthese was traced to local narrow-band FMcommunications. This signal was so strong thatdigital filtering methods (to be described below)were powerless to eliminate it. Consequently, anyevent containing such a signal was discarded forfurther analysis.

4.2.4. Low-frequency interference sources

Although the majority of survey work dealt withfrequencies above 25 MHz; some effort was madeto reproduce claims of low-frequency (‘‘LF’’)pulses [5], which for our purposes will be takento involve frequencies below 500 kHz: (The AMbroadcast band contains numerous signals above530 kHz; preventing the study of higher frequen-cies.) Initial surveys were performed using a SonySW-7600G all-band portable receiver and anICOM IC-706 amateur transceiver. However,considerably greater sensitivity was achieved usinga Palomar VLF converter which converts the band10–500 kHz to 3510–4000 kHZ; which was thendetected using the IC-706.

Table 1

Television stations broadcasting from site 65 km northeast of

Dugway

Call sign Channel Band Video Audio Power

(MHz) (MHz) (MHz) (kW)

KUTV 2 54–60 55.25 59.75 45.7

KTVX 4 66–72 67.25 71.75 32.4

KSL-TV 5 76–82 77.25 81.75 33.9

KUED 7 174–180 175.25 179.75 155.0

KULC 9 186–192 187.25 191.75 166.0

KBYU-TV 11 198–204 199.25 203.75 162.0

KSTU 13 210–216 211.25 215.75 112.0


The major source of interference at the site wasa non-directional aircraft beacon (NDB) operatingat the Dugway airport on 284 kHz: Other NDBsand other LF carriers above about 110 kHz weredetectable but considerably weaker. A custom-made filter was procured [27] to suppress thecarrier at 284 kHz and signals from the AMbroadcast band above 500 kHz: This filter wasemployed during some of the low-frequencystudies to be described below.

4.3. Measurement considerations and initial setup

As mentioned above, the location of thereceiving antenna (about 30 m east of the edge ofthe CASA array, at x ¼ 263:8 m; y ¼ 0 m), wasdictated by a compromise between proximity tothe array and reduction of noise. This noise wascarried, to a large extent, by the lightning-protection grid which overlays the array.

It was decided at an early stage to concentrateon the search for horizontally polarized pulses asdescribed in Section 2. Consequently, a broad-band antenna with linear polarization wasadopted. Initial surveys were taken with one ofthe original antennas from the Mt. Chacaltayaexperiments [2], which had been preserved fromthe 1960s. This antenna was a large modelmanufactured for VHF television reception, withsome elements which had been added by theexperimenters to improve low-frequency response.

The Mt. Chacaltaya antenna was mounted on aportable searchlight tower attached to a smalltrailer. The tower could be extended to a height ofabout 35 feet. The antenna was slightly damagedin a collapse of the tower as a result of improperlatching procedures. As insurance against furthersuch incidents, a portable military surplus log-periodic antenna was acquired. This antenna (aDorne and Margolin model to be described below)was found to have superior response in thefrequency range of interest and very robustconstruction (even surviving a subsequent towercollapse), and was adopted for subsequent studies.

The antenna was mounted on the fully-extendedsearchlight tower with its center at a height of 35feet above ground, with the favored direction ofreception arriving from the zenith, and with

arbitrary azimuthal orientation. Data were takenwith two orientations: ‘‘East–West’’ polarizationand ‘‘North–South’’ polarization, both referred tomagnetic North (141 east of true North [28] atDugway). In addition, a projecting arm of themounting bracket was used to suspend a 10-meter-long vertical antenna which was used for the low-frequency surveys.

The bandwidth to be covered by the RF searchwas not initially specified, but to be determined byexperience with survey experiments. Consequently,two main modes were used, a narrow-band modeand a broad-band mode. These are compared inTable 2, where we also list a low-frequency modeused in the LF survey. Their implementation isdescribed in Section 4.4.3.

Some previous investigations (e.g. [2,3]) wereable to detect RF pulses using a ‘‘stand-alone’’trigger based on the reception of transients alone.This possibility was investigated using a broad-band receiver with filters admitting several differ-ent frequency ranges, and demanding coincidencesof signals received in a minimum number ofchannels. It was found that the vast majority ofsuch transients at the Dugway site were notassociated with CASA/MIA events; they wereprobably due to atmospheric discharges. Such‘‘stand-alone’’ transients, in fact, were found toincrease during periods of enhanced atmosphericelectrical activity. As a result, our main resultsconcern RF data taken with a trigger based onlarge CASA/MIA events. We comment further onthe possibility of a ‘‘stand-alone’’ trigger for futureexperiments in Section 6.4.

The trigger was formed at the central CASA/MIA trailer, in a manner to be described in detailbelow. It was communicated to the RF trailer overRG-59 cable. The electrical length of the cable was

Table 2

Modes of filtering

Mode 3 dB bandpass-(MHz)

Narrow-band 25–35

Broad-band 25–250

Low-frequency 0.05–2.5a

aSuppression at 284 kHz and above 500 kHz in some runs.


found to correspond to a pulse delay of 2:15 ms:No evidence for pickup of this trigger pulse fromthe antenna was found. Other methods considered,and rejected in favor of the simpler electricalcommunication, included optical fiber and infra-red sensors.

4.4. Design features

4.4.1. Antenna system

A portable log-periodic antenna manufacturedby Dorne and Margolin, Model # DM ARM 160-5, with a nominal response of 30–76 MHz; wasacquired from FairRadio Co. in Lima, Ohio, forabout $60. (A spare was used for noise studies atthe University of Washington.) Overload protec-tion was provided by two 1N4148 diodes ofopposite polarity connected across the antennaterminals, leading to a maximum output voltage ofabout 70:6 V: A gas discharge tube manufacturedby Alpha/Delta provided lightning protection.Some properties of the antenna are summarizedin Table 3.

4.4.2. RF front-end

The RF amplification stage consisted primarilyof one or two ZFL-500LN low-noise broad-bandpreamplifiers manufactured by Mini-Circuits, andfor certain runs low-noise preamplifiers manufac-tured by ANZAC. Specifications of these pream-plifiers are summarized in Table 4.

4.4.3. Filtering

Table 5 contains a summary of all filters used inthe experiment with the exception of the 284 kHzfilter [27] described previously. These filters aremanufactured by Mini-Circuits; they were ob-tained with tubular cases fitted with BNC con-nectors.

A typical ‘‘narrow-band’’ configuration de-scribed in Table 2 involved feeding the signalfrom the antenna through the feedline, a BHP-25filter and a BLP-30 filter with combined 3 dBpoints of 25 and 35 MHz; a ZFL-500LN pre-amplifier with 26 dB of gain, a BBP-30 filter with3 dB points 25 and 35 MHz; another Mini-CircuitsZFL-500LN preamplifier with 26 dB of gain, anda BHP-250 filter to suppress any high-frequency

noise. (Some data runs involved permutations ofthese components. The above configuration wasfound to minimize feed-through of preamplifiernoise. Some runs involved a dual ANZACpreamplifier instead of a ZFL-500LN.)

A ‘‘broad-band’’ configuration involved thesame feedline and BHP-25 filter, a single ZFL-500LN preamplifier, and a BLP-250 filter. A ‘‘low-frequency’’ configuration involved the feedline, aBLP-1.9 filter and a ZFL-500LN preamplifier,with a 284 kHz notch filter inserted before or afterthe BLP-1.9 in some runs. The notch filter alsocontained a roll-off above 500 kHz:

4.4.4. ‘‘Large-event’’ trigger and design

A trigger based on the coincidence of seven ofthe eight outer muon ‘‘patches’’ (see Fig. 1) was setto select ‘‘large’’ showers in the following manner.Each muon patch was set to produce a trigger

Table 4

Properties of preamplifiers used for RF studies

Manufacturer Model DC power Gain Frequency

(V) (dB) range (MHz)

Mini-Circuits ZFL-500LN 13.6 26 DC–500

ANZAC AM-107 18 10 1–500

Table 3

Properties of log-periodic antenna used for RF studies

Nominal frequency range (MHz) 30–76

Usable frequency range (MHz) 28–170

Number of elements 9

Dimensions (m) 3� 3

Feedline RG-58U 60 feet

Table 5

Filters used in RF data acquisition

Model Type 3 dB point(s)

(MHz)

BLP-1.9 Low-pass 2.5

BHP-25 High-pass 25

BLP-30 Low-pass 35

BBP-30 Bandpass 25 35

BLP-250 Low-pass 250


pulse of length 5 ms and amplitude �120 mV whenn of its 64 counters registered a minimum-ionizingpulse within 5:2 ms of one another. For engineeringruns (until 12/28/96), n was set equal to 4, while forlater runs it was increased to 5 to favor largershowers and reduce noise. The pulses were thencombined in two groups of 4, feeding through two2X attenuators into two fan-in/fan-outs (to avoidsaturation of inputs) and the resulting pulsesfurther combined to produce a summed pulse.This signal was fed to a LeCroy 821 Discriminator,whose output was amplified to an amplitude ofabout �6 V and then sent over RG-59 cable to theRF trailer (see Fig. 1). The trigger pulse at the RFtrailer had an amplitude of about �2:4 V and aduration of 1 ms:

The above trigger was estimated to correspondto a minimum shower energy of somewhat below1016 eV; based on the integral rate [29] at 1018 eVof 0:17=km2=day=sr: At this level good correlationcould be established between trigger pulses andevents recorded by the CASA data acquisitionsystem.

Only shower radiation that is stronger than3 mV=m=MHz can exceed the average noise levelat CASA site by three standard deviations or more(Section 4.6). According to the original HaverahPark results (Eq. (1)), a typical shower that wouldlead to such radiation is a vertical shower ofenergy 1017 eV or higher at a distance of 210 m: Ifthe rate for showers with energy greater than E

behaves as 1=E2; showers above 1017 eV would beexpected to occur with a rate of 17=km2=day=sr:Since RF detection relies on muon triggering, theantenna can only detect radiation from thoseshowers whose cores pass inside the rectangle ofthe array. Just about 0:06 km2 of the array arealies inside the 210 m radius from the antenna. Withthe solid angle of observation limited by a zenithangle of 501; one expects about 2.25 detectableshower pulses per day.

4.4.5. Data acquisition

A Tektronix TDS-540B digitizing oscilloscoperegistered filtered and preamplified RF data on arolling basis. These data were captured and storedon hard disk using a National Instruments GPIBinterface upon receipt of a large-event trigger.

Data were taken using various computers atdifferent times, allowing for analysis both at theUniversity of Washington and at Chicago. TheWashington system used a Macintosh Quadra 950running Labview, with a latency time of about 8 sbetween events, while the Chicago system usedeither a Dell XPS200s desktop or a Dell LatitudeLM laptop running a C program adapted fromthose provided by National Instruments, with alatency time of about 2 s: Each trigger caused50 ms of RF data, centered around the trigger andacquired at 1 GSa=s; to be saved.

4.4.6. Rates and off-line processing

The total trigger rate ranged between about 20and 50 events per hour, depending on the value ofn ¼ 4 or 5 of muon counters chosen to generate apatch trigger pulse and on intermittent sources ofnoise sometimes present in the trigger system.Concurrently, the CASA on-line data acquisitionsystem was instructed via a special program calledMUTRIG to write files of events in which at least7 out of the 8 outermost muon patches produced apatch pulse. These files, one for each CASA run,typically overlapped with the records taken at theRF trailer to a good but not perfect extent [30] as aresult of occasional noise on the trigger line.Moreover, an undiagnosed timing problem occa-sionally caused the loss of a muon trigger pulse forcertain large events recorded by MUTRIG.

