Towards the identification of the primary particle nature by theradiodetection method with the CODALEMA experiment

A. Rebai1,∗

1 SUBATECH, IN2P3-CNRS, Université de Nantes, Ecole des Mines deFrance ; http ://codalema.in2p3.fr

Dated : November 18, 2011∗ Corresponding authors E-mail adresses ahmed.rebai@subatech.in2p3.fr (A. Rebai)

1 Abstract

Radio signal from extensive air showers studied by the Codalema experiment have been detected by meansof short fat antennas array. Delay distributions of radio signal with respect to the plane wavefront hypothesishave been analysed for individual events. Outputs from the fitting model have been compared with otherreconstruction models used in the same experiment. Results indicate that the radio shower core is systematicallyshifted from the particle shower core in a statistic analysis approach. It means that the model used in this paperpredict an excess negative charge during the developpement of the shower in the atmosphere. Comparisonbetween radius of curvature obtained with data and Xmax obtained with AIRES Monte Carlo simualtions for thesame set of events revealed a prelimenary study of the primary particle nature with the radiodetection method.

2 Introduction

Since the last decade, radiodetection of the ultra high energy cosmic rays has arised again as a complementarydetection technique to ground-based particle detector arrays and fluorescence telescopes. The lastest results fromCODALEMA and LOPES experiments have shown the potential and feasibility of this technique in terms ofsensitivity to the shower longitudinal development , the detection duty cycle was near to 100% and the low costof detectors. CODALEMA at Nançay has shown a north south asymmetry signature of a geomagnetic effect in theradio signal production mechanism [1]. On the other hand LOPES has shown the possibility of reconstruction ofthe radio lateral distribution function [2] that allows to have an observable linked to the shower developementand correlated with the primary particle energy [3] and [4]. The radio emission center is a very importantobservable since it is related to two properties of the primary particle its energy and its chemical compositionthrough the shower maximum developpement Xmax. In this paper, we discuss a new reconstruction method ofthe radio signal wave front radius of curvature. We use a parabolic model (PM) that fit the distribution of timeresiduals relative to plane wave hypothesis. We show the origin of the reconstruction model and the results fromthe CODALEMA data.

3 Experimental situation

Since 2002, CODALEMA experience [5], hosted on the radio observatory site at Nançay with geographicalcoordinates (47.3◦N, 2.1◦E and 137 m above sea level), aims to study the potential of the radiodetection techniquein the 1016 eV energy range(detection threshold) to 1018 eV (upper limit imposed by the area surface). It consistsof an array of 24 active dipole antennas spread over a surface of about 1

4 km2, an array of 17 particle scintillatordetectors and a 144 conic logarithmic antennas from the Nançay decametric array (see fig. 1).

1

Figure 1 – Set up of CODALEMA experience showing the disposition of the particle detectors array (red) and the dipole antenna array(yellow) used for this study.

Triggering the scintillator data acquisition system is defined by the passage in coincidence of secondaryparticles, created in extensive atmospheric shower, through each of the 5 central particle detectors. Triggerdetection threshold energy is equal to 5.1015 eV. The radio waves forms in each antenna is recorded in a 0-250MHz frequency band during a 2.5 µs time window with a 1GS/s sampling rate. Radio events that are detectedby dipole antenna array in coincidence with atmospheric shower events are identified during offline analysis[5] [1]. After this analysis phase, a data set containing the parameters of the shower reconstructed using theinformation provided by the particle detectors (arrival times distribution, arrival directions, shower core on theground and energy) and a set of observables for each radio antennas (arrival times distribution, radio signalamplitude) and the observables of the reconstructed shower by the use of radio data alone (arrival time, directionarrival, radio shower core on the ground, energy) are obtained event by event. These observations are used tostudy the curvature of the radio wave front that could be one of the discriminating variables the nature of theprimary (estimate of Xmax).

4 Experimental motivations

In the first approximation the radio signal front is assumed to be a plane perpendicular to the shower axis.Then, the primary particle direction of motion can be determined directly by triangulation using the time offlight between different antennas. According to this hypothesis if we take the first tagged antenna, in each event,as a reference for arrival time and we plot the theoretical time delay ∆ttheo as a function of the experimentaltime delay ∆texp (see Appendix A for time delay calculation methods). We should observe an alignment with theplane wave best line fit. But when this test is performed on data we see that points deviate from this line (seefig. 2) despite the 10 ns experimental timing uncertainty (See Appendix B for understanding the origin of suchuncertainties).

