Enhancement of the radar signal of air showers due to time compression
J. Stasielak, S. Baur, R. Engel, P. Neunteufel, J. Pekala, R. Šmída, F. Werner, H. Wilczyński
aa r X i v : . [ a s t r o - ph . H E ] O c t RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO T HE A STROPARTICLE P HYSICS C ONFERENCE
Enhancement of the radar signal of air showers due to time compression
J. S
TASIELAK , , S. B AUR , R. E NGEL , P. N EUNTEUFEL , J. P E ¸ KALA , R. ˇS M ´ IDA , F. W ERNER , H.W ILCZY ´ NSKI . Karlsruhe Institute of Technology, Karlsruhe, Germany Institute of Nuclear Physics PAN, Krakow, Poland [email protected]
Abstract:
We investigate the feasibility of detecting extensive air showers by the radar technique at viewingangles smaller than ∼ ◦ to the shower axis. Considering a bistatic radar setup and shower geometries in whichthe receiver points into the arriving shower, we simulate reflection of radio waves off the short-lived plasmaproduced by the high-energy shower particles in the air. Using the Thomson cross-section for scattering of radiowaves and summing coherently contributions of the reflected radio wave over the volume of the plasma disk, weobtain the time evolution of the signal. We analyze the spectral power density of the radar echo and the receivedpower. Based on the obtained results, we discuss possible modes of the radar detection of extensive air showers. Keywords: ultra-high energy cosmic rays, extensive air showers, radar, radio signal.
The remote sensing of extensive air showers (EAS) using abistatic radar system is a promising technique with almost100% duty cycle that is currently being developed. If suc-cessful, it will allow the next generation of cosmic ray ob-servatories to be built at much lower cost.The concept of implementing a radar for cosmic ray de-tection dates back to 1940 [1]. However, due to the lack ofexperimental confirmation of this method, it was not pur-sued for several decades. In recent years renewed attentionhas been given to this topic [2, 3, 4, 5, 6] and experimentalefforts to detect EAS using the radar technique were madeby several groups [7, 8, 9, 10, 11, 12].Detection of EAS via radar technique is based on theprinciple of scattering radio waves off the plasma pro-duced in the atmosphere by the high-energy particles ofthe shower. The locally produced plasma decays. For theplasma densities relevant for EAS and at low altitudes, thethree-body attachment to oxygen dominates the deioniza-tion process as it depends quadratically on the oxygen den-sity. This leads to the plasma lifetime of 10 ns at sea leveland about 100 ns at an altitude of 10 km [13, 14, 15].Some features of scattering of the radio waves from theionization column produced by meteors or lightnings areexpected to be similar to the scattering from the ionizationtrail left behind the shower front. Therefore, we can usethese similarities as a starting-point for analysis of theradar reflection from EAS.The ionization trail that results from meteors or light-nings is traditionally divided into underdense and over-dense regions, depending on the local plasma frequency n p .If the electron density is high enough that the plasma fre-quency exceeds the radar frequency then the radio waveis reflected from its surface. Such a region is called over-dense. In contrast, if the electron density is low enough thatthe local plasma frequency is lower than the frequency ofthe incoming radio wave, then the region is underdense andthe radio wave can penetrate the ionized region. In such acase the reflections are caused by the Thomson scatteringof the radio wave on individual free electrons. Gorham [3] considered radar reflection from the side ofa horizontal ionization trail left by ultra-high energy neu-trinos at an altitude of about 10 km. He suggested that themost inner (overdense) part of the ionization column is re-sponsible for the bulk of the radar reflection. By analogywith the reflective behaviour of the overdense region pro-duced by a meteor, he assumed that the radar cross-section(RCS) of the overdense trail produced by EAS is equal tothe RCS of a thin metallic wire.An alternative mode of EAS detection was discussed in[4], where reflection of the radar wave from the relativisti-cally moving shower front was considered. The reflectioncoefficient was obtained by solving Maxwell’s equationswith the corresponding boundary conditions. The speed ofthe shower front, however, was assumed to be that of elec-trons moving with the speed lower than the speed of lightin the air.In reality the shower front moves with the speed of thehighest energy particles in a shower and exceeds the localspeed of light at all altitudes of relevance. Therefore, a re-flected wave in the forward direction cannot exist becauseit would be immediately caught by the shower front. Inits place a second transmitted wave, so called transmittedbackscattered wave, is formed [16] and it follows in pur-suit of the ionization front while standing off from it.It follows that, in the case of scattering of the radiowaves incoming at small angles to the shower axis, onecan not treat plasma as overdense because it is transpar-ent to arbitrarily low-frequency incident radiation. Consid-ering the plasma as underdense and using the Thomsoncross-section for radar scattering seems to be justified inthis situation. Moreover, unlike the case of reflection fromthe side of the ionization trail, where the frequency doesnot change, the frequency of the backscattered radio wavewill be upshifted. One can then expect an enhancement ofthe backscattered signal due to its time compression. Toavoid confusion we will use the term ’reflected wave’ as asynonym of the scattered wave.Scattering of the radio wave from the ionization trailproduced by the EAS in the underdense plasma regime wasconsidered in [5]. The calculations were made for the for- nhancement of the radar signal of air showers due to time compression33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO j r Θ s d T X ’ Z ’ Y ’ X R G T r ® sc j t H r L L ds d R r ® Y ’ hh = 0 Z ’ s a T Rn e j t Α Figure 1 : A schematic diagram representing a bistaticradar system and reflection from the non-moving plasmaproduced by the EAS in the atmosphere. See the text for adetailed explanation.