4.4.7. Off-line overload rejection

Events were typically recorded at a gain suchthat the maxima and minima corresponded toabout 2/3 of the dynamic range of the oscillosco-pe’s 8-bit data acquisition system (ranging from�128 to 127 digitization units). Local intermittentmonochromatic RF signals occasionally saturatedthis dynamic range. Such events were rejected off-line by discarding any cases in which the maximaand minima exceeded 100 digitization units. In theconfiguration used for the final bounds on pulseamplitudes, corresponding to an oscilloscopesetting of 5 mV per division of 25 digitizationunits, we thus rejected all signals corresponding topreamplifier peak outputs greater than 720 mV:In some cases, with oscilloscope settings of 20 mVper division, we rejected signals with preamplifier


peak outputs greater than 780 mV: In all casesthese voltages were well below the manufacturer’sspecified limit of 7400

ffiffiffi2

pmV ð3 dBmÞ; and with-

in a satisfactorily linear range of preamplifierresponse.

4.4.8. Calibration

The average gain Gant of the antenna in itsforward direction rises from about 3 dBi (decibelswith respect to an isotropic radiator) at 30 MHz toa peak of about 5 dBi at 50 MHz, slowlydecreasing to 4 dBi at 76 MHz [31]. We shall takean average gain of 4 dBi ðGant ¼ 2:5Þ over thefrequency range of interest.

More precise calibration would involve model-ing of the gain pattern using a program such asEZNEC [32], and integrating over directions ofexpected signal arrival. This modeling also wouldhave been useful in order to emulate thefrequency-dependent phase distortion induced bythe antenna, but it was not found possible toobtain a sufficiently close fit to the antenna’smeasured standing-wave-ratio characteristics totake such a model seriously. Certainly this pointshould be addressed in any future studies. Onemight also utilize sources of known strength suchas amateur radio satellites broadcasting on29:4 MHz; FM and television stations, and galac-tic and solar noise. The existing data containsignals from FM and television stations broad-casting near Dugway, some of whose fieldstrengths are well enough known that they maybe usable for calibration. Alternatively, for futurework it would be helpful to calibrate antennas onan antenna range at some distance from animpulse generator, broadcasting through abroad-band antenna with already-determinedcharacteristics.

4.5. Signal processing

4.5.1. Fourier methods

In order to remove strong Fourier componentsassociated with signals which were approximatelyconstant over the duration of each data record, ashort MATLAB routine was written to performthe fast Fourier transform of the signal andrenormalize the large Fourier components to a

given maximum intensity. Fig. 2 shows the fastFourier transform of a typical RF signal beforeand after this procedure was applied. In each casethe data were acquired using the ‘‘wide-band’’filter configuration, whose response cuts offsharply below 23 MHz:

The effect of digital filtering on detectability of atransient is illustrated in Fig. 3. The top panelshows the RF record whose Fourier transform wasgiven in Fig. 2, on which has been superposed asimulated transient of peak amplitude 14.5 digiti-zation units. (The data acquisition scale rangesfrom �128 to þ127 digitization units; one scaledivision on the oscilloscope corresponds to 25units.) The transient is invisible beneath the largeamplitude associated with television and FM radiosignals. The middle panel shows the result afterapplication of the Fourier coefficient shrinkagealgorithm.

The event in Figs. 2 and 3 consisted of 32,768data points obtained at a 1 ns sampling interval,with the trigger at the 20,000th point. The

Fig. 2. Top panel: Fourier spectrum (in arbitrary units) of RF

signals acquired at Dugway site using high-pass 25 MHz and

low-pass 250 MHz filters. Prominent features include video and

audio carriers for TV Channels 2, 4, 5, 7, and 11 (see Table 1 for

frequencies), and the FM broadcast band between 88 and

108 MHz: Bottom panel: Fourier spectrum (same vertical scale)

after renormalization of large Fourier components to a

magnitude chosen here to be 3:16� 103: In practice best

sensitivity to transients was obtained by renormalizing to a

magnitude of 103:


frequency resolution in the fast Fourier transformis thus 500 MHz (the Nyquist frequency) dividedby 16,384, or about 30 kHz: This permits ratherfine distinction between frequencies containing astrong carrier and those which correspond to itsweaker sidebands. At the same time, it permitstime resolution to be preserved, allowing for theexamination of rather rapid transients. To theextent that these transients do not contain Fouriercoefficients exceeding a pre-determined threshold,they should be relatively unaffected by theshrinkage algorithm in the absence of interferingsignals. However, since at Dugway signals innearly the whole FM band (88–108 MHz) exceedthe threshold, some distortion is unavoidable usingsuch a method. In obtaining bounds on pulseamplitudes we therefore employ a method invol-ving the comparison of Fourier power in a giventime window with the average power obtained

over the whole data record for each Fouriercomponent. This method is described below.

4.5.2. Time-frequency analyses

One can perform a fast Fourier transform usinga small time window (typically 1024 ns) which isadvanced sequentially through the data record,typically in steps of 100 ns: The frequency resolu-tion of any given ‘‘snapshot’’ is then 500 MHzdivided by (typically) 512, or a bit better than1 MHz: A two-dimensional display of time vs.frequency then allows one to distinguish shorttransients (with components over many frequencybins) from continuous RF sources (with compo-nents in narrow frequency ranges over the entiretime record). One such plot appears in Fig. 11,Section 5.3.1, below. In practice one may wish tosuppress frequencies corresponding to the wholeFM band and known TV stations, so as not tooverload the dynamic range of the display. Analternative method [33] is to renormalize eachpoint in time–frequency space so that deviations

from the average in each frequency bin aredisplayed. This method is described further inSection 5.2. It was used for the main part of dataanalysis.

4.5.3. Wavelet techniques

The wavelet package Wavelab [34] contains adenoising routine which was adapted for ourpurposes. While an exhaustive search for opti-mized methods was not performed, good results inreducing noise levels were obtained using a 10-point symmlet routine with level L ¼ 4 [35]. Anexample of a denoised signal is shown in thebottom panel of Fig. 3. Here a simulated signal ofpositive peak amplitude 14.5 digitization units hasbeen added to an RF record otherwise free oftransients. The effect of wavelet denoising is toreduce the amplitude of random high-frequencyfluctuations while preserving edge effects such astransients.

4.6. Signal simulation

We wished to quantify the improvement asso-ciated with each method of signal processing. Wethus simulated the expected signal by generating it

Fig. 3. Effect of Fourier coefficient shrinkage on detectability

of a transient. Top panel: raw RF record (in arbitrary units)

with simulated signal superposed. Middle panel: record (same

scale) after Fourier coefficient shrinkage. Here a maximum

Fourier coefficient magnitude of 103 (in the units of Fig. 2) has

been imposed. Bottom panel: the same record after denoising

with a 10-point symmlet level L ¼ 4 routine [35].


using an arbitrary waveform generator, feeding itthrough the same preamplifier and filter config-urations used for data acquisition, and super-posing it on records otherwise free of transients.We successively reduced the amplitude of thesuperposed test signal until it could not bedistinguished from random noise peaks, therebyobtaining an estimate of sensitivity.

A Hewlett-Packard Arbitrary Waveform Gen-erator was used to generate signals whose char-acteristics are illustrated in Fig. 4. These signalswere taken to have the form f ðtÞ ¼ yðtÞAt2ðe�Bt �Ce�DtÞ with the coefficient C chosen so that f ðtÞhas no DC component, and D corresponding to along duration of the negative-amplitude compo-nent. For all pulses we chose D ¼ B=20; so thatC ¼ ð8000Þ�1 cancels the DC component. TheFourier components of the test pulse fall offsmoothly with frequency. The initial t2 behaviorwas chosen so that both the test pulse and its firstderivative vanish at t ¼ 0; as might be expected fora pulse from a developing shower.

The simulated pulses are summarized in Table 6.Instead of quoting the value of A; we quote themaximum positive value of the pulse, both before

and after filtration and preamplification. Thesevalues of Vpk reflect choices for convenience indisplay on the oscilloscope, and are otherwisearbitrary.

The shape of the pulse of Fig. 4 is affected bypreamplification and filtration as shown in Figs. 5(broad-band) and 6 (narrow-band). The noise inthese figures and the sharp feature at 125 MHz inFig. 5 are associated with the system used to

Fig. 4. Analytic depiction of typical pulse presented to filter-

preamplifier configuration. Top panel: time dependence of pulse

f ðtÞ ¼ yðtÞt2½e�0:4t � e�0:02t=8000� (t in ns); bottom panel: Four-

ier spectrum of pulse (calculated analytically). In the top panel,

the short bar above the pulse denotes d; the time difference

between onset and maximum, while the longer bar below the

pulse denotes D; the duration of the positive component.

Fig. 5. Test pulse of Fig. 4 after broad-band filtration ð>25 MHzÞ and preamplification. Top panel: time dependence

of pulse; bottom panel: Fourier spectrum of recorded pulse for

�20 msptp12:768 ms:

Fig. 6. Test pulse of Fig. 4 after narrow-band filtration (25–

35 MHz) and preamplification. Top panel: time dependence;

bottom panel: Fourier spectrum of recorded pulse for

�20 msptp12:768 ms:


generate the test pulse, and the fact that theFourier transform is taken over a much longertime than the duration of the pulse.

Systematic studies of signal-to-noise ratios havebeen performed so far only for the simulatedpulses with d ¼ 5 ns applied to a broad-band frontend ((b) in Table 6). The value of d is a measure ofthe distance R of closest approach of the showercore [3]. This choice corresponds to a typicaldistance RC200 m: A typical pulse of this typegave a front end output of 21 mV peak-to-peak,acquired at an oscilloscope sensitivity of 5 mV perdivision. Each division corresponds to 25 digitiza-tion units, so the peak-to-peak range is about 104digitization units, or slightly less than half thedynamic range (255 units, or 8 bits). Positive andnegative peaks are thus about 52 digitization unitseach.

The stored test signal is then multiplied by ascale factor and added algebraically to a collectionof RF records in which, in general, randomlyoccurring transients will be present. One theninspects these records to see if the transient can bedistinguished from random noise.

For the broad-band data we estimated thatpulses with input voltages corresponding to about1/5 the original test pulse amplitude can bedistinguished from average noise (not from noise

spikes!). Since the original test pulse had a peakvalue of 1:3 mV; this corresponds to sensitivity toan antenna output of about VpkC260 mV: Theability to detect such a pulse with an effectivebandwidth of about 30 MHz corresponds to athreshold sensitivity at the level of order3 mV=m=MHz (see Appendix B).

Preliminary studies of simulated pulses appliedto the narrow-band front end suggest a consider-ably poorer achievable signal-to-noise ratio, de-spite the expectation that the signal should have alarge portion of its energy between 23 and37 MHz: It appears difficult to detect a pulse fromthe antenna below about 0:7 mV; which for abandwidth of 14 MHz corresponds to a thresholdsensitivity of 7 mV=m=MHz; not sufficient for ourpurposes. Studies of possible improvements of theanalysis algorithm for the narrow-band data arecontinuing.

5. Results

5.1. Event sample

More than 20 000 triggers, obtained undervarious conditions of filtering, preamplification,and noise reduction during the period February1997–March 1998, are summarized in Table 7.Events recorded on a Macintosh Quadra 950 andthose recorded on a Dell LM Latitude laptopcomputer are listed separately because the powersupply of the latter introduced spurious transients.Our initial analysis concentrated on data takenwith the Macintosh. For reasons mentionedabove, we consider only the broad-band data atthis time. Thus, our usable sample consists of over9000 CASA triggers. In addition, periodic forcedtriggers were taken to monitor noise activity notassociated with CASA operation.

