Appendix A Radio Measurements at Tunka

Transcription

1 Appendix A Radi Measurements at Tunka The Tunka experiment measures Cherenkv light emitted by air shwers []. It is lcated clse t Irkutsk, Siberia, Russia, and cnsists f 33 phtmultiplier detectrs (with cm pht cathde diameter) in a hexagnal structure (see Fig. A.). Since Cherenkv measurements are sensitive t the lngitudinal shwer develpment, they allw a relatively gd estimatin f the primary energy and mass. Tunka perates in abut the same energy range as KASCADE-Grande (E. 8 ev) and will yield a cmplementary measurement f the csmic ray energy spectrum and its cmpsitin. Since Tunka is lcated in a radi-quiet rural area, it is an interesting site fr simultaneus peratin f a digital radi array. The additinal radi measurements f air shwers will have tw purpses. First, the radi measurements can be crsscalibrated with the Cherenkv measurements with respect t the energy and X max. This way, Tunka can imprve the understanding f the radi emissin mechanisms, which in turn is a valuable input fr ther radi experiments. Secnd, Tunka can prfit frm the radi measurements, e.g., t imprve the angular reslutin with a hybrid recnstructin. This will be similar t the situatin at the Pierre Auger Observatry, where the recnstructin f air shwers measured with flurescence telescpes is significantly enhanced by using the infrmatin f a simultaneus surface detectr measurement. T increase the event statistics f Tunka at high energies, it might als be pssible t cntinue radi measurements at day r during bad weather, when the PMTs cannt perate. Hwever, fr a radi stand-alne peratin, first a reliable self-trigger has t be develped, like it is presently dne fr AERA. T pave the way fr radi measurements at Tunka, a SALLA antenna was installed in summer 9, using AERA prttype hardware develped within the LOPES STAR setup. This antenna is lcated in ne f the inner Tunka clusters, cluster 7, clse t the central PMT detectr and the DAQ electrnics bx f this cluster. The clse distance t the electrnics was chsen t facilitate the F. G. Schröder, Instruments and Methds fr the Radi Detectin f High Energy Csmic Rays, Springer Theses, DOI:.7/ , Ó Springer-Verlag Berlin Heidelberg 5

2 5 Appendix A: Radi Measurements at Tunka

3 Appendix A: Radi Measurements at Tunka 53 b Fig. A. Tp map f the Tunka experiment with a hexagnal structure f phtmultiplier detectrs fr Cherenkv light emitted by air shwers [4]. It cvers an area f km. Bttm SALLA installed at Tunka cluster 7, cluster DAQ electrnics bx (white bx), and central phtmultiplier detectr. Published with kind permissin f Ó the Tunka Cllabratin 9 installatin f the SALLA. Hwever, it can be disadvantageus if the electrnics emit RFI. The results f the test measurements with this prttype antenna are presented in this appendix. Several radi candidate events have been fund within half a year f data taking. There is evidence that the radi pulses in the candidate events are linked t csmic ray air shwers. Hwever, it culd nt finally be reslved whether the detected radi pulses are directly emitted by the air shwer, r whether they are caused by crsstalk r secndary RFI pulses emitted by the Tunka PMTs r the DAQ electrnics. The fllwing paragraphs summarize the analysis. A mre detailed descriptin is available in Ref. [], and a shrt summary f the results is published in Ref. [3]. In September 9, a SALLA with tw plarizatin channels, east-west and nrth-suth, were deplyed at Tunka. The AERA prttype electrnics filters the signal t a limited bandwidth f 3 8 MHz. The amplified and filtered radi signal is digitized with a sampling frequency f MHz by the same Tunka electrnics used t digitize the PMT signals. The same trigger is used fr the PMTs and the SALLA. Wheneveluster 7 is triggered, bth channels f the SALLA are read ut simultaneusly with the seven PMT detectrs f this cluster. The trace length is 5: ls. Analyzing the first radi data includes several steps: First, a general investigatin f the radi backgrund at Tunka. Secnd, a check if the SALLA wrks reliably. Third, a search fr any radi pulses. Frth, an investigatin whether there are radi pulses causally linked t air shwers by crrelating with the Tunka recnstructin f air shwer events. And fifth, a careful analysis, if radi candidate events culd als be caused by crsstalk r RFI. Abut ; events frm 6 mnths have been analyzed, limited t the Tunka measurement perids during dark mnless nights. T check fr the system health and stability f the SALLA, backgrund spectra have been evaluated fr each mnth (see Fig. A. fr an example). The backgrund spectrum did nt change significantly ver time, even in the cld winters f Siberia (T min 4 C), which demnstrates the stability f the system. The spectrum shws several peaks f narrw band RFI within the measurement bandwidth f 3 8 MHz. These peaks can be mitigated during analysis, like it is usually dne in LOPES and AERA data cnditining. In general, the backgrund level is much lwer than at LOPES, and might be cmparable with the situatin at AERA in Argentina. Hwever, a final evaluatin f the backgrund will require abslute calibrated measurements at Tunka. Radi pulses have been fund in abut 8 % f the events with a threshld algrithm (see Fig. A.3 left). Since the arrival time f these radi pulses is mstly