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Figure 2 – The black line presents the plane wave best line fit, we see that despite the error bars of 10 ns on both axes. Many pointssystematically from the line which shows that the wavefront is not a plan

This deviation from planarity is not a systematic experimetal bias time measurements on antennas so it can beexplained by the fact that the wave front has not a plane form (shape) but another one and the signal generationregion in the shower was located at a distance Rc from the ground with respect to the arrival direction. To verifythis effect, simulations of wave propagation from this emission center have been performed with the triplegoal of reproducing event per event the geometric configuration, using of a spherical wave shape for simplicityreasons and approaching the real detection conditions in terms of time resolution by random number generator(See Appendix C). The figure 2 shows a simulation where we have used the same parameters of the event (seefig. 2) and the emission center is distant of 3, 5 and 10 km from the ground. We can conclude two importanteffects : the simulations reproduced the data in the context that the wavefront shape is different from a plan andthe emission center moving away from the ground more points in the figure approaches from the best fit line isa clear tendency to the normal plane wave.

5 Theoretical foundation of the reconstruction model

As explicitly mentionned above, we have demonstrated that the wave front is slightly curved. This curvatureis due to the fact that the source of the radio signal is space-localized. We now propose to reconstruct the emissioncenter position. Our reconstruction is not based upon adjusting the wavefront shape which has a complicatedgeometry dependent on the shower developpement but based on fitting the difference between real and ahypothetical plane wavefront by a parabola this is correct for basic geometrical consideration 3. Modeling ofthis difference requires four hypothesis :

– The lateral spread is ignored.– The emission region is situated at a large distance Rc compared to distances between antennas and shower

axis (Rc >> d) (see fig. 3).– Radio waves are supposed to travel at the speed of light.– Antenna and shower core coordinates need to be changed into the shower coordinate system by 2 angular

rotation.We can write this difference as follows :

∆ = MG −MO,

= (d2 + R2c )

12 − Rc,

= Rc(((d

Rc)2 + 1)

12 − 1),

3

≈ Rc((12

(d

Rc)2 + 1) − 1),

≈12

d2

Rc,

Figure 3 – Sketch of a simplified relation between wavefront shape and curvature radius

Developing more the four hypothesis assumed at this section : Let’s start with the first hypothesis, one canbe considered the air shower particles responsible for the radio emission are concentrated in a region of spaceclose to the shower axis. The coherence property of the signal leeds to a lateral spatial extension variate between3 m to 13 m order the chosen frequency band. For the longitudinal thickness of the region, it is known afterthe work of Linsley [6] that the particles swarm has a few meters of longitudinal thickness. It is clear now thatmost electrons/positrons are concentrated in a small symmetric cylindrically volume with negligible dimensionscompared to the distances between the emission center and the array of antennas which explains the aboveapproximation Rc >> d. Finally, the last hypothesis was necessary to generalize the reconstruction model to allshowers with different zenith angles.

Yet, the difference ∆ is a parabolic function of the distance d. In term of arrival times, ∆ is expressed by the timedelay between the instant tpred

i predicted by the hypothetical passage of the plane wave front on antenna i andthe instant tmax

i measured experimentaly by the slightly curved wave front on the same antenna (see AppendixA). In order to ensure identical treatment for all showers despite of their zenith angles θ. The coordinates of theantennas (xi, yi, zi = 0) and times (tmax

i ,tpredi ) must be expressed in a new frame called the shower frame defined

by two rotation involves both the azimuthal and zenithal angles (φ,θ) as used in [7]. This correspondence is thenwritten for an antenna i as follows :

c(tmaxi − tpred

i ) = a +1

2Rc(dr

i )2,

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where dri the distance between antenna i and the shower axis in the shower frame,

dri =√

(xri − xr

c)2 + (yri − yr

c)2 + (zri − zr

c)2,

The 3D rotation matrix used is as follows :xr

iyr

izr

i

=

cos(φ).cos(θ) cos(θ).sin(φ) sin(θ)−sin(φ) cos(φ) 0

−cos(φ).sin(θ) −sin(θ).sin(φ) cos(θ)

xiyizi

The development of calculation gives the following system of equations.