The broad-band data recorded on the Macin-tosh Quadra, summarized in Table 8, are sub-divided into several categories. Data were takenwith both East–West (EW) and North–South (NS)antenna polarizations. Moreover, since noise fromCASA boxes was found to be a significant sourceof RF transients, data were taken with some or allCASA boxes disabled by turning off the high

Table 6

Parameters of test signals

B d D Vpk Vout S

ðns�1Þ (ns) (ns) (mV) (mV) (mV/div)

0.8 2.5 12 1.2 (a) 86 20

6.0 (b) 124 20

0.4 5 24 0.7 (a) 70 20

1.3 (b) 21 5

0.2 10 47 0.7 (a) 71 10

7.0 (b) 67 10

0.1 20 95 1.5 (a) 75 10

7.6 (b) 32 5

d is the time between pulse onset and maximum, while D is the

duration of the positive component of the pulse. Vpk is the peak

(positive) input voltage to the filter-preamplifier configuration.

The letter after the peak voltage denotes (a) narrow-band (25–

35 MHz) or (b) broad-band ð> 25 MHzÞ configuration (see

Section 4.3). Vout is the peak-to-peak amplitude of the pulse

emerging from the filter-preamplifier configuration. S is the

scale factor with which data were recorded on oscilloscope.


voltage (HV) supply to the photomultipliers. Evenwhen HV is supplied only to boxes that are furtherthan 100 m from the antenna, the RF transientsfrom these boxes provide a strong background.(See the discussion in Section 5.2 and Fig. 10below.) One is unlikely to distinguish the RFpulses of the showers from this noise. Therefore,we concentrated on data with CASA HV off, with859 triggers taken with EW antenna polarization(21.88 active hours) and 582 triggers taken withNS antenna polarization (23.25 active hours). Forsubsequent sensitivity calculations, a subset ofdata was used consisting of 756 EW triggersð17:25 hÞ and 528 NS triggers ð21:12 hÞ: Theremaining data with CASA HV off occurred invery short runs (52 EW triggers and 19 NStriggers) or was contaminated by local VHFcommunication signals (51 EW triggers and 35NS triggers). Data with CASA HV on or partiallydisabled were not used for the present analysis.

5.2. Characterization of transients associated with

CASA operation

Several means were used to characterize tran-sients. One method with good time resolutioninvolved the shrinkage of large Fourier coefficientsto a fixed maximum intensity, as in Figs. 2 and 3.

Another, which we have used for results to bepresented below, involves generation of a time-vs.-frequency intensity plot by Fourier-transforming1024-ns subsets of the 50 ms data record, spaced by100 ns steps. Since the data are sampled at 1 nsintervals, the frequency resolution of this methodis thus about 1 MHz: The intensity Sðn; tÞ is thenaveraged over time t for each frequency n to forman average intensity %SðnÞ: The quantity Sðn; tÞ= %SðnÞis an estimate of the degree to which the intensityat a given frequency n and time t exceeds theaverage over the 50 ms sampling time. We thenaverage Sðn; tÞ= %SðnÞ over n to search for events inwhich the average intensity at a given time isexceeded in many simultaneous frequency bands.

One can then search for peaks of each datarecord (there may be several peaks in a record),plotting intensity of their maxima against timerelative to the trigger. One such plot is shown inFig. 7 for a data run in which CASA HV wasdelivered to all boxes. A strong accumulation oftransients, mostly with intensity just above thearbitrarily chosen threshold (mean + 3 s for eachtrigger sample), is visible at times �5 to �7 msrelative to the trigger. In a comparable plot for arun in which CASA HV was completely disabled(Fig. 8), only a small accumulation at times �6 to�7 ms is present. This excess appears due to

Table 7

Triggers associated with CASA operation taken under various conditions

Front end Macintosh Dell Total

Narrow-band 5849 ð139:78 hÞ 1952 ð48:97 hÞ 7801 ð188:75 hÞBroad-band 9603 (272.57 h) 5416 ð121:62 hÞ 15 019 ð394:18 hÞLow-frequency 0 505 ð17:67 hÞ 505 ð17:67 hÞ

Total 15 452 ð412:35 hÞ 7873 ð188:25 hÞ 23 325 ð600:6 hÞ

Table 8

Broad-band data recorded on Macintosh Quadra

Antenna polarization CASA HV on CASA HV off Partial CASA HV Total events

East–West 4966 ð119:03 hÞ 859 ð21:88 hÞ 1957 ð53:08 hÞ 7782 ð194:0 hÞNorth–South 696 ð30:53 hÞ 582 ð23:25 hÞ 543 ð24:78 hÞ 1821 ð78:57 hÞ

Total events 5662 ð149:57 hÞ 1441 ð45:14 hÞ 2500 ð77:87 hÞ 9603 ð272:57 hÞ


transients with predominantly high-frequencycomponents (over 100 MHz). Since signal pulsesare expected to have more power below 100 MHz(see Fig. 5, bottom) we believe that this accumula-tion is not due to shower radiation, but most likelyarises from the muon patches, one of which iswithin 75 m of the antenna.

A typical transient occurring in a run withCASA HV on is shown in Fig. 9. The transientsare highly suppressed (though not in all runs)when CASA boxes within 100 m of the antennaare disabled, as shown in Fig. 10.

The time distribution of pulse maxima above anarbitrary threshold for 880 pulses detected with

Fig. 7. Top panel: intensity-vs.-time plot for maxima of 880

pulses recorded in 698 triggers in January 1998 with CASA HV

supplied to all stations. Bottom panel: time distribution of

transients. All events recorded with East–West antenna

polarization.


pulses in 691 triggers recorded in January 1998 with CASA HV

disabled. Bottom panel: time distribution of transients. All

events recorded with East–West antenna polarization.

Fig. 9. Signal of a typical transient associated with CASA

operation. Top panel: before denoising; bottom panel: after

denoising.


pulses recorded in 620 triggers in January 1998 with CASA HV

disabled for boxes within 100 m of antenna. Bottom panel: time

distribution of transients. All events recorded with East–West

antenna polarization.


CASA HV on (one run from January 1998composed of 698 files of data) is shown in thebottom panel of Fig. 7. The mean arrival time isabout 6 ms before the trigger, with a distributionwhich is slightly broader for pulses arriving earlierthan the mean. This broadening may correspondto some jitter in forming the trigger pulse from thesum of muon patch pulses.

As mentioned earlier, the time for the triggerpulse to propagate from the central station to theRF trailer was measured to be 2:15 ms: One expectsa similar or slightly greater travel time for pulses toarrive from muon patches to the central station(see Fig. 1). Moreover, the muon patch signalsare subjected to delays so that they all arrive at thecentral station at the same time for a verticallyincident shower. Thus, the peak in Fig. 7 isconsistent with being associated with the initialdetection of a shower by CASA boxes. Thiscircumstance was checked by recording CASAtrigger request signals simultaneously withother data; they coincide with transients such asthose illustrated in Fig. 9 within better than1=2 ms:

The RF signals from the shower are expected toarrive no later than, or at most several hundrednanoseconds before, the transients associated withCASA operation. They would propagate directlyfrom the shower to the antenna, whereas transientsfrom CASA stations are associated with a longertotal path length from the shower via the CASAstation to the antenna. There will also be somesmall delay at a CASA station in forming thetrigger request pulse. Thus, we expect a genuinesignal also to show up around 6–7 ms before thetrigger.

The time coincidence of the CASA RF transi-ents and the shower signals is a significant ob-stacle to detecting genuine pulses. Therefore,data with CASA HV on or partially disabledwere not used for the present analysis. As weshow below in Sections 5.3.1–5.3.3, no significantpeak is visible around 6–7 ms before the triggerfor data recorded with CASA HV off. The upperlimit on the rate of events giving rise to such apeak can be used to set a limit on RF pulsesassociated with air showers, as we demonstrate inSection 5.3.4.

5.3. Estimated upper bounds on broad-band signals

As mentioned in Section 5.1, the followingdiscussion is based on 17.25 active hours of dataaccumulation with EW antenna polarization and21:12 h with NS antenna polarization. The smallduration of this subset of data limits its sensitivityto RF signals from the shower.

5.3.1. Criteria used to distinguish noise and signal

transients

The main difficulty associated with pulse detec-tion is that signal pulses are not easily distinguish-able from large spurious pulses originating fromatmospheric discharges. Both air shower pulsesand these background noise pulses can consider-ably exceed the average noise level. Several criteriacan be used to distinguish signal pulses from noise.The conventional criteria of the previous studieshave been that the pulse should be (1) larger thanthe average noise level by some small specifiedamount, (2) time coincident with shower particles,and (3) bandwidth limited [3]. All these criteriawere adopted in this study and one more has beenadded: The pulse should have approximatelyuniform distribution over frequency within itslimited bandwidth (see (c) below).

We now note the particular criteria used todistinguish signal pulses in this study.

(a) Pulse magnitude. Continuous RF interfer-ence in each frequency channel was removed byadvancing a moving 1024-ns window in 100 nssteps through the data record to produce a time-vs.-frequency plot (Section 4.5.2) and then usingthe averaging procedure described in Section 5.2.Defining the average signal as 1 (in arbitraryunits), the pulse threshold in each event was takento be the larger of either (a) the mean plus threestandard deviations, or (b) 1.8 (in the same units).The former permitted removal of an average noiselevel; the latter discriminated against small noisetransients. The final result was not affected by thechoice of the factor 1.8 since the subsequentanalysis (Section 5.3.3) used a considerably higherthreshold.

(b) Limited bandwidth of pulses. Broad-bandfiltering limits the frequency range to 23–250 MHz(Section 4.4.3). The investigation of the simulated


pulses on a two-dimensional-plot of intensity vs.time and frequency suggested that, unlike somestrong noise transients, the signal pulse intensitydeclines drastically in the range above approxi-mately 100 MHz (Fig. 11). This feature is con-sistent with theoretical predictions for theshower pulse spectrum [36]. It can be chosen as acriterion for separating noise and signal tran-sients. The ratio of mean intensities averaged over23–100 MHz relative to that averaged over100–250 MHz was found to be greater than 1 forall simulated pulses and smaller than 1 for somenoise pulses.

One can consider intensities averaged over apart of the whole frequency range. To facilitateseparation of signal transients it is preferable tochoose a region where the signal-to-noise ratio isparticularly large. Unfortunately, the whole regionfrom 23 to 100 MHz cannot be effectively used forthis purpose. The 54–82 MHz range is occupied byTV channels 2, 4 and 5, which leads to high noiselevels. The same is true for the whole FM band(88–108 MHz) (Section 4.2.1). However, this is notthe case in the 24–54 MHz range. The noise level

in this range is mostly uniform, and simulatedpulse intensities are particularly large there incomparison with the noise level. The assumptionthat the 24–54 MHz range provides the bestsignal-to-noise intensity ratio has been tested.The results for this range have been comparedwith the ones obtained in the 10–54 MHz and 24–86 MHz regions and were found to be superior.Subsequently, the range of 24–54 MHz was chosenas the main region of investigation.

After that, it was natural to choose the ratio ofmean intensities averaged over 24–54 MHz rela-tive to that averaged over 55–250 MHz at themoment of each pulse as a criterion for discrimi-nating noise and signal pulses. For all simulatedpulses this ratio was greater than 1. All pulses forwhich this ratio was smaller than 1 were assumedto be noise transients and discarded. Also, a ratioparameter threshold other than 1 can be chosen.The parameters that provided best results werefound to lie between 1.4 and 1.8 (Section 5.3.4).

(c) Approximately uniform distribution of pulse

intensity over frequency in the 24–54 MHz range.The most intense noise transients that met criteria(a) and (b) were found to display a peculiarfeature: Their intensities were concentrated in asmall region of approximately 10 MHz widthsomewhere in the 24–54 MHz range. This non-uniformity allowed such pulses to be ruled out. Ifthe pulse intensity, integrated over any 9 MHzwidth window (in the 24–54 MHz range), wasgreater than the intensity integrated over theremaining 21 MHz; then such a non-uniform pulsewas discarded as a noise transient. The reason forchoosing a 9 MHz width window was that mostsimulated pulses passed this test, while many noisetransients did not.