4 54 Appendix A: Radi Measurements at Tunka received pwer [db] nrth-suth east-west ADC cunts east-west nrth-suth frequency [MHz] time [ns] Fig. A. Left: backgrund spectrum measured with the SALLA at Tunka cluster 7, averaged ver successive events. Right: example fr a radi pulse detected with a threshld algrithm in bth plarizatin channels f the SALLA. Mst likely it is a RFI pulse because it is nt in cincidence with PMT pulses typically ccurring at 3 ls ADC cunts 5 PMT statin -7 Radi antenna: east-west nrth-suth time [ns] number f events pulse arrival time [ns] Fig. A.3 Left example event with a radi pulse cincident with PMT pulses. Right arrival time distributin f radi pulses in cincidence with Tunka events, in which at least 5 f the 7 PMTs f cluster 7 exceeded a threshld f 7 ADC cunts, i.e., a SNR f. The first peak is nly visible fr high energy events and rughly at the same time as the PMT pulses. Hence, radi pulses at this time are candidate events. The secnd peak is already visible withut any threshld cut n the PMTs, and prbable arises frm RFI rsstalk randm, they prbably riginate frm uncrrelated backgrund perturbatins. Hwever, the situatin changes if an additinal threshld cut is applied n the PMT signal. When high energy events are selected, a fractin f the radi pulses is detected at abut the same time than the PMT pulses (see Fig. A.3 right). This way, 74 events are selected, in which the radi pulse is cincident with strng PMT pulses. Fr nly f these 74 events als a Tunka recnstructin is available, since the remaining 4 events have been recrded either during test runs r bad weather. Thus, there are radi candidate events. Apart frm the cincident arrival time with the PMT pulses, there is additinal evidence that the radi candidate events are linked t air shwers. A selectin f 78 Tunka events with energy E [ 7 ev, zenith angle h \ 45, and lateral distance t the SALLA R. 3 m cntains f the candidate events much

5 Appendix A: Radi Measurements at Tunka 55 radi amplitude [ADC cunts] radi detectin in nrth-suth east-west all selected events (energy distributin) lg (energy/tev) radi amplitude [ADC cunts] radi detectin in nrth-suth east-west all selected events (distance distributin) 3 lateral distance [m] Fig. A.4 Energies E and lateral distances R f Tunka events selected with E [ 7 ev, h\45 and R\3 m, and amplitude f the radi candidate events cntained in the selectin. The crrelatin matches the expectatins fr radi pulses riginating frm air shwers: The radi amplitude shuld be rughly prprtinal t the primary energy, and shuld be higher at small lateral distances. Thus, the detectin prbability shuld increase with E, and decrease with R mre than expected by chance. Furthermre, there is a clearrelatin f these radi candidates with the energy and the lateral distance: there is an accumulatin f events clse t the SALLA and at high primary energy. This is expected if the radi pulses are by any means caused by air shwers. Hwever, it is nt enugh t prf that the detected pulses riginate directly frm the air shwer, since the same crrelatin is expected fr Cherenkv pulses detected by the PMTs. Cnsequently, any secndary RFI pulses caused by the PMT rsstalk in the electrnics wuld exhibit the same crrelatin between the radi pulses and the energy and lateral distance. A definite prf that the radi pulses are directly emitted by the air shwer, requires the investigatin f a shwer parameter which is crrelated with radi and Cherenkv pulses in a distinct way, e.g., the gemagnetic angle. This is currently analyzed []. Summarizing, the analysis f the first Tunka radi data shwed the difficulty t judge with nly ne antenna if detected radi pulses riginate directly frm air shwers r nt. At least a fractin f the radi candidate events might be caused either by RFI emitted by the PMTs rsstalk inside f the electrnics bx. In the first case, it is advisable t place further antennas as far away frm the PMTs as pssible, i.e., in the center between three PMTs. Then, primary air shwer pulses and secndary PMT pulses can be distinguished by their arrival times. In the latter case, the shielding inside f the electrnics bx has t be imprved. Taking data ver a lnger perid with a discnnected antenna will allw t distinguish between bth cases. N external radi pulses, but nly RFI pulses cause by crsstalk shuld still be present in the data if the antenna is discnnected (Fig. A.4). Furthermre, a cmparisn f detected radi pulses with REAS3 simulatins can help t identify radi pulses emitted by air shwers. Since n abslute calibratin is available fr the SALLA at Tunka, yet, the abslute amplitude f the radi pulse is nt a gd quantity fr this cmparisn. Nevertheless, the amplitude

6 56 Appendix A: Radi Measurements at Tunka rati between bth plarizatin channels will be a gd quantity, since it is independent f the abslute calibratin. Once real pulses have been identified, the cmparisn with REAS3 can even yield a rugh abslute calibratin, because REAS n average predicts the crrect amplitude, as prven by cmparisns with the abslute calibrated LOPES experiment (see Chap. 7). Finally, mre antennas will be needed. With three r mre antennas, a recnstructin f the arrival directin, and an estimatin f the primary energy and mass will be pssible. A cmparisn f these parameters t the Tunka recnstructin will help in the decisin, whether an additinal radi array can imprve the recnstructin f high energy events sufficiently t make the effrt wrthwhile. A beacn can be used t imprve the relative timing precisin frm t ns required fr digital radi interfermetry, which will lwer the detectin threshld and increase the recnstructin quality.