xri = cos(θ).(cos(φ).xi + sin(φ).yi) + sin(θ).zi(1)

yri = −sin(φ).xi + cos(φ).yi(2)

zri = −sin(θ).(cos(φ).xi + sin(φ).yi) + cos(θ).zi(3)

The same transformation is performed to the shower core coordinates (xc, yc, zc). The term time will not be

affected by the transformation since the difference will remove the same added termzr

ic . Giving the χ2 function :

χ2 =

N∑i=1

(c(tmaxi − tpred

i ) − a −(xr

i − xrc)2 + (yr

i − yrc)2 + (zr

i − zrc)2

2Rc)2

This estimator has five free parameters the constant a, the radius of curvature Rc and (xrc, yr

c, zrc) expressed in the

shower frame. The nonlinear terms force us to use a numerical method for the χ2 minimization. Both the matlabCurvefitting toolbox and Optimization toolbox have been used and give the same results. We found that the moreappropriate algorithm for the resolution of the minimization problem was the Levenberg-Marquardt designedfor non-linear problems.

6 Data analysis and events selection Criteria

6.1 Selection strategy

Our strategy for estimating the radius of curvature demanded the selection of only those events in which weare sure of their quality and their parameters reconstructed by other models in order to facilitate comparisonbetween different models. For this we have chosen a selection with cuts similar to those used to fit the lateraldistribution function [8]. The data used in this paper were collected by the CODALEMA experiment duringover than 3 years between november 2006 and january 2010. We find a yield of 196526 events detected by thescintillator array after selections we use 450 internal events.

Thus the key ingredients for selecting our set of events are the following :– Selection of radio events candidate by choosing events were detected in coincidence between scintillator

and antennas array. je parle ici de l’arbre la fenetre en temps et la fenetre angulaire the following criteria mustbe met : a time coincidence with +/-100 ns and an angular difference smaller than 20 degree in the arrivaldirections reconstructed from both the particle and radio arrays. je peux parler ici du taux du trigger et detaux d’evets fisiks par jour comme c’est indique dans ma presentation au SF2A

– Selection of internal events to be sure that shower core was situated inside the two array with a very goodestimation of energy (Fenergy=1).

– Multiplicity 1 5 because our model has 5 free parameters– Only tagged antennas by event. This cut is applied to eliminate the antennas that have a low signal to

noise ratio in order to improve reconstruction.

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This last cut does not remove any event although it improves their quality by getting rid of not tagged antennas.

Figure 4

6.2 Events Samples

Table shows the numbers of collected events and their types. We report here the efficiency of samples.

Type Number EfficiencyTrigger SD 196526 100%

Coincidences (SD and antennas) 2030 1.03%Internal events 450 22.17%

7 Verification and Confirmation of Results

Numerical minimization of the χ2 function gives the shower core position (xrc, yr

c, zrc) expressed in the shower

coordinate system. For using coordinates its need to be transformed by an inverse transformation that involvesthe inverse rotation matrix (see Appendix D) to the ground frame. Our approach for the validation of the modelis based on the comparison of these reconstructed parameters with other models and with confirmed physicalvalues.

7.1 Consistent shower core elevation

The CODALEMA experiment is situated on a flat land of geographical altitude of 134 meters. Given thelateral extension of the antenna array. We can be considered with a good approximation that antennas have analtitude equal to zero meter in the ground local reference. The figure 5 shows a histogram of the shower corealtitudes for selected events. We can conclude that elevations are consistent with the geometric configuration ofthe antenna array. Then the model give a correct zc consistent with zero. j’ajoute une etude statistique pour les evetsqui ont un z vraiment egale a 0 et les z qui sont a peu pres different quantification avec des pourcentages

6

Figure 5 – histogram of shower core elevation for selected events

7.2 Confirmation of the radio core east shifting signature of charge excess mechanism

We can consider that the real test of validation of our experimental reconstruction is whether it predictsthe systematic shift between the radio core and the particle radio. This shifting is an evidence of a negativecharge excess in the electromagnetic component during the shower developement. This effect was predicted byAskaryan [9] in the sixties of the last century. According to [9], this negative charge excess acts as a monopolythat moves with the speed of light and which contributes to the emission by coherent radio signal. The processesresponsible for this negative charge excess are :

– Compton recoil electrons ejected into shower by photons with energy less than 20 MeV.– δ-ray process which consist of electrons ejected from external atomic orbital under the influence of elec-

tromagnetic cascade.– Fast annihilation of positrons in flight.