The effectiveness of these three criteria isillustrated in Table 9. For simulated pulses thatare stronger than 3:43 mV=m=MHz the combina-tion of criteria (b), (c) and a very high intensitythreshold provides a 84:1=4:75E18 times increasefor their relative fraction with respect to noisetransients.

5.3.2. Method outline

The time coincidence of the pulse with airshower particles implies that a signal pulse should

Fig. 11. Simulated pulse (horizontal band at 0 ms) and noise

transient (horizontal band at about 15 ms) on a two dimensional

plot of intensity (grayscale) vs. time (vertical axis) and

frequency (horizontal axis). Unlike the simulated pulse, the

noise transient contains high frequency components. Grayscale:

black color denotes the highest intensities, white the lowest.

Vertical bands indicate continuous RF sources in the 54–

200 MHz range.


be looked for in the range between �7 and �6 ms(Section 5.2), which will be referred to in whatfollows as ‘‘the interesting time bin’’. It isimportant to note that the aforementioned testcriteria are not efficient if applied only to thepulses found in this time bin. Indeed, some noisepulses in the bin meet all criteria. Hence, acceptingall the pulses that pass this test would notguarantee that signal pulses are present amongthem at all. We developed a different approach.

The time distribution of noise pulses is assumedto be uniform. Hence, the following technique canbe adopted. First, the time distribution histogramof the pulse maxima (from the whole data run) canbe plotted. Then, in the absence of signal pulses,the number of pulses in a time bin should obey aPoisson distribution with the average being equalto the average pulse number per bin. Suppose thatan accumulation of pulses in the interesting timebin ð�7;�6Þ ms is large enough that its probabilityaccording to the Poisson distribution is less than5%. Then this signifies the presence of signalpulses with a confidence level of 95%.

Thus, a sufficiently large relative accumulationof entries in the interesting time bin was adoptedas a key criterion in search of signal pulses.

5.3.3. Detailed description

A routine was designed to scan all events in thewhole data run and select the transients thatpassed criterion (a) in Section 5.3.1. The ratioparameter (see above) and uniformity parameter(1, if criterion (c) was satisfied, and 0, if not) wererecorded along with time relative to the trigger and

intensity of a transient. The intensity vs. time plotof pulse maxima selected in this manner for thedata taken with East–West antenna polarization isshown in Fig. 12.

In order to be detectable, signal pulses should bestronger than the average noise transient, whoseintensity equals 2.5 as a result of the specificcriteria imposed. Hence, it is reasonable to set theintensity threshold sufficiently high to enhance therelative accumulation in the ð�7;�6Þ ms time bin.One can set a high threshold and determine thenumber of pulses that pass through it. Divided by

Table 9

Fraction of noise pulses passing criterion (a) that can also pass criteria (c) and (b) with ratio parameter threshold of 1.4, and whose

maximum intensities are larger than some very high intensity threshold fraction of simulated pulses of different strengths (in

mV=m=MHz), that can pass criteria (c) and (b) with ratio parameter threshold of 1.4, and whose maximum intensities (after they are

superimposed on noise) are larger than the same high intensity threshold. The strengths of the pulses are chosen to be stronger than 1=n

times an original test pulse amplitude of 13:7 mV=m=MHz; n ¼ 2; 3; 4;y; 7

Noise pulses Simulated pulses that are stronger than

6.85 4.57 3.43 2.74 2.28 1.96

mV=m=MHz

North–South 4.47% 94.1% 91.7% 85.2% 66.9% 47.7% 36.7%

East–West 4.75% 98.8% 93.4% 84.1% 67.7% 48.7% 41.4%

Fig. 12. Intensity vs. time plot for maxima of transients in 756

files of data with East–West antenna polarization and CASA

HV off. The horizontal line denotes the threshold taken to lie at

the level of the 17th strongest pulse. Only criterion (a) of

Section 5.3.1 was employed, resulting in a large (1367) number

of entries.


number of bins, this number gives the averagepulse number per bin. This, in turn, can be used asan average value of the Poisson distribution todetermine whether the probability of the observedaccumulation in the interesting bin is less than 5%.

The effectiveness of this technique depends onthe choice of intensity threshold. If the threshold istoo low, the histogram includes many noise pulses.Then, the signal pulse accumulation in the inter-esting time bin becomes too small to be distin-guished from statistical fluctuations. If thethreshold is too high, it may cut out some signalpulses and the remaining ones may not make up asignificant accumulation. The choice of the opti-mum threshold is discussed below.

Optimum intensity threshold. Suppose we lookfor an accumulation of 2 or more entries. Suchan accumulation is significant (i.e., its probabilityis p5%) if the average number of pulses perbin is about 0.355. Indeed, according to Poissondistribution, Pð0 entriesÞ ¼ expð�0:355ÞE0:701;Pð1 entryÞ ¼ 0:355 expð�0:355ÞE0:249; so PðX2 entriesÞ ¼ 1� 0:701� 0:249 ¼ 0:05: Since thestandard histogram used in the study contained48 bins (of 1 ms each), the average value of 0.355pulses per bin would correspond to a total numberof 0:355 48E17 pulses. These considerationssuggest that the intensity threshold would nothave some fixed value but would correspond to theintensity of the 17th strongest pulse (see Fig. 12).Then, the total number of entries in the histogramis 17 and the average number of entries per bin isabout 0.355. So, 2 or more entries in the interestingbin, if observed, would have the probability of 5%and would reveal the presence of signal pulses with95% CL.

Naturally, the probability of 3 or more entrieswould be even smaller and approximately equalto PðX3 entriesÞ ¼PðX2 entriesÞ �Pð2 entriesÞ ¼0:05� 0:3552=2! expð�0:355ÞE0:006: That is, ifsuch an accumulation were observed, the presenceof signal pulses could be claimed with a confidencelevel of 99.4%. However, in reality it is unlikelythat signal pulses could be detected with such aconfidence level. To improve the detectionchances, it is advantageous to lower the thresholdto the 39th strongest pulse. This sets the averagenumber of entries per bin to 39=48E0:813 and

makes the probability of 3 entries equal to 5%.The threshold of the 39th strongest pulse is thelowest one that still guarantees a confidence levelof at least 95%.

Thus, the convenient threshold depends on thesignificant accumulation number one is lookingfor. For any particular accumulation, one canchoose the optimum threshold which wouldguarantee a confidence level of at least 95%. Thesignificant accumulation number and the corre-sponding optimum threshold can be found inTable 10.

This method did not reveal any significantaccumulation in the interesting time bin. So far,however, only criterion (a) and intensity thresh-olds were applied to detected pulses. As wasalready mentioned in the beginning of this Section,the ratio and uniformity parameters were recordedfor each simulated or noise pulse. This made iteasy to impose criterion (b) with different ratio

Table 10

Significant accumulation of entries in the interesting time bin

and the corresponding optimum threshold (calculated accord-

ing to Poisson distribution)

Number of entries

in the interesting

time bin one is

looking for

Average number

of entries per bin

at which the

probability of this

accumulation

becomes p5%

Corresponding

total number of

entries in the 48

bin histogram

(optimum

threshold)

2 0.355 17

3 0.817 39

4 1.366 65

5 1.970 94

6 2.613 125

7 3.285 157

8 3.980 191

9 4.695 225

10 5.425 260

11 6.170 296

12 6.924 332

13 7.690 369

14 8.464 406

15 9.245 443

16 10.035 481

17 10.832 519

18 11.635 558

19 12.443 597

20 13.256 636


parameter thresholds and criterion (c). Theirapplication should have increased the ratio ofsignal pulse number to noise pulse number.Unfortunately, no significant accumulation hasbeen detected (see Fig. 13). This means that signalpulses are quite rare, so that the resultingaccumulation is not significant. However, upperlimits can be placed on the rate (in h�1) of signalpulses that are stronger than some fixed value.This will be our aim for the next subsection.

5.3.4. Upper limits on the rate

The total number n of observed transients in theinteresting time bin consists of both noise andsignal events. The former are Poisson-distributedwith known average m: The latter obey a binomialdistribution with a known probability P to passthresholds and an unknown total number N ofsignal events contained in the run. Using a unifiedapproach to the statistical analysis of small signals[37], we construct 95% confidence belts forunknown N : For any choice of imposed thresholds,the lower end of confidence intervals is 0, i.e.,only upper limit on the total number of signals inthe run can be placed.

Probability PsðkÞ that the interesting bin contains

k signal events. Formula (1) (Section 3) shows thatEn is directly proportional to primary energy Ep:The differential rate of primaries is known to fallapproximately as 1=E3

p [29]. Similarly, the differ-ential rate of En’s should be proportional to 1=E3

n :Simulated pulses of different strength En greater

than some E0n can be added to each event of the

data run. To simulate the expected rate for En; aMonte-Carlo simulation was performed in such away that the number of added simulated pulseswith strength En falls as 1=E

3n :

Each event underwent the averaging proceduredescribed in Section 5.2. The averaged intensitiesof simulated pulses were compared to the values ofthe 17th (or 39th, 65th, etc.) strongest noise pulseof the initial data (without added simulatedpulses). The fraction of simulated signal pulsesthat were higher than this threshold gives theprobability P for a signal pulse with strengthgreater than some E0

n to exceed this threshold. Wedetermined the value of P as a function of E0

n ; theintensity threshold, and the set of criteria ((a)–(c),or some combination of them) imposed on bothnoise and signal pulses. Then, these values wereused to make an analytical estimate of theprobability to detect a significant accumulationnumber of entries in the interesting bin.

By making an assumption for the total numberof signal pulses N during the run and using thebinomial distribution, one can calculate the prob-ability that k out of these N signal pulses exceedthe threshold: PsðkÞ ¼ CðN ; kÞ Pk ð1� PÞN�k;where CðN; kÞ is the standard binomial coefficient.This probability not only depends on E0

n ; theintensity threshold, and the set of imposed criteriabut also on the aforementioned assumption for thenumber N:

Determining upper limits Nup: Suppose, forinstance, that we are looking for 3 or moresignificant entries in a bin.

First, we impose a particular set of criteria on allpulses in the run, pick the 39 strongest of them anddetermine the number n of entries in the interestingbin. 39 pulses in the histogram correspond to anaverage m ¼ 39=48E0:813 entries per bin. ThePoisson distribution PnðkÞ ¼ mke�m=k! determinesthe probability to have k noise pulses in a bin.

-20 -15 -10 -5 0 5 10 15 200

1

2

3

4Time distribution histogram of the pulse maxima (65 entries)

Time relative to trigger (µsec)

Num

ber

of e

ntrie

s

Fig. 13. Time distribution histogram for maxima of the 65

strongest pulses extracted from 756 files of the EW data with

(a), (b) and (c) imposed. The ratio parameter threshold for

criterion (b) is 1.4. An accumulation of 4 or more pulses in the

(–7,–6) ms bin would signify the presence of signal pulses. Such

an accumulation was not detected.


Second, we set the intensity threshold at thelevel of the 39th pulse. Then we determine PsðkÞfor the same set of imposed criteria, this intensitythreshold and any total number N of signaltransients in the run.

Consider the construction of an acceptanceinterval of n values for some fixed total numberN of signal transients in the run. n entries in theinteresting bin can be the result of differentcombinations of noise and signal entries. Wecalculate the probability to detect n entries in thebin as

PðnjNÞ ¼Xn

k¼0

PsðkÞPnðn � kÞ ¼ e�mXn

k¼0

CðN; kÞ

� Pk ð1� PÞN�kmn�k=ðn � kÞ!