7 Appendix B Up-Sampling and Envelpe The LOPES standard analysis pipeline (Sect. 3..) includes tw majr steps f signal cnditining: up-sampling and calculatin f an envelpe by a Hilbert transfrm (Hilbert envelpe). These tw steps increase the precisin f the amplitude and arrival time measurement f a radi pulse. Theretically, in ideal circumstances, the precisin culd be arbitrarily high nly limited by cmputing time. Practically, the precisin f amplitude and arrival time measurements is still limited by calibratin uncertainties and nise (Chap. 6), but, after up-sampling, nt anymre by the sampling rate. The value f any measured physical functin, like the electric field strength, cannt change arbitrarily fast with time. There exists a maximum frequency with which the value can change, and smetimes als a minimum frequency. Fr example at LOPES, a bandpass filter ensures that the electrical field strength is measured in the frequency band frm 4 8 MHz nly. Hence, the measured field strength (signal and nise) must be a sum f scillatins with frequencies between 4 and 8 MHz. Any scillatins with ther frequencies wuld be unphysical. This is called a band-limited measurement. Cnsequently, it is nt necessary t sample the electric field strength at an infinite rate t recrd the full physical infrmatin. Accrding t the Nyquist therem (sampling therem) [5], it is sufficient t sample a band-limited functin with a frequency f twice the bandwidth. Then, any values between the samples are well-defined, and can be retrieved by up-sampling which is the crrect way f interplatin. Up-sampling increases the number f samples withut adding any further physical infrmatin. In cmparisn t ther methds f signal cnditining, fr instance fitting a wave frm r applying a matched filter, up-sampling requires n further presumptins n the band-limited signal. There exist several up-sampling algrithms (see e.g., [6]). The ne used in the sftwares f LOPES and AERA is zer-padding in the frequency dmain, which cnsists f several steps and invlves Fast Furier Transfrms (FFTs). F. G. Schröder, Instruments and Methds fr the Radi Detectin f High Energy Csmic Rays, Springer Theses, DOI:.7/ , Ó Springer-Verlag Berlin Heidelberg 57

8 58 Appendix B: Up-Sampling and Envelpe. FFT n the time-series f the electric field strength: By a FFT f the time-series, the frequency spectrum is btained. In the case f LOPES, frequencies are in descending rder since the electric field strength has been sampled in the secnd Nyquist dmain (i.e., frm 8 t 4 MHz). Hence, as first step after the FFT, the rder has t be reverted t ascending frequencies. In the case f AERA, data are sampled in the first Nyquist dmain, and frequencies are already in ascending rder.. Zer Padding: The spectrum is extended and filled with zers. Therefre, additinal frequencies are inserted up t a frequency N N times the riginal band-width, keeping the frequency spacing f the FFT. In the case f LOPES, this means that the additinal frequencies are inserted frm t 4 MHz and abve 8 MHz. This way, the number f data pints in the frequency spectrum is effectively increased by the up-sampling factr N. The inserted data pints reflect that the pwer f the signal is zer utside f the measurement bandwidth. 3. FFT f the frequency spectrum: The zer-padded frequency spectrum is transfrmed back t the time dmain. The resulting time-series f the electrical field strength cntains N times mre data pints than the riginal time-series. All riginal data pints have been cnserved and the new data pints are the physical crrect interplatin f the band-limited time-series. By making use f up-sampling, the carse sampling rate f LOPES des nt anymre limit the measurement precisin. This has successfully been tested at LOPES, using test pulses emitted at different times with respect t the sampling clck f :5 ns. Hence, the measurement precisin f LOPES is nly limited by the calibratin and nise. The Hilbert envelpe is the instantaneus amplitude f the electrical field strength [6]. The Hilbert envelpe is always psitive. Its maximum is usually slightly higher than the maximum f the abslute electrical field strength (a few % at LOPES), and at a slightly different time (a few ns at LOPES). In the frame f LOPES STAR, several methds fr envelpe calculatin have been investigated, deeming the Hilbert envelpe as preferred methd [7]. Thus, the Hilbert envelpe is used in this thesis t determine pulse arrival times and amplitudes. Calculating the Hilbert envelpe is based n the Hilbert transfrm F Hi ðtþ which in cmmunicatin engineering is als knwn as quadrature functin f f ðtþ, and is defined as: F Hi ðtþ ¼ Z þ f ðt Þ p t t dt ðb:þ In principle, btaining a physical meaningful nrmalizatin f the first and the last data pint f the FFT requires sme effrt. Hwever, by design f the analg bandpass filter, the influence f these bundary bins is strngly suppressed and the crrect nrmalizatin becmes unimprtant. Furthermre, setting the bundary bins plainly t zer is an elegant way t remve any unphysical DC ffset frm the measurement.

9 Appendix B: Up-Sampling and Envelpe 59 The Hilbert envelpe is defined as jf ðtþ if Hi ðtþj, when f ðtþ is the (up-sampled) time-series f the electrical field strength. Thrughut this thesis, there are several examples fr Hilbert envelpes (e.g., Figs. 4.7 and 6.3). Fr further reading, any text bks abut cmmunicatin engineering, signal prcessing and Furier transfrms are recmmended, fr instance [6].