Further explanations are compiled in the Allan review [10]. This effect has several signatures. it appears inthe polarization of the electric field on the ground as shown in [11] also in the systematic shift between radioshower core and particle shower core seen in data with [12] and [13] and explained by simulations in [14]. Thereconstruction model used in these papers assume that the lateral density profile (LDF) of the radio shower

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follow a decreasing exponential as mentionned by Allan in [10]. Then, the electric field has this formula

E = E0.exp(−

√((x − xc)2 + (y − yc)2 − ((x − xc).cos(φ).sin(θ) + (y − yc).sin(φ).sin(θ))2)

d0)

with xld fc , yld f

c were coordinates of the radio shower core by the LDF model. The radio core were expressed inparticle core frame with the next geometrical transformation

~S = ~rr − ~rp

with ~rr and ~rp are vectors respectively for radio and particle shower cores and ~S the vector which represent thesystematic shift.

Figure 6 demonstrates a comparaison between the east-west projection of the systematic shift ~SEW measuredby PM and LDF models. Obtained curves are fitted by a gaussian. According to our statistical approach, it canbe concluded that the radio shower cores are shifted towards the east with respect to the particle shower cores.This shift is a physical effect verified by both methods. We remember that the two methods are completelyindependent. PM method is based on the distribution of arrival times and the LDF method is based on theamplitudes of the radio signal on the antennas. One can interpret the difference in the mean shift value betweenthe two models by the signal to noise ratio is different for the two methods. LDF model is based on the radiosignal amplitudes on the antennas. CODALEMA antennas are occupied by a low noise amplifier (LNA) arevery sensitive to the signals detected. Knowing that the noise level of the galactic background is worth ? ? andthe value of a signal typically developed by a shower with an energy of 1017 in the range of ? ? ? ? µV/m. Thissensibility can expect a ratio of the order ? ? ?

8

Figure 6 – vers la gauche de la distribution rouge on voit que il y a plusieurs bins qui s’eloignent de la gaussienne on peut expliquerpar le fait que le LDF exponentielle decroissante n’est pas tres adapte, ici je prepare le terrain pour le modele gaussien maisje contente uniquement de dire le ldf gaussien ca sera l’objet d’une prochaine publication je dois pas oublier de mentionnerque le fit a pris uniquement les bins qui contiennent un nbre assez grand d’evenement cad pour eviter les outliers pts qui setrouvent tres loin dans la queue de la distribution

Figure 7 – pieds de gerbe avec 3 méthodes ici je dois mettre les courbes bi-dim pour la comparaison des pieds de gerbes

9

Figure 8 – pieds de gerbe avec 3 méthodes ici je dois mettre les courbes bi-dim pour la comparaison des pieds de gerbes

8 Results of the Curvature Radius reconstruction

J’insere l’histogramme des rayons de courbure avec une explication du pic vers 4 km et du queue de la distribution lesRc tres grands qui sont peut etre les evenements qui ont un centre d’emission tres loin qui donne d’une onde plane ou biende defauts de reconstruction ou bien le modele arrive a ces limites il y a la these autrichienne qui montre un histogrammedes Rc dans Auger reconstruit avec la methode particule je peux prendre l’interpretation qui se trouve dans cette these. Theshower front curvature radius at the core also represents the apparent distance to the initial cosmic ray interaction withatmospheric nucleus with the atmosphere. the dist of the apparent fisrt interaction height Rcostheta shows a distinct peakat 7 km which is the height at which most air shower signals seems to originateComme une explication possible du queue de la distri des Rc qui presente des Rc tres grands on peut expliquer ca par lamultiplicite des evets cad moins l’event a touches d’antennes moins la reconstruction est bonne ou bien precise un autreargument a passer avec l argument de l’eloignement du centre d’emission

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Figure 9 – Histogram of the radius of curvature for 1010 events show a peak at about 4 km.

il faut aussi montrer la courbe Rc en fct de theta ou bien en fonction du cos(theta) pour discuter le fait que Rc augmenteavec l’angle zenithal je pense qu’il faut ajuster avec une loi de forme R = cte1 + cte2*(theta)n pour comparer apres entre d0= cte1 + cte2*(theta)n l’idee est de tirer une similarite entre les deux observables physiques R et d0 et theta

Figure 10 – Courbes de corrélation entre Rc et θ. On remaque que en moyenne le rayon de courbure augmente en fonction de l’anglezénithal.