Take some values of n and N; for example, n ¼ n0

and N ¼ N0: The probability Pðn0jN0Þ might besmall but not so small with respect to Pðn0jNbestÞ;where Nbest is such an alternate hypothesiswhich maximizes Pðn0jNÞ: The ratio R ¼Pðn0jN0Þ=Pðn0jNbestÞ is the basis of the orderingprinciple outlined in Ref. [37].

For any N we add values of n into theacceptance interval in decreasing order of R: Assoon as the sum of PðnjNÞ exceeds the confidencelevel of 0.95, the acceptance interval is completed.The confidence belts that can be constructed usingthis procedure are shown in Fig. 14. For anyobserved number n of entries in the interesting bin,these belts provide intervals for allowed values ofN: For any choice of imposed criteria and for allvalues of n measured in the experiment, the lowerend of the intervals was 0. Thus, the actual signaltransients were not detected and only the upperlimit Nup on their number during the run can beplaced.

Upper limit RupðEn > E0nÞ: Divided by the total

run time (17:245 h with EW antenna polarizationand 21:116 h with NS polarization), Nup gives theupper limit on the rate of signal pulses of strengthgreater than E0

n : We will denote it RupðEn > E0nÞ: Of

course, one can obtain different values of RupðEn >E0nÞ when looking for a different significant

number of entries in the interesting bin. Wesearched for the accumulation values from 2 to20 in the bin ð�7;�6Þ ms: The lowest RupðEn > E0

nÞ

gives the most stringent upper limit on the rate. Itsvalue also depends on criteria imposed on bothsignal and noise pulses. The best results wereachieved when all three criteria (a), (b) and (c)were employed. The ratio threshold parameter forcriterion (b) was tested in the region from 1 to 2.4with step 0.2. The thresholds that give the bestresults were found to be 1.4 for EW and both 1.6and 1.8 for NS data. Compared to the analysiswith neither (b) nor (c) employed, these thresholdparameters provide up to 28% lower upper limits.The resulting values of RupðEn > E0

nÞ are shown asdots in Fig. 15 for several values of E0

n for the datataken with both East–West and North–Southpolarizations. Signal pulses stronger than4:57 mV=m=MHz are expected to be quite rareand were definitely absent from the NS data, justlike pulses stronger than 6:85 mV=m=MHz wereabsent from the EW data. Zero upper limits on

0 8642 10 120

2

4

6

8

10

12

14

16

18

Nlow

Nup

N

Observed n

Fig. 14. Confidence belt based on ordering principle of

reference [37], for 95% CL intervals for unknown total number

N of signal pulses in the run. The probability P ¼ 0:841 for a

signal pulse to go through a set of cuts, and the Poisson

background mean m ¼ 65=48 ¼ 1:354; are the parameters of the

plot. The presence of nX4 entries in the interesting time bin

from the total of 65 entries in the histogram would signify the

presence of signal pulses in the run (see Table 10). This is also

reflected in this figure as for nX4 N low becomes non-zero. P ¼0:841 corresponds to the probability for signal pulses stronger

than 1/4 the original test pulse amplitude to pass criteria (b), (c),

and an intensity threshold at the level of the 65th strongest

pulse of the EW data (see Table 9). The ratio parameter

threshold for criterion (b) is 1.4. Only one of the 65 strongest

pulses was observed in the interesting time bin (see Fig. 13),

implying the upper limit Nup ¼ 2 (see also the corresponding

dot in Fig. 15(b) at E0n ¼ 3:43 mV=m=MHzÞ:


the rates of these events are indicators of thesefacts.

As was mentioned above, the differential rateRðEnÞ should be proportional to 1=E3

n : Then, therate of signal pulses of the strength greater than E0

nis

RðEn > E0nÞ ¼

Z þN

E0n

RðEnÞ dEnp

Z þN

E0n

1

E3n

dEn

p1

ðE0nÞ

2

i.e., proportional to 1=ðE0nÞ

2: Hence, the lowestcurve c=ðE0

nÞ2 passing through one of the non-zero

dots (solid line in Fig. 15) represents the strictestupper limit on this rate. The value of thecoefficient c was found to be 0.555 for the NSdata and 0.889 for the EW data:

RupðEnNS > E0nÞ ¼ 0:555=ðE0

nÞ2 h�1 ð2Þ

RupðEnEW > E0nÞ ¼ 0:889=ðE0

nÞ2 h�1 ð3Þ

where E0n is in mV=m=MHz: These results should

be interpreted as the upper limits on the rates ofevents where the North–South (or East–West)projection of the signal pulse was greater thansome value. We will use them in Appendix A forsensitivity calculations.

5.4. Discussion and summary

The small duration of the present subset of dataprevents us from confirming or refuting previousclaims for shower pulses. As mentioned, thissubset was taken with CASA HV off, and wasinitially collected in order to check indications of asignal which occurred with CASA HV on. Usingthe estimate of 2.25 strong signal pulses per day(Section 4.4.4), one expects about three or fourdetectable shower pulses during 38:36 h of ob-servation. Three or four detectable particles thatmight give a strong signal during the experimentwould be too scanty an amount to be detected overthe noise background, which closely mimicsgenuine signals.

Nonetheless, we were able to place upper limitson the integral rate of signal pulses. Under certainsimplifying assumptions these upper limits can beused for evaluating the numerical calibratingfactor s: This factor was set to 20 in Eq. (1) butthere remained an uncertainty regarding its value.In fact, subsequent reports claimed values as smallas 1.6. We could only set upper limits on s: so31from the EW and so34 from the NS data (seeAppendix A). The former was obtained under theassumption of the transverse current radiationmechanism, the latter under an alternative radia-tion mechanism discussed in Appendix A. Figs. 16and 17 compare our results with those of previousexperiments.

Had additional observation time with CASAboxes disabled been available, more signal pulses

2 3 4 5 6 7

0.0

0.1

0.2

2 3 4 5 6 70.0

0.1

0.2

0

1

22

3

4

3 3

2

1

0 0

Rat

e (h

-1)

Rat

e (h

-1)

Strength Eν0 (µV/m/MHz)

(a)

(b)

Rup(Eν>Eν0) = 0.555*(1.8/G)/(Eν

0)2

Rup(Eν>Eν0) = 0.889*(1.8/G)/(Eν

0)2

Fig. 15. Upper limit RupðEn > E0n Þ on the rate of signal pulses

stronger than a fixed strength E0n : Plotted dots show the upper

limit for antenna system gain G ¼ 1:8: Small numbers near the

dots indicate Nup; the upper limit on the number of the signal

events in the run. The dots were plotted for the pulses that are

stronger than 1=n times the original test pulse amplitude of

13:7 mV=m=MHz; n ¼ 2; 3;y; 7: The solid line represents the

lowest upper limit corresponding to them. Data were taken with

(a) North–South ð21:12 hÞ and (b) East–West ð17:25 hÞ antennapolarization.


and more noise transients would be recorded.Would it be easier to prove the presence of showersignals in the data? Taking into account that theaverage signal pulse from a high energy air showeris much stronger than the average noise pulse, thecontent of the most intense transients (thosestronger than 17th strongest, 39th, etc.) wouldshift in favor of more signal pulses. Thus,additional running time with CASA HV off wouldhave allowed one to at least place a stricter upperlimit on the rate of shower pulses, if not to detectthem.

6. Issues specific to a giant array

6.1. Frequency range

The study of pulse components above 30 MHzremains a useful restriction in view of the changingRF environment encountered at lower frequencies.During years of sunspot minima the whole rangeof frequencies above 23 MHz remained relativelyclear of broadcast interference, while as thesunspot numbers increased toward the end of1997, daytime interference became particularly

2 3 4 5 6 7

1E-4

1E-3

0.01

0.1

Strength Eν0 (µV/m/MHz)

Rup(Eν>Eν0) = 0.889/(Eν

0)2

R(Eν>Eν0) = (0.37+0.42)/(Eν

0)2

Rat

e (h

-1)

-0.26

R(Eν>Eν0) = (77+25)10-3/(Eν

0)2-21

R(Eν>Eν0) = (23+7.5)10-4/(Eν

0)2-6.4

Fig. 16. Rate of events at the CASA detection area in which the

East–West projection of the signal pulse is greater than some

E0n : The lower three curves show the predicted rates based on

different values of s: s ¼ 2079:5 (dash-dotted line, the original

Haverah Park result [3] based onB100 detected shower pulses);

s ¼ 9:271:4 (dashed line, the Soviet group result [4] based on

B1000 pulses), and s ¼ 1:670:24 (dotted line, the updated

Haverah Park result [4] based on B1000 pulses). The

uncertainty in the latter two values is 15% [4]. We evaluated

the uncertainty in the former as beingffiffiffiffiffi10

p 15%E47%: In this

logarithmic plot the error bars have constant lengths along their

corresponding curves. The top curve is the upper limit in this

paper which corresponds to s ¼ 31: These four curves are

determined under the assumption of a transverse current

radiation mechanism [10].

1E-4

1E-3

0.01

0.1

Rat

e (h

-1)

2 3 4 5 6 7Strength Eν

0 (µV/m/MHz)

Rup(Eν>Eν0) = 0.555/(Eν

0)2

R(Eν>Eν0) = (0.19+0.23)/(Eν

0)2-0.14

R(Eν>Eν0) = (41+13)10-3/(Eν

0)2-11

R(Eν>Eν0) = (12+4.1)10-4/(Eν

0)2-3.4

Fig. 17. Rate of events at the CASA detection area in which the

North–South projection of the signal pulse is greater than some

E0n : The lower three curves show the predicted rates based on

different values of s: s ¼ 2079:5 (dash-dotted line, the original

Haverah Park result [3] based onB100 detected shower pulses);

s ¼ 9:271:4 (dashed line, the Soviet group result [4] based on

B1000 pulses), and s ¼ 1:670:24 (dotted line, the updated

Haverah Park result [4] based on B1000 pulses). The

uncertainty in the latter two values is 15% [4]. We evaluated

the uncertainty in the former as beingffiffiffiffiffi10

p 15%E47%: In this

logarithmic plot the error bars have constant lengths along their

corresponding curves. The top curve is the upper limit in this

paper which corresponds to s ¼ 34: These four curves are

determined under the assumption of a particular radiation

mechanism discussed in Appendix A.


intense from the citizen’s band just above 27 MHz:This interference typically subsided at sunset. Ifobservations below 30 MHz are contemplated,they would be most useful during years of expectedsunspot minima (e.g., 2006–7), to minimize effectsof long-distance ionospheric reflections.

6.2. Number and spacing of receiving sites

It is expected [3] that signals above 30 MHzdecrease rapidly as a function of distance betweenthe antenna and the shower core’s closest ap-proach. Thus, we expect that in the Auger array,with spacing of 1:5 km between sites in ahexagonal array, RF stations would have to bedistributed with roughly the same or greaterdensity. One possibility for minimizing RF inter-ference from Auger stations would be to place theRF station at the interstices between them. Thiswould raise the cost per station, since it wouldrequire microwave communication with Augersites and auxiliary sources of power.

At each station it may be helpful to have twoantennas, one registering pulses of east–westpolarization and one for north–south polarization.Differential signals as well as individual onesshould be recorded. Coincidences among severalstations may be associated with particularly largeshowers. Frequency-dependent antenna phaseresponse should be modeled or measured, as notedin Section 4.4.8.

6.3. Digitization requirements

Previous work by one of us (JFW) involveddetection of electromagnetic pulses, includingthose possibly produced by cosmic-ray-inducedelectromagnetic discharges, with frequencies in the30–100 MHz range. Part of this work includedbuilding hardware for self-triggering on shortduration wide-band RF pulses. Many of the pulseidentification, fast-digitization and memory pro-blems were identical to those for pulse detection atCASA/MIA. Time-frequency plots were obtainedsimilar to those one would generate in a survey atCASA/MIA. Similar requirements also are en-countered for digitization of data from the Kam-LAND Experiment [38].