Figure 2 : Distribution of the factors by which the emittedfrequency is up-shifted ( f r ) for the radio wave scattered offdifferent parts of the shower disk. The altitude of the diskelement is given by h , whereas its distance to the receiverin the horizontal plane is d . A vertical shower headingtowards the transmitter is considered.ward scattered signal assuming that the ionization occursin a line along the shower axis, i.e. that contributions fromthe laterally distributed electrons are coherent. The trans-mitter and receiver were located 50 km apart. The com-puted case lies in between side scattering and front scat-tering with respect to the ionization column. Thus, the fre-quency upshift of the received signal reaches only modestvalues.In this paper, which is an extension of our previous work[6], we investigate the feasibility of detecting EAS by thebistatic radar technique at viewing angles smaller than ∼ ◦ to the shower axis. Simulations are performed for theunderdense regime using the Thomson cross-section forscattering of radio waves off the short-lived, non-movingplasma. We neglect absorption, multiple scattering, andcurrents induced in the plasma. We sum coherently con-tributions of the radio wave reflection on each individualelectron over the volume of the disk-like ionization trailand obtain the time evolution of the radar echo. The finalresult depends on the individual phase factors of the scat-tering electrons. A schematic diagram representing the concept of the EASdetection using radar technique is shown in Figure 1. Aground-based radio transmitter (T) irradiates a short-lived, disk-like, non-moving plasma left behind the shower front.The radio signal is scattered by free electrons in the ioniza-tion trail and subsequently received by the ground-basedantenna (R). The geometry of the bistatic radar system isdetermined by the polar coordinates of the transmitter andthe receiver, i.e. by the distances from the shower core tothe transmitter ( d T ) and to the receiver ( d R ) together withthe angles j t and j r .Let us consider the radar reflection from the disk ele-ment with coordinates ( r L , j ), altitude h , and electron den-sity n e . Its contribution to the radar echo at the receiver attime t is given by U ( t , s , r L , j ) = sin a r G T A R p r d s T d W n e e i w t + j × e − i R r n k · d r e − i R rsc n k sc · d r sc | r || r sc | , (1)where G T is the transmitter antenna gain, A R is the effec-tive area of the receiver antenna, k and k sc are the altitude-dependent wave vectors of incoming and scattered radiowave, j is the initial phase of the emitted signal, d s T / d W is the differential Thomson cross-section, s is the projec-tion of the distance between the shower core and the con-sidered disk element on the shower axis, a is the inclina-tion angle of the reflected radio wave, and n is the refrac-tive index of the air derived from the fit to the US stan-dard atmosphere. The factor sin a is included to take intoaccount the dependence of the receiver antenna gain on thedirection. We assume that the receiver is oriented verticallyupwards.The signal received by the antenna at a given time t isthe sum of the signals scattered at different times and fromdifferent parts of the plasma disk. These individual contri-butions interfere with each other and only the integral overthe whole volume V ( t ) , from which they arrive simultane-ously, gives us the correct total signal. The relative ampli-tude of the radio wave at the receiver antenna is given by U ( t ) = Z V ( t ) U ( t , s , r L , j ) r L d r L d j d s . (2)The factor U ( t ) is defined in such a way that the ratioof the ’instantaneous’ power P R ( t ) received by the detectorantenna to the power emitted by the transmitter P T is equalto P R ( t ) / P T = R ( t ) , (3)where R ( t ) is the real part of U ( t ) . The term R ( t ) is pro-portional to the electric field strength detected by the re-ceiver. It is used in the Fourier analysis to obtain thepower spectrum of the recorded signal. The ’real’ powerreceived by the detector P R can be obtained by averaging R ( t ) (according to the time resolution of the detector), i.e. P R = P T < P R ( t ) / P T > . Note that P R / P T ∼ G T A R .Alternatively, the radar reflection can be described interms of the effective RCS, which is a measure of the targetequivalent physical area of an ideal scattering surface. Theeffective shower RCS can be defined, by analogy with [3],in the following way s ( t ) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) Z V ( t ) e − i R r n k · d r e − i R rsc n k sc · d r sc n e r d s T d W d V (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) . (4) nhancement of the radar signal of air showers due to time compression33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO d R =