10 Appendix C LOPES Antenna Psitins This appendix lists the psitins and plarizatins (alignments) f the LOPES 3 and LOPES Dual setups (Tables C. and C.). Fr the definitin f the crdinate system and a discussin f the measurement uncertainties see Sect Table C. Antenna psitins f the LOPES 3 setup, height relative t antenna Antenna ID Nrthing x (m) Easting y (m) Height z (m) Plarizatin EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW EW (cntinued) F. G. Schröder, Instruments and Methds fr the Radi Detectin f High Energy Csmic Rays, Springer Theses, DOI:.7/ , Ó Springer-Verlag Berlin Heidelberg 6

11 6 Appendix C: LOPES Antenna Psitins Table C. (cntinued) Antenna ID Nrthing x (m) Easting y (m) Height z (m) Plarizatin EW EW EW EW EW EW EW EW Table C. Antenna psitins f the LOPES Dual setup, height relative t the grund plane f KASCADE Antenna ID Nrthing x (m) Easting y (m) Height z K (m) Plarizatin NS EW NS EW EW NS NS EW EW NS NS EW EW NS NS EW EW NS EW NS EW EW NS EW EW NS NS EW NS NS

12 Appendix D Example Events This appendix tries t give an unbiased verview ver LOPES events. Due t the large number f LOPES events, nly a small subset f events can be shwn. Six events fr each f the fur selectins (see Table 7.) have been chsen by an autmated prcedure. These fur selectins are: events frm the LOPES 3 and LOPES Dual setups with cre inside f the KASCADE and Grande array, respectively. Only events passing all selectin and quality cuts are shwn (cf., Tables 7.3 and 8.). Fr each event, there are three pairs f plts: Traces and crss-crrelatin beam Left: Calibrated electrical field strength in individual antennas (different clrs), up-sampled t 8 MHz, after beamfrming, i.e., traces are shifted by the gemetrical delays. Right: Smthed crss-crrelatin beam (dark blue), Gaussian fit t the smthed crss-crrelatin beam (light blue), pwer beam (brwn). Lateral distributin Lateral distributin f pulse amplitudes in individual antennas, and an expnential fit with an amplitude parameter and a slpe parameter R. In additin t the LOPES measurements, the crrespnding REAS3 simulatin selected by the mun number are shwn (left: fr prtn primaries; right: fr irn primaries). Fr the simulated data pints there are n errr bars. Pulse arrival time distributin Distributin f pulse arrival times in individual antennas, a spherical wavefrnt fit with a curvature radius (left), and a cnical wavefrnt fit with a cne parameter q (right). The crrespnding REAS3 simulatin selected by the mun number are shwn fr prtn primaries (blue full squares) and fr irn primaries (red pen squares). Fr the simulated data pints there are n errr bars. Clr figures are available in nline versin F. G. Schröder, Instruments and Methds fr the Radi Detectin f High Energy Csmic Rays, Springer Theses, DOI:.7/ , Ó Springer-Verlag Berlin Heidelberg 63

13 64 Appendix D: Example Events GT Antennas 4 GT CC-Beam and Pwer χ 3.97 / 5 GT ± ± 7. χ.738 / ±.547 R [m] -REAS3p 97 ± χ 3.97 / 5 GT ± ± 7. χ. / ±.44 R [m] -REAS3Fe 4. ± χ / 6 - LOPES [m] 5373 ± 547 χ 3.3 / 6 -REAS3p [m] 566 ± 5.5 χ 3.8 / 6 -REAS3Fe [m] 5843 ± χ / 6 ρ -LOPES [rad]. ±.57 χ / 6 ρ -REAS3p [rad].8 ±.3 χ 6.6 / 6 ρ -REAS3Fe [rad].4 ± Fig. D. Event GT (LOPES 3, EW, KASCADE): h ¼ 34:6, / ¼ 53:7, a ¼ 5:8, E ¼ : EeV, ln A ¼ 3:9 The arrival directin shwn in the plts is recnstructed with LOPES by crsscrrelatin beamfrming, but the shwer parameters given in the figure captin are recnstructed by KASCADE r Grande, respectively. They are the zenith angle h, the azimuth angle /, the gemagnetic angle a, the energy E, and the mass f the primary particle A given as ln A (ln A ¼ crrespnds t a prtn, and ln A 4t an irn nucleus). While all angles are measured very precisely with KASCADE- Grande (better than ), the energy E and the mass A are nly estimated rughly with typical errrs f 4 % fr the energy and abut fr ln A (Figs. D., D., D.3, D.4, D.5, D.6, D.7, D.8, D.9, D., D., D., D.3, D.4, D.5, D.6, D.7, D.8, D.9, D., D., D., D.3 and D.4).

14 Appendix D: Example Events 65 GT Antennas GT CC-Beam and Pwer GT χ / ± ± 5.7 χ.84 / ±.83 R [m] -REAS3p 6.5 ± GT χ / ± ± 5.7 χ.973 / ±.6948 R [m] -REAS3Fe 7.5 ± χ.75 / 5 - LOPES [m] 3 ± χ 3.68 / 5 -REAS3p [m] 444 ±.5 χ.68 / 5 -REAS3Fe [m] 436 ± χ.554 / 5 ρ -LOPES [rad].96 ±.64 χ.6 / 5 ρ -REAS3p [rad].34 ±. χ.8753 / 5 ρ -REAS3Fe [rad].5 ± Fig. D. Event GT (LOPES 3, EW, KASCADE): h ¼ 9:8, / ¼ 48:8, a ¼ 49:6, E ¼ :5 EeV, ln A ¼ 3:3