Our experience with the present system indicatesthe need for expanded dynamic range if contin-uous-wave sources of RF interference (such asFM and TV broadcast stations) are to beeliminated digitally. Thus, one needs at least10-bit and probably 12-bit range, with a digitiza-tion rate of at least 400 MHz so as to be sensitiveto frequencies up to 200 MHz: Although theexpected signal is likely to be concentrated atlower frequencies (probably below 100 MHz),the expanded frequency range has proved usefulin distinguishing expected signals from othertransients.

6.4. Stand-alone trigger

Our results do not indicate that a trigger basedon RF signals alone can yield useful correlationswith air shower events. This result may be specificto the location of the CASA/MIA array; such atrigger may be less subject to noise at a remotelocation such as the Southern Hemisphere Augersite. An RF survey performed there would beuseful in determining the utility of such a trigger.At such a site, more free from man-made noisethan the CASA/MIA site, one would have toperform further studies allowing discriminationbetween random triggers (such as those induced byatmospheric discharges) and those induced by airshowers. One would also attempt to detect galacticnoise as a further indication that the site wassufficiently quiet.

6.5. Integration into the data stream

The data of CASA/MIA and that of the RFdetection experiment were only integrated off-line.Any further studies should allow for simultaneousacquisition of both sets of data. Since the Augerproject proposes to use microwave communicationbetween stations, this same link should beconsidered for communicating RF signal acquisi-tion results to a central data stream.

6.6. Status of GHz detection

David Wilkinson, who visited the University ofChicago during the spring of 1995, has proposed


looking into the power radiated at frequencies ofseveral GHz, where new opportunities existassociated with the availability of low-noisereceivers. These techniques have now been im-plemented in the RICE project [39], which seeks todetect pulses with frequency components around250 MHz in Antarctic polar ice.

6.7. Other options

Dispersion between arrival times of GPS signalson two different frequencies may serve as a usefulmonitor of air shower activity. The possibility ofcorrelation of large showers with such dispersionevents could be investigated.

It may be possible to monitor commercialbroadcast signals in the 54–216 MHz range todetect momentary enhancements associated withlarge showers, in the same sense that meteorshowers produce such enhancements. Televisionchannels for which no nearby stations exist offerone possibility. The data taken at CASA/MIAhave not yet been analyzed in terms of suchenhancements, but represent a potential source ofinformation. In Table 11 we note the locations ofTV stations broadcasting on VHF channels other

than those assigned to the Salt Lake Citymetropolitan area within 400 km of Dugway.These are channels 3 (60–66 MHz), 6 (82–88 MHz), 8 (180–186 MHz), 10 (192–198 MHz),and 12 (204–210 MHz). The availability of at leasttwo stations on Channel 3 and three on Channel 6

at greatly differing headings indicates that thismethod may have some promise.

Radar detection of showers offers anotherexciting possibility [19]. This method resemblesthe use of distant fixed VHF stations for generat-ing reflections off showers, but allows for a morecarefully controlled environment.

7. Conclusions

A prototype system for the detection of radio-frequency (RF) pulses associated with extensive airshowers of cosmic rays was tested at the ChicagoAir Shower Array and Michigan Muon Array(CASA/MIA) in Dugway, Utah. This system wasunder consideration for use in conjunction withthe Pierre Auger Project, which seeks to studyshowers with energies above 1019 eV:

The system utilized a trigger based on thecoincidence of 7 out of 8 buried muon detectorsaround the periphery of the CASA array. Tran-sients were indeed detected in conjunction withlarge showers, but they were identified as arisingfrom the CASA modules themselves, most likelyfrom the electronics generating trigger request(TRQ) pulses. Such transients could be eliminatedwhen the high voltage (HV) on CASA phototubeswas turned off; in such cases the muon triggercontinued to function. By comparing upper limitson detected transients with simulated pulses, it waspossible to place upper bounds on the rate of

Table 11

Television stations within 400 km of Dugway on channels not assigned to the Salt Lake City metropolitan area. Ref. [26] also lists four

‘‘new’’ (unidentified) stations on Channel 3 for Price, UT (distance C160 km; heading C1101) and two on Channel 12 for Logan, UT

(distance 178 km; heading 141)

Call Location Channel Power Distance from Heading

sign (kW) Dugway (km) ð3Þ

KBJN Ely, NV 3 100 212 239

KIDK Idaho Falls, ID 3 100 363 1

KBNY Ely, NV 6 100 212 239

KPVI Pocatello, ID 6 100 301 6

KBCJ Vernal, UT 6 83.2 306 87

KIFI-TV Idaho Falls, ID 8 316 363 1

KENV Elko, NV 10 3.09 272 280

KISU-TV Pocatello, ID 10 123 301 6

KUSG St. George, UT 12 10 359 191


detection of RF pulses of various intensities. Theseupper bounds are summarized in Fig. 15; theytypically involve rates of one every few hours forthe largest field strengths claimed in the literature[4]. Based on our estimates, it is unlikely that thepresent experiment can reach the sensitivity limitsof the Haverah Park results, which reported lowerfield strengths in their latest work [4].

A number of lessons have been learned from thepresent exercise. These are probably most relevantfor any installation contemplated in conjunctionwith the proposed Auger project [14].

(1) One must take special care to surveytransients produced by components of the array.For the Auger detector, one must install one ormore antennae close to the proposed Cherenkovdetectors and their associated digitizers, and studythe response to artificially induced signals. Basedon our experience, in which the present bounds arebased on a small subset ð38 hÞ of the total datasample ð600 hÞ; one should focus as soon aspossible on a configuration in which usable datacan be gathered.

(2) The method of communication betweenAuger modules will affect what form of RFdetection is feasible. If radio links employingmicrowave ð> 800 MHzÞ frequencies are used, thepresent system will not be as seriously compro-mised as it apparently was by the communicationsystem used at CASA/MIA. On the other hand,detection of RF signals above 1 GHz will sufferinterference from such a system.

(3) Consideration should be given to placementof antennas at sites sufficiently far from surfacedetector modules that pulses from these modulesdo not constitute a serious source of interference.In the Auger case, the modules are arranged in atriangular array with 1:5 km spacing, so that themaximum spacing between an antenna inside thearray and any module could be as large as1:5=

ffiffiffi3

pC0:87 km if the antenna is placed at an

equal distance from the three closest modules.(4) Coincidence between RF signals detected at

several antennas is desirable, as was found in theearliest experiments [2].

(5) The digital filtering algorithms employed inthe present study, although not yet pushed to theiroptimal efficiencies, appear to be limited by the

8-bit dynamic range employed in detection using adigitizing oscilloscope. Consideration should begiven to a system with larger dynamic range, atleast 10-bit but preferably 12-bit.

(6) One can probably afford to economize byreducing the sampling rate, certainly to 500 MSa=sbut perhaps as low as 200 MSa=s; since transientsare expected to have their main frequency compo-nents below 100 MHz; and by reducing the activesampling window from the present value of 50 msto a lower value, depending on the geometry of thearray.

(7) The frequency range studied in the presentwork (23–200 MHz) will be more useful ifcontinuous RF sources, such as FM and televisionstations, are much weaker than they were at theDugway site. This is a possibility in the remoteArgentine site at which the first Auger array is tobe constructed [14]; a survey of field strengthsthere would be desirable.

(8) One should take data simultaneously withtwo antennas polarized in perpendicular (EW andNS) directions. This allows the determination oftwo components of the electric vector, not just oneof its projections.

Although no RF signals have been detected inconjunction with CASA/MIA events, the presentstudy has revealed a number of useful criteria forfuture experiments of similar type. It is hoped thata prototype at an Auger site will further focusthese criteria.

Acknowledgements

It is a pleasure to thank Mike Cassidy, JimCronin, Brian Fick, Lucy Fortson, Joe Fowler,Rachel Gall, Brian Newport, Rene Ong, ScottOser, Daniel F. Sullivan, Fritz Toevs, Kort Travis,and Augustine Urbas for collaboration and sup-port on various aspects of this experiment. Thanksare also due to Bruce Allen, Dave Besson, MauriceGivens, Peter Gorham, Kenny Gross, DickGustafson, Gerard Jendraszkiewicz, Larry Jones,Dave Peterson, John Ralston, Leslie Rosenberg,David Saltzberg, Dave Smith, M. Teshima,Stephan Wegerich, and David Wilkinson foruseful discussions. This work was supported in


part by the Enrico Fermi Institute, the Louis BlockFund, and the Physics Department of the Uni-versity of Chicago and in part by the USDepartment of Energy under Grant No. DEFG02 90ER40560.

Appendix A. Sensitivity calculation

One of the aims of this study was to evaluate theantenna response as a function of shower para-meters. The dependence on R; y; a;Ep has beenestablished in Ref. [3] (Eq. (1)). However, thereremained an uncertainty as regards the calibratingfactor s; for which experimental data do notsupply an exact value. Indeed, we have quoted atleast three versions of it: first, in Eq. (1) it is set to20; second, the Haverah Park group subsequentlyreported that EN

n ¼ 0:6; while the Soviet groupclaimed the value of 3.4 [4]. To make theconnection between EN

n and s; let us note thatsCEN

n =expð�1Þ: Thus, we can infer that theHaverah Park group updated Eq. (1) to s ¼ 1:6;and the Soviet group to s ¼ 9:2:

Ideally, we would like to calculate the calibrat-ing factor precisely from the rate RðEnEW > E0

nÞ;but unfortunately this rate cannot be obtainedaccurately from experiment; we could only set anupper bound on it (Section 5.3.4). Hence, in thisAppendix we will be able to set only an upper limiton s to get at least some evaluation of the possiblerange of its values. We will do it in the followingway.

Eq. (1) and the exact knowledge of the coeffi-cient k in the formula for the rate of primaries as afunction of their energy RðEpÞ ¼ k=E3

p [29] can beused to calculate the rate RðEnEW > E0

nÞ: The resultwill certainly depend on the calibrating factor s:Comparing this rate with the experimental upperbound, RupðEnEW > E0

nÞ; an upper limit will beplaced on the calibrating factor.

In the process of evaluating RðEnEW > E0nÞ we

will need to integrate the rate of primaries RðEpÞover solid angle, energy, and detection area. Thequestion of detection area is of great importancesince its lack of symmetry with respect to theantenna compelled us to make an importantsimplifying assumption.

A.1. Detection area

Core locations of showers that fire muontriggering are shown in Fig. 18. Their distributionover the outlined area appears to be approximatelyuniform. To simplify the integration over solidangle, area, and energy, let us consider a biggerarea: part of the ring with inner radius of 100 m;outer radius of 400 m; inside the same angle of 2radians. The rate of showers passing through thisarea is bigger than through the one shown inFig. 18. Integration over the bigger area will leadto a greater value for RðEnEW > E0

nÞ: However, thatvalue will differ from the one calculated afterintegration over the outlined area by less than 5%,as we show below in Calculation.

As was mentioned in Section 4.6, systematicstudies have been performed only for simulatedpulses with d ¼ 5 ns. Thus, RupðEnEW > E0

nÞ(Fig. 15(b)) was obtained under the assumptionRC200 m: Though in reality the detection area isnot limited to the area around 200 m; we are goingto accept that result as a reasonable approxima-tion.