100 m Ν= - - - Σ @ m D - R @ - D
20 40 60 80 100 120 140t @ ns D - - - < P R (cid:144) P T > @ d B D Figure 3 : The effective RCS, the waveform of the radarecho, and the ratio of the power received by the detector tothe emitted one (averaged over a 100 ns running time win-dow) calculated for a vertical shower with energy 10 eVheading towards the transmitter. The shower core-receiverdistance is d R =
100 m and the frequency of the incidentradar wave is n = t = sin a | r || r sc | from the definition of U ( t , s , r L , j ) we obtain s ( t ) (cid:181) | U ( t ) | .The factor s ( t ) , which is defined by equation (4), hasthe meaning of cross-section only when the radio transmit-ter and receiver are sufficiently far away from the scatter-ing plasma or the volume of the scattering plasma is verysmall itself. These conditions will not always be met. Inreality, the volume from which the scattered radio wavesarrive simultaneously to the detector can have a consider-able size for a small viewing angle to the shower axis. It iscaused partly by the time compression of the reflected sig-nal. The estimation of the EAS radar cross-section givenby s ( t ) is used only for comparison. Despite the fact that the radio wave is scattered on a non-moving plasma, the ionization front moves with relativis-tic velocity, and thus we observe a Doppler shift of the re-ceived signal. Figure 2 shows the factors by which the emit-ted frequency is up-shifted ( f r ) for the radio wave scatteredon different parts of the disk-like plasma produced by thevertical shower heading towards the transmitter. The alti-tude of the plasma element is given by h , whereas its dis-tance to the receiver in the horizontal plane is d .The frequency upshift depends on the wave directionand the refractive index of the air. It has the highest valuefor the case in which the viewing angle coincides with theCherenkov angle. The typical f r is high enough to upshifta MHz signal into the GHz range. Therefore, it might bepossible to observe the radar echo in the GHz range using a d R =
500 m Ν= - - - - - - Σ @ m D - - R @ - D
200 400 600 800 1000 1200t @ ns D - - < P R (cid:144) P T > @ d B D Figure 4 : The same as figure 3 but for the transmitter-receiver distance of d R =
500 m and radar frequency of n = < P R / P T > is averaged overa 500 ns running time window.CROME-like setup [17] supplemented with a commercialhigh power MHz transmitter. The electron density of the plasma, produced by the high-energy shower particles in the air, is estimated using the av-erage longitudinal profile of proton showers parametrizedby the Gaisser-Hillas function and assuming the Gora func-tion [18] as the lateral distribution. We assume that eachshower particle deposits on average 2.3 MeV/g/cm andthat all of the deposited energy goes into ionization. Themean energy per ion-pair production is 33.8 eV. We planto improve the calculation of the plasma density by incor-porating the method used in [15].Since the received power of the radar echo is stronglydiminished by the geometrical factor of | r | − | r sc | − , thestrongest signal will be obtained from altitudes close to theground level, so we can assume an exponential decay ofthe static plasma with the characteristic time of 10 ns.As for the bistatic radar system, we assume that the ef-fective area of the receiver antenna is A R =1 m and thetransmitter emits signal into the whole upper hemisphere(i.e. G T = Figures 3 and 4 show the effective RCS, the waveforms R of the radar echo, and the ratios of the power received bythe detector to the emitted one < P R / P T > (averaged overa running time window) calculated for different frequen-cies n of the radar wave and different shower core-receiverdistances d R . In both cases the receiver is outside theCherenkov cone (see figure 2) and a vertical shower withenergy 10 eV heading towards the transmitter is consid-ered. The time t = < P R / P T > , nhancement of the radar signal of air showers due to time compression33 RD I NTERNATIONAL C OSMIC R AY C ONFERENCE , R
IO DE J ANEIRO