15 66 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ 7. / 4 GT ± R [m] - LOPES 488 ± 64.4 χ.595 / ±.593 R [m] -REAS3p 36.5 ± χ 7. / 4 GT ± R [m] - LOPES 488 ± 64.4 χ.36 / ±.445 R [m] -REAS3Fe 46. ± χ 9.36 / 5 - LOPES [m] 75 ± 93.5 χ 6.48 / 5 -REAS3p [m] 53 ± 76.3 χ 6.89 / 5 -REAS3Fe [m] 5566 ± χ / 5 ρ -LOPES [rad].89 ±.66 χ.5 / 5 ρ -REAS3p [rad].3 ±. χ.687 / 5 ρ -REAS3Fe [rad].98 ± Fig. D.3 Event GT 4754 (LOPES 3, EW, KASCADE): h ¼ 4:7, / ¼ 344:5, a ¼ 66:, E ¼ :6 EeV, ln A ¼ 4:7

16 Appendix D: Example Events 67 GT Antennas GT CC-Beam and Pwer χ.98 / 6 GT ± ± 4.5 χ.95 / ±.949 R [m] -REAS3p 3.3 ± GT χ.98 / ± ± 4.5 χ.5 / ±.864 R [m] -REAS3Fe 6. ± χ 6. / 7 - LOPES [m] 6336 ± 38 χ 4. / 7 -REAS3p [m] 663 ± 87.6 χ.6 / 7 -REAS3Fe [m] 6853 ±.7 4 χ 7.7 / 7 ρ -LOPES [rad].4 ±.46 χ / 7 ρ -REAS3p [rad].43 ±.3 χ / 7 ρ -REAS3Fe [rad].7 ± Fig. D.4 Event GT (LOPES 3, EW, KASCADE): h ¼ 35:, / ¼ 66:8, a ¼ 49:8, E ¼ :4 EeV, ln A ¼ 4:4

17 68 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ / 3 GT ± R [m] - LOPES.9 ±.9 χ.56 / ±.5663 R [m] -REAS3p 3. ± χ / 3 GT ± R [m] - LOPES.9 ±.9 χ.7 / ±.4565 R [m] -REAS3Fe 4 ± χ 9.5 / 4 - LOPES [m] 3795 ± 5 χ 9.58 / 4 -REAS3p [m] 4674 ± 67.3 χ 3.3 / 4 -REAS3Fe [m] 484 ± 79 4 χ.33 / 4 ρ -LOPES [rad].67 ±.53 χ / 4 ρ -REAS3p [rad].56 ±. χ / 4 ρ -REAS3Fe [rad].5 ± Fig. D.5 Event GT (LOPES 3, EW, KASCADE): h ¼ 3:5, / ¼ 354:4, a ¼ 38:5, E ¼ :7 EeV, ln A ¼ :4

18 Appendix D: Example Events 69 GT Antennas GT CC-Beam and Pwer χ 46.8 / 4 GT ± ± χ / ±.35 R [m] -REAS3p ± χ 46.8 / 4 GT ± ± χ.9 / ±.686 R [m] -REAS3Fe 35 ± χ 35.4 / 5 - LOPES [m] 48 ± 389 χ 5.8 / 5 -REAS3p [m] 338 ± 84. χ 35.8 / 5 -REAS3Fe [m] 43 ± χ / 5 ρ -LOPES [rad].4 ±.58 χ 4.44 / 5 ρ -REAS3p [rad].8 ±.3 χ / 5 ρ -REAS3Fe [rad].47 ± Fig. D.6 Event GT (LOPES 3, EW, KASCADE): h ¼ :7, / ¼ 4:, a ¼ 4:7, E ¼ :6 EeV, ln A ¼ :3

19 7 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer GT χ 9.85 / ± ± 88.8 χ.469 / ±.3 R [m] -REAS3p 7.8 ± χ.59 / 7 - LOPES [m] 996 ± χ 3.8 / 7 -REAS3p [m] 8733 ±.8 χ 7.79 / 7 -REAS3Fe [m] 9458 ± GT χ.47 / 7 ρ -LOPES [rad].35 ±.3 χ / 7 ρ -REAS3p [rad].48 ±.3 χ 9.85 / ± ± 88.8 χ.943 / ±. R [m] -REAS3Fe 7.8 ± 3.73 χ 3.47 / 7 ρ -REAS3Fe [rad].37 ±.3 Fig. D.7 Event GT (LOPES 3, EW, Grande): h ¼ 44:, / ¼ 34:6, a ¼ 65:7, E ¼ : EeV, ln A ¼ 5:8

20 Appendix D: Example Events 7 GT Antennas.5 GT CC-Beam and Pwer χ.7 / GT ± ± 5.75 χ.494 /.8 ±.5699 R [m] -REAS3p 69.9 ± χ.7 / GT ± ± 5.75 χ.63 / 9.75 ±.594 R [m] -REAS3Fe ±.6 4 χ / 3 - LOPES [m].66e+4 ± 595 χ 45.5 / 3 -REAS3p [m] 7 ± 6.7 χ 9.9 / 3 -REAS3Fe [m] 849 ± χ / 3 ρ -LOPES [rad].3 ±.8 χ / 3 ρ -REAS3p [rad].89 ±.3 χ.96 / 3 ρ -REAS3Fe [rad].58 ± Fig. D.8 Event GT (LOPES 3, EW, Grande): h ¼ 35:6, / ¼ 5:8, a ¼ 54:, E ¼ :37 EeV, ln A ¼ :5