Unfortunately, the area under consideration isnot the full ring. If it were, it could have beenproven that the angular distribution of the electric

Fig. 18. Core locations for 1702 showers giving rise to muon

triggering. The opening angle at the antenna vertex is 2 rad. The

radii of the inner and outer circular arcs are 100 and 400 m;respectively. Axes relative to center of array are x (geographic

East) and y (geographic North), in meters.


vector in the horizontal plane is approximatelyuniform. Then it would have been easy to deriveRðEnEW > E0

nÞ after calculating RðEn > E0nÞ: In that

case we would not have to worry about thepolarization of radiation from individual showers.

In our case, however, the area is not symmetric.The general approach of calculating EnEW forshowers with different zenith angles, azimuth anglesand core locations and then integrating would betoo difficult to implement. Therefore, it would bereasonable to simplify the problem by making theassumption that all showers are vertical. This willlead to a rough estimate of the upper limit that canbe placed on the calibrating factor.

Now we are almost ready to perform integra-tion. Only one thing is missing: Since RupðEnEW >E0nÞ was calculated for the EW projection of the

electric field vector, we will need a relation betweenEn and EnEW for showers with different corelocations. For this purpose let us turn to thequestion of polarization of radiation produced bya shower.

A.2. Polarization

The conventional approach assumes linear po-larization in the direction perpendicular to bothshower axis and magnetic field vector. The sourceof such radiation is the transverse current of showerparticles [10]. Alternatively, one can consider radioemission due to particles’ acceleration in the Earth’smagnetic field. For the time being we will pursuethe latter approach but at the end of this Appendixwe will give results for both alternatives.

The magnitude and direction of the electric fieldvector for a radiating particle are governed by thegeneral formula

Eðx; tÞ ¼ en� b

g2ð1� b nÞ3 l2

� �ret

þe

c

n� ½ðn� bÞ � ’b�

ð1� b nÞ3l

� �ret

ðA:1Þ

where b is the velocity vector in the units of c;’b ¼ db=dt is the acceleration vector, divided by c;n is a unit vector from the radiating particle to theantenna, and l is the distance to the particle [40].The square brackets with subscript ‘‘ret’’ mean

that the quantities in the brackets are evaluated atthe retarded time. Eq. (A.1) does not consider theinfluence of the index of refraction of air. Here weare primarily interested in the direction of theelectric field vector and for R > 100 m the effect ofthe refraction index on polarization is insignif-icant. Ref. [36] will give a full calculation ofshower radiation, employing a modified formulaEq. (A.1) to take into account the refraction index.

The first term in Eq. (A.1) decreases withdistance as 1=l2 and represents a boosted Coulombfield. It does not produce any radiation. Themagnitudes of two terms in Eq. (A.1) are related as1=ðg2lÞ and j ’bj=c: The characteristic acceleration ofa 30 MeV electron ðgE60Þ of an air shower in theEarth’s magnetic field ðBE0:5 GÞ is jaj ¼ecB=ðgmÞE4:4� 1013 m=s2: Even when an elec-tron is as close to the antenna as 1000 m; the firstterm is three orders of magnitude smaller than thesecond and can be neglected. The second term fallsas 1=l and is associated with a radiation field. Itdescribes the electric field of a single radiatingparticle for most geometries relevant to extensiveair showers.

Consider the frame centered at the antenna,with axis Ox going to the magnetic West, Oy to theSouth and Oz directly up. For vertical showers inthis frame b ¼ ð0; 0;�1Þ; while ’b is parallel to Ox;or, in other words, to the ð1; 0; 0Þ vector (seeFig. 19). Let c be the angle between Ox andthe direction to the shower core, R the distanceto the core, and h the altitude of the radiatingparticle. Then n¼ ð�R cos c=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ R2

p;�R sin c=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h2 þ R2p

;�h=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2 þ R2

pÞ: Typical values for R

are a few hundred meters, and for h several

kilometers, so R=h can be considered small. The

denominator of the second term of Eq. (A.1) is

independent of c: The numerator determines that,

to leading (second) order in R=h; the electric field

vector lies in the horizontal plane and is parallel to

ðcos 2c; sin 2c; 0Þ: The magnitude of the numera-

tor is independent of the angle c up to terms of the

order R4=h4:This result shows that although particles are

accelerated by the Earth’s magnetic field in the EWdirection regardless of the angle c; the radiationreceived at the antenna does not show preference


for EW polarization. Instead, it is directly relatedto the angle c: In other words, assuming uniformdistribution of shower cores around the antenna(uniform distribution of c), one obtains a uniformangular distribution of the electric field vector.

The most important result of this section for thefollowing calculation is the relation between EnEW

and En:

EnEW ¼ Enj cos 2cj

A.3. Calculation

Let us now calculate the rate RðEnEW > E0nÞ as a

function of s: For vertical showers Eq. (1) becomes

En ¼ sEp

1017 eVcos gd exp �

R

R0ðn; 0Þ

� �mV=m=MHz

where s is the calibrating factor, and gd is a dip angle(the angle between the magnetic field vector and thedirection to magnetic North). R0ðn; yÞ only dependsslightly on y when yo351: The dependence on n isnot very significant, either. Ref. [2] quotes twonumbers: At n ¼ 55 MHz R0 equals 110 m; while atn ¼ 32 MHz R0 equals 140 m: The form of thedependence is not well known, although it is clearthat R0 becomes larger as n decreases. Assuminglinear dependence for simplicity, one can evaluateR0 ¼ 130 m at n ¼ 39 MHz; the median frequencyof the main region of investigation (Section 5.3.1(b)). This value of R0 will be used in this Appendix.

Consider showers with impact parameter R;direction to the core given by angle c; and primaryenergy

Ep > E0pðE

0n ;R;cÞ ¼ E0

n1017

s cos gd

expðR=R0Þjcos 2cj

eV

where E0n is expressed in m V=m=MHz: Only these

showers induce EnEW ¼ En jcos 2cj > E0n : So, the

rate of events where the East–West projection ofthe pulse is greater than some value, RðEnEW > E0

nÞ;equals the rate Z of such showers passing throughthe detection area.

Now let us determine the limits of integration.We assume that although we consider verticalshowers only, the solid angle of observation islimited by a zenith angle ym ¼ 501:

We also take into account that magnetic Northat Dugway is located 141 east of true North.Therefore, the detection area is bound by lines c ¼571þ 141 ¼ 711 and c ¼ �571þ 141 ¼ �431:

We know that the rate of primaries (ineV�1=km2=sr=h) is given by RðEpÞ ¼ k=E3

p: Hence,the integration over solid angle, area and energygives the desired rate Z (in h�1)

Z ¼Z

dOZ

dA

Z þN

E0pðE

0n ;R;cÞ

RðEpÞ dEp

¼ 2pZ ym

0

sin y dyZ 711

�431

dcZ 400 m

100 m

R dR

�Z þN

E0pðE

0n ;R;cÞ

k

E3p

dEp

¼ 2pð1� cos ymÞZ 711

�431

dcZ 400 m

100 m

R dRk

2E02p

¼ pkð1� cos ymÞs cos gd1017E0

n

!2Z 711

�431

cos2 2c dc

�Z 400 m

100 m

Re�2R=R0 dR: ðA:2Þ

Both integrals in Eq. (A.2) can be readily calcu-lated to obtain the following expression:

RðEnEW > E0nÞ

¼ ZEpkð1� cos ymÞs cos gd1017E0

n

!2

2:0� 103 h�1

β

ψ

R

h

l

βn

Bγd

Antennax

y

z

W E

S

N

Core

Fig. 19. Geometry of a vertical shower. Axes relative to

antenna are x (magnetic West), y (magnetic South) and z

(up). Vector B lies in the yOz plane.


where k is in eV2=m2=sr=h and E0n is in

m V=m=MHz: Let us note here that integrationover the area outlined in Fig. 18 (instead of thepart of the ring) has also been calculatednumerically with the help of Mathematica, withthe result

RðEnEW > E0nÞ

Epkð1� cos ymÞs cos gd1017E0

n

!2

1:9� 103 h�1

i.e., only a 5% difference. Thus, the rapidlydecreasing exponential suppresses the contri-bution at large distances from the antenna wherethe part of the ring does not overlap the outlinedarea.

Now we can place an upper limit on s using thisformula for the rate RðEnEW > E0

nÞ and the experi-mental upper limit on this rate, RupðEnEW > E0

nÞfrom Section 5.3.4:

RðEnEW > E0nÞ

Epkð1� cos ymÞs cos gd1017E0

n

!2

1:9� 103

oRupðEnEW > E0nÞ ðA:3Þ

so1017E0

n

cos gd

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRupðEnEW > E0

nÞpkð1� cos ymÞ1:9� 103

s: ðA:4Þ

From Eq. (3), E0n

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiRupðEnEW > E0

nÞq

E0:943 mV=m=MHz=h1=2: This value, substituted into (A.4)together with k ¼ 3:84� 1024=eV2=m2=sr=s ¼1:38� 1028=eV2=m2=sr=h [29], ym ¼ 501 and gd ¼681; gives the final result: so46: A similarcalculation employing North–South results(Eq. (2)) gives so34:

If the main source of radiation is transversecurrent, not particles’ acceleration, then E isparallel to b � B [10] and for vertical showersEnEW ¼ En: This changes the integral of cos2 2cover c in formula (A.2) to the integral of 1 over c;leading to so31: This is the smallest upper limit wecan place on s: Unfortunately, this upper limit isnot quite small enough to rule out the initialHaverah Park group claim of s ¼ 20; let alone thevalues of 9.2 or 1.6. To facilitate comparison ofresults of different studies, let us rewrite formula

(A.3) under the assumption of the transversecurrent mechanism. In simplified form it is

RðEnEW > E0nÞE9:16� 10�4 s

E0n

!2

:

The transverse current mechanism cannot ac-count for the NS component for vertical showersso we will employ the model discussed above inPolarization. According to it, EnNS ¼ Enjsin 2cj:Then, formula (A.3) transforms into

RðEnNS > E0nÞE4:86� 10�4 s

E0n

!2

:

The plots of RðEnEW > E0nÞ and RðEnNS > E0

nÞfor different values of s are shown in Figs. 16and 17.

The noise level at Dugway is too high and theacquired sample is too limited in statistics anddynamic range to allow us to place upper limitsstrict enough to check the claims of the twogroups. We hope that further improvement of thedata processing technique will reduce the noisecontribution. The dip angle gd is much smaller atthe Auger site in Argentina (341 versus 681 atUtah). This leads to bigger electric fields forvertical showers, facilitating the detection ofshower radiation. We also expect that the Argen-tina site will be quieter than Dugway and someclarity as regards the calibrating factor will beestablished.