9 Towards a primary particle nature identification with the radio method

On peut considerer que la composition chimique des UHECR en fonction de leurs energies reste un mystereen astrophysique. Cette mesures est tres importante puisqu’elle permet de repondre a une question plus fonda-mentale qui est liee a l’orgine de ces particules. ici je dois introduire pourquoi il est important d’utiliser l’observableradio pour

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9.1 Atmospheric density profile

The earth’s atmosphere acts like a layer of matter with 1000g.cm−2 of thickness. The earth’s atmosphere actslike a volume of detection where the primary particle deposits its energy as huge number of secondary. Then,any attempt for the determination of chemical composition of UHECR passes through the fine understandingof the atmosphere density variation as function of the altitude above the sea level exactly at the experiment sitein France. For these reasons, the atmospheric density profile is a highly required knowledge for converting thereconstructed radius of curvature into the shower maximum Xmax using this formula :

Xradiomax =

f Linsley(Rc.cos(θ)))cos(θ))

where fLinsley is a function following the Linsley’s parameterization which divides the atmosphere into five layersand give a realistic approximation. So we have compiled data from the US standard atmosphere cited in Airesuser manual [?] and from the middle europe atmosphere in 7 months implemented in Corsika package [?]. Wehave used the Linsley’s parameterization [?]. Our compilation shows that both atmospheres have very similarcharacteristics (see fig. 11). The same figure shows that the error in the Xmax estimation due to the atmospherecollected data is the order of σatm = 45g.cm−2 which represents a first source of systematic error on the ourchemical composition estimation.

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Figure 11 – (Above) Compilation of data that represent the vertical atmospheric depth according to the altitude above the sea level withrespect to the Linsley’s parameterization. Atmospheric data are collected from the US standard atmosphere (dash blackcurve) [?] and the middle Europe atmosphere with measurements at 7 different months (colored solid curve) [?]. (Below)Comparison between the same data taking as reference the US standard atmosphere XEU − XUS.

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9.2 Composition results :Preliminary

il est tres important d’interpreter les courbes d’identification avec les simulations et les resultats theoriques je doisapprendre comment mettre les droites theoriques SIBYL et QSJET. je dois aussi lire la these de Frank Schrodder.

Figure 12 – Courbe d’identification sur 38 événements communs entre deux Reconstructions sphériques

Dans le cadre du modele de Greisen (il faut inclure la formule du modele qui se trouve dans les livres des RC ou le coursjoliot curie) d’une gerbe electromagnetique on peut lier directement le Xmax a l’energie de la particule primaire (la formulese trouve dans ma presentation dans le SF2A) cette formule nous permet connaissons rayon de courbure et en utilisant lemodele de l’atmosphere de Linsley pour l’atmosphere americain et l’atmosphere allemands (qui se trouve dans le manuel ducorsika) le modele americain se trouve dans le manuel du AIRES) (see fig. 11)

14

Figure 13

10 Conclusions

11 Appendix A. Calculation method for theoretical and experimental time delays

11.1 Theoretical time delay calculation

We assume here that the signal propagation is carried out with a constant speed which is the speed of lightin the vacuum c and in the hypothesis that the radio signal wave front is a plan perpendicular to the arrivaldirection. The plan equation can be written as :

u.x + v.y + w.z + d = 0,

with (u, v,w) = (cos(φ).sin(θ), sin(φ).sin(θ), cos(θ)) are the coordinates of the unit vector ~n normal to the plane.Now we take the first tagged antenna (fta) as reference to calculate the constant d. the equation becomes :

u.x + v.y + w.z − (u.x f ta + v.y f ta + w.z f ta) = 0,

The distance between this plane and the other tagged antennas located at positions (xi, yi, zi) with i = 1, ...,N isgiven by this formula :

di =|u.xi + v.yi + w.zi − (u.x f ta + v.y f ta + w.z f ta)|

√

u2 + v2 + w2

The arrival time of the plan on each antenna is given by simple division of the distance di by c then :

tpredi = t f ta +

di

c.

this formula allows to reproduce the plane wave propagation from the first tagged antenna until other antennas.Theoretical delay is then written :

∆ttheoi = tpred

i − t f ta =di

c.