21 7 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ 36.7 / 4 GT ± R [m] - LOPES 59.7 ± 3.7 χ.43 / ±.658 R [m] -REAS3p 63.7 ± χ 36.7 / 4 GT ± R [m] - LOPES 59.7 ± 3.7 χ.93 / ±.46 R [m] -REAS3Fe 3.6 ± χ.65 / 5 - LOPES [m] 4954 ± 7 χ 3.88 / 5 -REAS3p [m] 59 ± 8.6 χ 45. / 5 -REAS3Fe [m] 57 ± 9. 4 χ.73 / 5 ρ -LOPES [rad].43 ±.49 χ 4.95 / 5 ρ -REAS3p [rad].4 ±. χ / 5 ρ -REAS3Fe [rad].55 ± Fig. D.9 Event GT (LOPES 3, EW, Grande): h ¼ 3:4, / ¼ 354:, a ¼ 56:3, E ¼ : EeV, ln A ¼ 4:

22 Appendix D: Example Events 73 GT Antennas GT CC-Beam and Pwer χ.7 / 4 GT ± ± 68. χ.756 / ±.5 R [m] -REAS3p 3.6 ± χ.7 / 4 GT ± ± 68. χ.9 / ±.64 R [m] -REAS3Fe 8.7 ± χ / 5 - LOPES [m] 5744 ± 844 χ.7 / 5 -REAS3p [m] 4337 ±.7 χ 5.98 / 5 -REAS3Fe [m] 5 ± χ / 5 ρ -LOPES [rad]. ±.36 χ.584 / 5 ρ -REAS3p [rad].6 ±.3 χ.35 / 5 ρ -REAS3Fe [rad].38 ± Fig. D. Event GT (LOPES 3, EW, Grande): h ¼ 33:7, / ¼ 347:, a ¼ 58:3, E ¼ :7 EeV, ln A ¼ 4:9-5

23 74 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ 9.7 / 5 GT ± ±.95 χ / 5.53 ±.788 R [m] -REAS3p 86.5 ± χ 9.7 / 5 GT ± ±.95 χ 3.9 / 5.7 ±.473 R [m] -REAS3Fe 3.6 ± χ 9.8 / 6 - LOPES [m] 666 ± χ.7 / 6 -REAS3p [m] 78 ± 6.8 χ 9.63 / 6 -REAS3Fe [m] 837 ± χ / 6 χ / 6 ρ -LOPES [rad].43 ±. ρ -REAS3Fe [rad]. ±. χ / 6 ρ -REAS3p [rad].5 ± Fig. D. Event GT (LOPES 3, EW, Grande): h ¼ 44:6, / ¼ 356:9, a ¼ 69:6, E ¼ :6 EeV, ln A ¼ :

24 Appendix D: Example Events 75 GT Antennas GT CC-Beam and Pwer GT χ 7.76 / ±.3 R [m] - LOPES 36.4 ± 7.6 χ.485 / ±. R [m] -REAS3p 9 ± GT χ 7.76 / ±.3 R [m] - LOPES 36.4 ± 7.6 χ.35 / ±.48 R [m] -REAS3Fe 44. ± χ / 4 - LOPES [m] 5357 ± 8 χ 9.39 / 4 -REAS3p [m] 4748 ±.9 χ 6.54 / 4 -REAS3Fe [m] 536 ± χ / 4 ρ -LOPES [rad].5 ±.7 χ.373 / 4 ρ -REAS3p [rad].6 ±. χ.47 / 4 ρ -REAS3Fe [rad].43 ± Fig. D. Event GT (LOPES 3, EW, Grande): h ¼ 3:, / ¼ 68:8, a ¼ 37:9, E ¼ :7 EeV, ln A ¼ 4:

25 76 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ 6.89 / GT ± R [m] - LOPES 6.6 ± 7.49 χ.65 / ±.85 R [m] -REAS3p 9.8 ± χ 6.89 / GT ± R [m] - LOPES 6.6 ± 7.49 χ.43 / 6.73 ±.79 R [m] -REAS3Fe. ± χ 3.64 / 3 - LOPES [m] 45 ± 89 χ 3.89 / 3 -REAS3p [m] 46 ± 3.3 χ 3.38 / 3 -REAS3Fe [m] 4337 ± χ.64 / 3 ρ -LOPES [rad].54 ±.57 χ.745 / 3 ρ -REAS3p [rad].7 ±.3 χ.877 / 3 ρ -REAS3Fe [rad].58 ± Fig. D.3 Event GT (LOPES Dual, EW, KASCADE): h ¼ 5:5, / ¼ 336:5, a ¼ 39:6, E ¼ :8 EeV, ln A ¼ :5

26 Appendix D: Example Events 77 GT Antennas GT CC-Beam and Pwer χ 5.9 / 3 GT ± ± 96. χ.8346 / ±.734 R [m] -REAS3p 57. ± χ 5.9 / 3 GT ± ± 96. χ.694 / ±.5964 R [m] -REAS3Fe 69.8 ± χ 7.8 / 4 - LOPES [m] 3494 ± 896 χ 3.83 / 4 -REAS3p [m] 57 ± 84.8 χ 3.7 / 4 -REAS3Fe [m] 533 ± 3. 4 χ / 4 ρ -LOPES [rad].65 ±.45 χ.487 / 4 ρ -REAS3p [rad].3 ±. χ.6696 / 4 ρ -REAS3Fe [rad].8 ± Fig. D.4 Event GT (LOPES Dual, EW, KASCADE): h ¼ 33:3, / ¼ 39:4, a ¼ 5:4, E ¼ :5 EeV, ln A ¼ 6:8