Appendix B. Relation between simulated pulse

strength and peak detected voltage

Within the bandwidth dn; the antenna feelsthe electric field Endn: Then, the instantaneouspower flow is given by ðEndnÞ

2=ð120pÞ; where120p O is the impedance of free space. Theantenna effective aperture is equal to Gantðl

2=4pÞ;GantC2:5 being the antenna gain. Hence, itsupplies a power of

W ¼ðEndnÞ

2

ð120pÞGant

l2

4p

to the input of the feedline cable. Subsequently,this power is transmitted by 60 feet of RG-58U


cable with average attenuation at 39 MHzestimated to be 1:44 dB or a factor of LC1:4 inpower. So, the power at the input of thepreamplifier is W=L: The impedances inthe antenna system were matched, in particular,the resistance of the preamplifier was equal to thecharacteristic impedance of the cable, R ¼ 50 O:The power at the input of the preamplifier istransformed into a peak voltage Vpk across thepreamplifier resistance R; i.e., W=L ¼ V 2

pk=R:Thus,

En ¼1

dn

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiW

480p2

Gantl2

s¼

ndn

2Vpk

c

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi120p2LGantR

s

¼ndn

2Vpk

c

ffiffiffiffiffiffiffiffiffiffiffiffi120p2

GR

s

where G ¼ Gant=LC1:8 is the antenna-cable sys-tem gain. For specific values used in data analysis(Section 5.3.1.) dn ¼ 54� 24 ¼ 30 MHz; n ¼39 MHz;

En ¼ 0:042Vpkffiffiffiffi

Gp ¼ 0:031

VpkffiffiffiffiffiffiffiffiffiffiffiffiG=1:8

p mV=m=MHz

where Vpk is in mV:The above derivation implies that the electric

field perceived by the antenna is due to frequenciesin the dn range only. However, the simulatedpulse voltage with Vpk ¼ 1:3 mV has componentsin the whole frequency range (see Fig. 4, bottom),i.e., it is the result of an imaginary ‘‘electricfield’’ with very diverse frequencies. To findwhat Vpk would be if our antenna were sensitiveto 24–54 MHz only, the forward and then inverse(for 24–54 MHz region) Fourier transforms ofthe simulated pulse voltage have been performed.The contribution of the 24–54 MHz regioninto the pulse peak voltage of 1.3 mV appearedto be equal to 442 mV: This leads to a correctedformula:

En ¼ 0:031442

1300

VpkffiffiffiffiffiffiffiffiffiffiffiffiG=1:8

p ¼ 0:011

�VpkffiffiffiffiffiffiffiffiffiffiffiffiG=1:8

p mV=m=MHz

This formula establishes the relation betweenthe simulated pulse strength En and its peak

voltage Vpk at the filter-preamplifier configuration.G ¼ 1:8 was assumed throughout the paper.

Appendix C. Cost considerations for Auger project

At present we can only present a rough sketch ofcriteria for detection in the 30–100 MHz range.Data would be digitized at a 500 MHz rate at eachstation and stored in a rolling manner, with at least20 ms of data in the pipeline at any moment. Uponreceipt of a trigger signaling the presence of a‘‘large’’ shower ð> 1018 eVÞ; these data would bemerged into the rest of the data stream at eachstation.

Per station, we estimate the following additionalcosts, in US dollars, for RF pulse detection(Table 12)

The above estimate assumes that one can powerthe preamps and DAQ electronics from the supplyat each station without substantial added cost. Italso assumes that a ‘‘large-event trigger’’ will beavailable at each station. One consideration maybe the acquisition of antennas robust enough towithstand extreme weather (particularly wind)conditions.

Table 12

Two antennas and protection circuitry 200 (a)

Mounting hardware 100 (b)

Cables and connectors 200 (c)

Preamps 500 (d)

Digitization and memory electronics 2000 (e)

Total per station 3000 (f)

(a) Two military-surplus log-periodic antennas; crossed polar-

izations. (b) Highly dependent on other installations at site.

Antennas are to be pointed vertically but optimum elevation

not yet determined. (c) Antennas are mounted near central data

acquisition site of each station, but sufficiently far from any

sources of RF interference such as switching power supplies.

Alternative location of receiving stations at interstitial positions

in the array would require microwave communication links and

auxiliary power supplies and would add to cost. (d) Commercial

GaAsFET preamps and gas discharge tubes. (e) Subject to

prototype development experience. Power requirements not yet

known. (f) The number of stations to be equipped with RF

detection will depend on further prototype experience.


For detection at frequencies above or below 30–100 MHz; the criteria are not yet well enoughdeveloped to permit any cost estimate.

References

[1] J.V. Jelley, et al., Nature 205 (1965) 327;

J.V. Jelley, et al., Nuovo Cimento A46 (1966) 649;

N.A. Porter, et al., Phys. Lett. 19 (1965) 415;

T. Weekes, in: D. Saltzberg, P. Gorham (Eds.), Radio

Detection of High Energy Particles, Proceedings of First

International Workshop RADHEP 2000, Los Angeles,

CA, 16–18 November 2000, AIP Conference Proceedings.

No. 579, AIP, Melville, NY, 2001, p. 3.

[2] P.R. Barker, W.E. Hazen, A.Z. Hendel, Phys. Rev. Lett.

18 (1967) 51;

W.E. Hazen, et al., Phys. Rev. Lett. 22 (1969) 35;

W.E. Hazen, et al., Phys. Rev. Lett. 24 (1970) 476.

[3] H.R. Allan, in: J.G. Wilson, S.G. Wouthuysen (Eds.),

Progress in Elementary Particles and Cosmic Ray Physics,

Vol. 10, North-Holland, Amsterdam, 1971, p. 171, and

references therein.

[4] V.B. Atrashkevich, et al., Yad. Fiz. 28 (1978) 366.

[5] K. Kadota et al., Proceedings of the 23rd International

Conference on Cosmic Rays (ICRC-23), Vol. 4, Calgary,

1993, p. 262; Tokyo Workshop on Techniques for the

Study of Extremely High Energy Cosmic Rays, Tanashi,

Tokyo, 27–30 September 1993.

[6] C. Castagnoli, et al., Proceedings of the ICRC-23, Vol. 4,

Calgary, 1993, p. 258.

[7] P.I. Golubnichii, A.D. Filonenko, V.I. Yakovlev, Izv.

Akad. Nauk 58 (1994) 45.

[8] R. Baishya, et al., Proceedings of the ICRC-23, Vol. 4,

Calgary, 1993, p. 266; Gauhati University Collaboration;

P. Datta et al., Proceedings of RADHEP 2000 [1], p. 98.

[9] G.A. Askar’yan, Zh. Eksp. Teor. Fiz. 41 (1961) 616;

G.A. Askar’yan, Sov. Phys.–JETP 14 (1962) 441;

G.A. Askar’yan, Zh. Eksp. Teor. Fiz. 48 (1965) 988;

G.A. Askar’yan, Sov. Phys.–JETP 21 (1965) 658.

[10] F.D. Kahn, I. Lerche, Proc. Roy. Soc. A 289 (1966)

206.

[11] S.A. Colgate, J. Geophys. Res. 72 (1972) 4869.

[12] R.R. Wilson, Phys. Rev. 108 (1967) 155.

[13] R.A. Roussel-Dupr!e, A.V. Gurevitch, T. Tunnell, G.M.

Milikh, Los Alamos National Laboratory Report LA-

12601-MS, November, 1993.

[14] Auger Collaboration, Pierre Auger Project Design Report

(2nd Edition, November, 1996, revised March 14, 1997),

Fermilab, 1997 (unpublished);

J.W. Cronin, Rev. Mod. Phys. 71 (1999) S165.

[15] J.L. Rosner, D.A. Suprun, Proceedings of RADHEP 2000

[1], p. 81.

[16] E. Zas, F. Halzen, T. Stanev, Phys. Rev. D 45 (1992)

362.

[17] P. Gorham, et al., Phys. Rev. E 62 (2000) 8590;

D. Saltzberg, et al., Phys. Rev. Lett. 86 (2001) 2802;

D. Saltzberg, et al., Proceedings of RADHEP 2000 [1],

p. 225.

[18] P.M.S. Blackett, A.C.B. Lovell, Proc. Roy. Soc. 177 (1941)

183.

[19] P.W. Gorham, Astropart. Phys. 15 (2001) 177.

[20] S.N. Vernov, et al., Pis’ma v ZhETF 5 (1967) 157;

[Sov. Phys.–JETP Lett. 5 (1967) 126];

S.N. Vernov, et al., Can. J. Phys. 46 (1968) S241.

[21] A. Borione, et al., Nucl. Instr. and Meth. A 346 (1994)

329.

[22] D.A. Smith, et al., J. Geophys. Res. 104 (1999) 4189.

[23] L.F. Fortson et al., in: Proceedings of the 26th Interna-

tional Conference on Cosmic Rays (ICRC 99), Vol. 3, Salt

Lake City, 17–25 August 1999, p. 125;

L.F. Fortson, et al., in: Proceedings of the 26th Interna-

tional Conference on Cosmic Rays (ICRC99), Vol. 5, Salt

Lake City, 4–25 August 1999, pp. 332, 335;

J. Fowler, Ph.D. Thesis, University of Chicago, 1999

(unpublished).

[24] K. Boothby, et al., Astrophys. J. 491 (1997) L35;

D.B. Kieda, S.P. Swordy, in: Proceedings of the 26th

International Conference on Cosmic Rays (ICRC 99), Vol.

3, Salt Lake City, 17–25 August 1999, p. 191;

S.P. Swordy, D.B. Kieda, Astropart. Phys. 13 (2000) 137.

[25] T. Abu-Zayyad, et al., in: Proceedings of the 26th

International Conference on Cosmic Rays (ICRC 99),

Vol. 3, Salt Lake City, 17–25 August 1999, p. 260;

T. Abu-Zayyad, et al., in: Proceedings of the 26th

International Conference on Cosmic Rays (ICRC 99),

Vol. 5, Salt Lake City, 7–25 August 1999, p. 365;

T. Abu-Zayyad, et al., Nucl. Instr. and Meth. A 450 (2000)

253.

[26] As listed on the Web site http://stations.triathlon.net/cgi-

radio/.

[27] Microwave Filter Company, Inc., 6743 East Kinne St.,

East Syracuse, NY 13057.

[28] The magnetic declination (141 east of true north) and

inclination ðC681NÞ are taken, respectively, from a USGS

chart of the Dugway site and the map site http://

geomag.usgs.gov/dod.html.

[29] M.A. Lawrence, R.J.O. Reid, A.A. Watson, J. Phys. G 17

(1991) 733.

[30] R. Gall, K.D. Green, UMC-CASA note, August 23, 1996

(unpublished).

[31] P. Mooney, private communication of specifications from

Dorne and Margolin.

[32] See http://www.eznec.com for further information and a

demonstration version.

[33] K. Gross, private communication.

[34] Wavelab, Stanford University. See http://www-stat.stan-

ford.edu/~wavelab/.

[35] D.F. Sullivan, Master’s Thesis, University of Chicago,

1999 (unpublished).

[36] D.A. Suprun, P.W. Gorham, J.L. Rosner, Preprint astro-

ph/0211273, to be submitted to Astroparticle Physics.

[37] G.J. Feldman, R.D. Cousins, Phys. Rev. D 57 (1998)

3873.


http://stations.triathlon.net/cgi-radio/

http://stations.triathlon.net/cgi-radio/

http://geomag.usgs.gov/dod.html

http://geomag.usgs.gov/dod.html

http://www.eznec.com

http://www-stat.stanford.edu/~wavelab/

http://www-stat.stanford.edu/~wavelab/

[38] A.D. Marino (for the KamLAND Collaboration), Wave-

form digitization in the KamLAND experiment, in: E.

Norman, G. Wozniak (Eds.), Nuclear Physics in the 21st

century, INPC conference, Berkeley, CA, 30 July–3

August, 2001; KamLAND Collaboration;

F. Beiseer, et al., Waveform digitization for KamLAND,

Poster P58, in: J. Law, et al. (Eds.), Proceedings of the 19th

International Conference on Neutrino Physics and Astro-

physics (Neutrino 2000), Sudbury, Canada, 16–21 June

2000, North-Holland, Amsterdam, 2001, Nucl. Phys. B

Proc. Suppl. 91 (2001).

[39] G. Frichter, D.W. McKay, J.P. Ralston, Phys. Rev. D 53

(1996) 1684;

RICE Collaboration, in: M.S. Potgieter, B.C. Raubenhei-

mer, D.J. van der Walt (Eds.), Proceedings of 25th

International Cosmic Ray Conference, Durban, South

Africa, 28 July–8 August 1997, World Scientific, 1998,

preprint astro-ph/9709223;

I. Kravchenko et al., preprint astro-ph/0112372 (to be

published in Astroparticle Physics).

[40] J.D. Jackson, Classical Electrodynamics, 2nd Edition,

Wiley, New York, 1975, p. 657.


Documents

A prototype system for detecting the radio-frequency pulse associated with cosmic ray air showers