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11.2 Experimental time delay calculation

The filtered signals maximum in each antenna enable the determination of the experimental arrival time thereal time noted tmax

i . Experimental delay is then written :

∆texpi = tmax

i − tmaxf ta =

di

c.

∆ttheoi and ∆texp

i are used in the begining of this paper for showing the deviation from the plane wave model.

12 Appendix B. Time uncertainty calculation

ici je developpe la methode pour estimer la resolution temporelle des antennes de l’experience Codalemales erreurs temporels sont dues a la methode de filtrage numerique par le filtre. Codalema utilise la bande 23-83 Mhz propredes emetteurs parasites. Ce filtrage donne des signaux qui oscillent avec des periodes variantes entre 12 et 43 ns et puisqueon s’interesse au maximum positif des signaux filtres (qui correspondent a une supeposition non destrcuctive des emissionsradio qui proviennent de la gerbe. des signaux en phase). alors on divise ces periodes par un facteur 2 d’ou l’utilisation de10 ns d’erreur.timing errors are due to the method of digital filtering by the filter. Codalema uses the 23-83 Mhz band cleanfrom the parasites transmitters. This filtering gives signals that oscillate with periods ranging between 12 and 43ns. and since we are interested in the maximum positive signal filters (which correspond to a non supepositiondestrcuctive radio emissions coming from the shower)

13 Appendix C. Simulations of wave front propagation with spheric shape

Simulated events generation is based on purely geometric considerations (In this study, we did not usecomplete simulation given by REAS3 or SELFAS2 but its can be used for future more realistic tests). To generatea simulated event, we fix the radius of curvature Rc, azimuthal and zenith angles values (φ, θ) and coordinatesof the shower core (xc, yc, zc), we calculate the coordinates of the the emission center with :

x0 = R.cos(φ).sin(θ) + xc(1)y0 = R.sin(φ).sin(θ) + yc(2)

z0 = R.cos(θ) + zc(3)

These coordinates allow us to determine the distance between a given antenna and the center of emission.d =

√(x0 − xi)2 + (y0 − yi)2 + (z0 − zi)2. We calculate the wave arrival time at each antenna by the following

formula : ti = t0 + d/c. Since the antenna has a time resolution and non-zero error that affects off-line analysis,one must take into account in our simulation so we fluctuates over time on the antenna of a normal distributionwith this formula : ti = t0 + d

c .gauss(0, 1).σtime with gauss(0, 1) =1

σ√

2πexp(−0.5λ2)

Références

[1] D. Ardouin al Astroparticle Phys, vol. 31, pp. 192–200, 2009.

[2] W. Apel al Astroparticle Phys, vol. 32, pp. 294–303, 2010.

[3] P. Lautridou, “Contribution to the ricap conference, roma,” 2011.

[4] A. Haungs, “Contribution to the ricap conference, roma,” 2011.

[5] D. Ardouin al Astroparticle Phys, vol. 26, pp. 341–350, 2006.

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[6] J. Linsley, “Thickness of the particle swarm in cosmic-ray air showers,” Journal of Physics G : Nuclear Physics,vol. 12, no. 1, p. 51, 1986.

[7] H. H. Kh., A. Anvari, M. Bahmanabadi, J. Samimi, and M. K. Ghomi, “A new simple method for the analysisof extensive air showers,” Astroparticle Physics, vol. 34, no. 9, pp. 699 – 704, 2011.

[8] O. Ravel, “doi :10.1016/j.nima.2010.12.057,” Nucl. Instrum. methods A.

[9] G. Askaryan J. Exp. Theor. Phy, vol. 21, p. 658, 1962.

[10] H. Allan, “Amesterdam,” Progress in Elementary Particles and Cosmic Ray Physics, vol. 10, p. 171, 1971.

[11] H. Schoorlemmer, “Results from polarization studies of radio signals induced by cosmic rays at the pierreauger observatory,” Nuclear Instruments and Methods in Physics Research Section A : Accelerators, Spectrometers,Detectors and Associated Equipment, vol. In Press, Corrected Proof, pp. –, 2010.

[12] A. B. A. Lecacheux, “Proc. of the 31st icrc,” for the CODALEMA collaboration,, 2009.

[13] A. Bellétoile, “Submitted to phys rev d,” al.

[14] V. Marin, “Proc. of the 32 icrc,” for the CODALEMA collaboration,, 2011.

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