27 78 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer GT χ 6.99 / ±.676 R [m] - LOPES 99.6 ± 865 χ.745 / ±.849 R [m] -REAS3p ± GT χ 6.99 / ±.676 R [m] - LOPES 99.6 ± 865 χ.569 / ±.799 R [m] -REAS3Fe ± χ 3.64 / 4 - LOPES [m] 386 ± 34 χ 6.3 / 4 -REAS3p [m] 5457 ± 37. χ 6.57 / 4 -REAS3Fe [m] 5448 ± χ 3.63 / 4 ρ -LOPES [rad].47 ±.8 χ.4 / 4 ρ -REAS3p [rad]. ±.3 χ.3 / 4 ρ -REAS3Fe [rad]. ± Fig. D.5 Event GT (LOPES Dual, EW, KASCADE): h ¼ 4:5, / ¼ 84:5, a ¼ 48:5, E ¼ :3 EeV, ln A ¼ 4:9

28 Appendix D: Example Events 79 GT Antennas GT CC-Beam and Pwer GT χ 3.98 / 3 8. ±.558 ±.57 χ 3.44 / 3.87 ±.439 R [m] -REAS3p 5.3 ± GT χ 3.98 / 3 8. ±.558 ±.57 χ.4 / 3.69 ±.55 R [m] -REAS3Fe 39.6 ± χ / 4 - LOPES [m] 48 ± 7.4 χ 3.95 / 4 -REAS3p [m] 5386 ± 9. χ.99 / 4 -REAS3Fe [m] 58 ± χ.758 / 4 ρ -LOPES [rad].77 ±.3 χ.778 / 4 ρ -REAS3p [rad].4 ±.3 χ.8 / 4 ρ -REAS3Fe [rad].3 ± Fig. D.6 Event GT (LOPES Dual, EW, KASCADE): h ¼ 3:9, / ¼ 33:, a ¼ 54:, E ¼ :8 EeV, ln A ¼ :5

29 8 Appendix D: Example Events GT Antennas χ.6 / 3 GT ± R [m] - LOPES 98. ±.57 χ / ±.638 R [m] -REAS3p ± χ.69 / 4 - LOPES [m] 46 ± 53 χ 34. / 4 -REAS3p [m] 49 ± χ.4 / 4 -REAS3Fe [m] 585 ± GT CC-Beam and Pwer χ.6 / 3 GT ± R [m] - LOPES 98. ±.57 χ.44 / ±.4 R [m] -REAS3Fe 35. ± χ.65 / 4 ρ -LOPES [rad]. ±.65 χ 3.97 / 4 ρ -REAS3p [rad].66 ± χ.6485 / 4 ρ -REAS3Fe [rad].37 ±.3 Fig. D.7 Event GT (LOPES Dual, EW, KASCADE): h ¼ :5, / ¼ 87:3, a ¼ 37:9, E ¼ :3 EeV, ln A ¼ :5

30 Appendix D: Example Events 8 4 GT Antennas GT CC-Beam and Pwer χ 6.83 / GT ± ± 363 χ.4 / ±.97 R [m] -REAS3p 9.66 ± χ 6.83 / GT ± ± 363 χ.6 / 4.45 ±.784 R [m] -REAS3Fe 6 ± χ 6.53 / 3 - LOPES [m] ± 59.7 χ.96 / 3 -REAS3p [m] 36 ± 6.7 χ 5.68 / 3 -REAS3Fe [m] 434 ± χ 6.35 / 3 ρ -LOPES [rad].63 ±.75 χ.85 / 3 ρ -REAS3p [rad].6 ±.3 χ.968 / 3 ρ -REAS3Fe [rad].39 ± Fig. D.8 Event GT (LOPES Dual, EW, KASCADE): h ¼ 3:9, / ¼ 39:8, a ¼ 45:8, E ¼ : EeV, ln A ¼ :9

31 8 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ 8.74 / 3 GT ± ± 6.6 χ.4383 / 3.4 ±.434 R [m] -REAS3p ±. χ 8.74 / 3 GT ± ± 6.6 χ.496 / ±.77 R [m] -REAS3Fe 4. ± χ 4 / 4 - LOPES [m] 8859 ± 8 χ 6.38 / 4 -REAS3p [m] 6879 ± 85.6 χ 8.83 / 4 -REAS3Fe [m] 797 ± 8. 4 χ 3.4 / 4 ρ -LOPES [rad].8 ±.3 χ 4.98 / 4 ρ -REAS3p [rad].77 ±.3 χ.487 / 4 ρ -REAS3Fe [rad].53 ± Fig. D.9 Event GT (LOPES Dual, EW, Grande): h ¼ 34:, / ¼ 39:, a ¼ 55:, E ¼ : EeV, ln A ¼ 3: -

32 Appendix D: Example Events 83 GT Antennas GT CC-Beam and Pwer χ.94 / 3 GT ± R [m] - LOPES 3.7 ±.63 χ.9 / ±.8846 R [m] -REAS3p 98.6 ± GT χ.94 / ±.4593 R [m] - LOPES 3.7 ±.63 χ.7 / ±.854 R [m] -REAS3Fe 5.6 ± χ 5.84 / 4 - LOPES [m] 3676 ± 9.3 χ 9.74 / 4 -REAS3p [m] 4849 ± 44.3 χ 6.8 / 4 -REAS3Fe [m] 9 ± χ 4.9 / 4 ρ -LOPES [rad].96 ±.47 χ.8654 / 4 ρ -REAS3p [rad].7 ±. χ.939 / 4 ρ -REAS3Fe [rad].64 ± Fig. D. Event GT (LOPES Dual, EW, Grande): h ¼ 6:7, / ¼ 69:8, a ¼ 9:7, E ¼ : EeV, ln A ¼ 4:

33 84 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer χ.73 / 3 GT ± ± 3. χ.397 / ±.758 R [m] -REAS3p ± χ.73 / 3 GT ± ± 3. χ.868 / ±.68 R [m] -REAS3Fe 83. ±.78 6 χ 5.8 / 4 - LOPES [m] 9665 ± χ 46.7 / 4 -REAS3p [m] 9379 ± χ 38.4 / 4 -REAS3Fe [m] 9855 ± χ / 4 ρ -LOPES [rad].38 ±.3 χ / 4 ρ -REAS3p [rad].64 ±.6 χ / 4 ρ -REAS3Fe [rad].57 ± Fig. D. Event GT (LOPES Dual, EW, Grande): h ¼ 37:, / ¼ 56:8, a ¼ 54:3, E ¼ :33 EeV, ln A ¼ 3:7 -

34 Appendix D: Example Events 85 GT Antennas GT CC-Beam and Pwer χ 3.7 / 3 GT ± ± 4.8 χ.36 / ±.94 R [m] -REAS3p 96.5 ± χ 3.7 / 3 GT ± ± 4.8 χ.5 / ±.97 R [m] -REAS3Fe 5.6 ± χ 4.5 / 4 - LOPES [m] 685 ± 77 χ 8.9 / 4 -REAS3p [m] 76 ± 34. χ 5. / 4 -REAS3Fe [m] 79 ± 35 4 χ 4.94 / 4 ρ -LOPES [rad].58 ±.8 χ.5744 / 4 ρ -REAS3p [rad].64 ±.3 χ.864 / 4 ρ -REAS3Fe [rad].58 ± Fig. D. Event GT 5587 (LOPES Dual, EW, Grande): h ¼ 8:, / ¼ 338:, a ¼ 5:, E ¼ :9 EeV, ln A ¼ :9 -

35 86 Appendix D: Example Events GT Antennas GT CC-Beam and Pwer GT χ 8.5 / ±.5587 R [m] - LOPES 9 ± 8.4 χ.5669 / ±.78 R [m] -REAS3p 5. ± χ 8.5 / GT ± R [m] - LOPES 9 ± 8.4 χ.345 / 3.34 ±.546 R [m] -REAS3Fe 55.8 ± χ / - LOPES [m] 366 ± 7 χ 8.65 / -REAS3p [m] 4996 ± 33.9 χ. / -REAS3Fe [m] 637 ± 85.5 χ 3.77 / ρ -LOPES [rad]. ±.69 χ / ρ -REAS3p [rad].64 ±.3 χ.4667 / ρ -REAS3Fe [rad].33 ± Fig. D.3 Event GT (LOPES Dual, EW, Grande): h ¼ 9:, / ¼ 7:7, a ¼ 43:7, E ¼ : EeV, ln A ¼ :

36 Appendix D: Example Events 87 6 GT Antennas GT CC-Beam and Pwer GT χ 4.4 / 45.4 ± ± 56.4 χ 9.6 / [ μv/m/mhz] ±.94 R [m] -REAS3p 36 ± GT χ 4.4 / 45.4 ± ± 56.4 χ 38.5 / 7.58 ±.657 R [m] -REAS3Fe.4 ± χ. / - LOPES [m] 743 ± 3.3 χ 93 / -REAS3p [m] 3343 ± 69. χ / -REAS3Fe [m] 438 ± χ.6 / ρ -LOPES [rad].4 ±.4 χ 4.84 / ρ -REAS3p [rad].7 ±.7 χ / ρ -REAS3Fe [rad].63 ± Fig. D.4 Event GT (LOPES Dual, EW, Grande): h ¼ 6:9, / ¼ :6, a ¼ 8:4, E ¼ : EeV, ln A ¼ :7 References. N. M. Budnev et al. - Tunka Cllabratin. The Tunka-33 EAS Chrenkv array - status, first results and plans. In Prceedings f the 3st ICRC, Łódź, Pland, number 69, 9. astr-ph/ J. Oertlin. Radi Data Analysis f a Prttype Antenna at the Tunka-33 Experiment. Bachelr Thesis, Karlsruhe Institute f Technlgy, S. F. Berezhnev et al. - Tunka Cllabratin. The Tunka-33 EAS Cherenkv light array: Status f. In Nucl. Instr. and Meth. A; Prceedings f RICAP, Rma, Italy, 69: 98 5,. 4. Tunka-5 EAS Cherenkv Light Array.

37 88 Appendix D: Example Events 5. H. Nyquist. Certain Tpics in Telegraph Transmissin Thery. American Institute f Electrical Engineers, Transactins f the, 47():67 644, R. N. Bracewell. The Furier Transfrm and Its Applicatins (Secnd Editin, Revised). McGraw-Hill Bk Cmpany, T. Asch. Self-Triggering f Radi Signals frm Csmic Ray Air Shwers. FZKA Reprt 7459, Frschungszentrum Karlsruhe, 9.