Figure 5 : Spectrogram of the radar echo for the verticalshower with energy 10 eV heading towards the transmit-ter. The radar frequency and transmitter-receiver distanceare equal to n =
10 MHz and d R =
500 m, respectively.The time window of 500 ns was used in the spectrogramcalculation.which is an equivalent of the return power, is calculatedfrom the spectrogram of the waveform assuming an infi-nite bandwidth detector. Note that the waveforms are givenin units of 10 − .As we can see, the frequencies of the received signalare higher than that of the emitted one, despite the factthat the Thomson scattering preserves the frequency ofthe scattered radio wave. The observed upshift is causedby the interference of the radio waves reflected from theplasma volume at different stages of its development, i.e.at different times.Since we are outside the Cherenkov cone, which is themost common case expected in experiments, the ampli-tudes of the waveforms increase with time. It is a geomet-rical effect of the reflections from the lower parts of theatmosphere. In accordance with the behavior of the sig-nal amplitude, the return power grows with time. For caseswhen the receiver is inside the Cherenkov cone, the timesequence is reversed: the lower part of the shower is seenfirst and the amplitude decreases with time.Figures 3 and 4 show the enhancement of the RCS atthe beginning of the signal. It is a combined effect of theincrease in the size of the region from which the scatteredwaves arrive simultaneously to the detector and the timecompression of the received signal. These two interrelatedfactors lead to an increase in the size of the region fromwhich we get the coherent signal. The part of the radarecho with the highest frequency upshifts arrives to thedetector from large altitudes. Therefore, despite the factthat the scattered signal is enhanced due to increase of theshower RCS, the return power of the radar echo is smalldue to the geometrical factor of | r | − | r sc | − .Figure 5 shows an example of the radar echo spec-trogram. As expected, the frequency decreases with time.Note the low-frequency component at the end of the radarecho, which is caused by the modulation of the receivedsignal by the factor e i w t (see equation (1)).The values of the power ratio < P R / P T > for differentshowers are given in table 1. It is evident that the strengthof the signal decreases with increasing radar frequency.The size of the region from which one gets a coherent sig-nal decreases with the wavelength and destructive interfer-ence cancels out the signal from the other regions. We have studied the feasibility of EAS detection by thebistatic radar technique at small viewing angles to the
Table 1 : The maximum values of the received to the emit-ted power ratio for shower with different energies E , fre-quencies n of the radar wave, and transmitter-receiver dis-tances d R . In all cases a vertical shower heading towardsthe transmitter is considered. The signal is averaged over a100 ns time window. E eV 10 eV 10 eV n \ d R
100 m 500 m 200 m 200 m1 MHz -133 dB -158 dB -119 dB -98 dB5 MHz -154 dB -174 dB -138 dB -117 dB10 MHz -162 dB -182 dB -146 dB -124 dB20 MHz -172 dB -191 dB -156 dB -134 dBshower axis.Due to the time compression, the signal scattered off theplasma is enhanced. The effect is strongest for the initialpart of the radar echo with the highest frequency upshifts.However, the resulting return power is strongly diminisheddue to the large distance of the scattering plasma to thedetector.The typical signal consists of two parts: a short sig-nal upshifted to high-frequency with low amplitudes and along signal with modest frequency upshifts and larger am-plitudes. In principle, the last part of the signal, with thetypical ratio of the received to the emitted power between-100 dB and -190 dB, should be observable. Since thestrength of the signal decreases with the radar frequency, itis recommended to use low frequencies of the radar wave.A note should be added, that the shown time traces arefor an infinite bandwidth detector − a realistic detectorwould only be able to detect the signal in a narrow fre-quency range. Moreover, it will only see the shower for acertain fraction of its development. Acknowledgment:
This work has been supported in part bythe KIT start-up grant 2066995641, the ASPERA project BMBF05A11VKA and the National Centre for Research and Develop-ment (NCBiR) grant ERA-NET-ASPERA/01/11.