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T. Fujii1,2, P. Privitera1, J. Jiang1, A. Matalon1, P. Motloch1,
M. Casolino3, Y. Takizawa3, M. Bertaina4,
J. N. Matthews5, K. Yamazaki6, B. Dawson7, M. Malacari7
1KICP University of Chicago, 2ICRR University of Tokyo, 3RIKEN, 4University of Torino,
5University of Utah, 6Osaka City University, 7University of Adelaide
2014/Oct/15, UHECR 2014
fujii@kicp.uchicago.edu
Segmented mirror telescope
Variable angles of elevation – steps.
construction is still in development
15 deg 45 deg
Joint Laboratory of Optics Olomouc – March 2014
7
Development of a prototype for Fluorescence
detector Array of Single-pixel Telescopes
(FAST)
Physics Goal and Future Prospects
2
Origin and Nature of UHECRs
Particle Interaction at the Highest Energies
Exposure and full sky coverage
TA×4 + Auger
JEM-EUSO: Pioneer detection
from space and sizable increase
of exposure
Detector R&D
Radio,
SiPM detector,
FD or SD
“Precision” measurement
Auger Muon Upgrade
Low energy enhancement
(TALE+TA-muon+NICHE,
Auger infill+HEAT+AMIGA)
5 - 10 years
P. Privitera et al.,
KICP workshop,
September, 2013
Next Generation Observatories
In space (100×exposure)
Ground (10×exposure with high
quality events)
10 - 20 years
Segmented mirror telescope
Variable angles of elevation – steps.
15 deg 45 deg
Fine pixelated camera (Auger, TA)
Low cost single pixel telescope (FAST)
✦ Target : > 1019.5 eV, UHE nuclei and neutral particles
✦ Huge target volume ⇒ Fluorescence detector array
Fluorescence detector Array of
Single-Pixel Telescopes (FAST)
Too expensive to cover
a large area
Shower profile reconstruction
by given geometry
4
20 km
✦ Reference design: 1 m2
aperture, 15°×15° FoV
per single PMT
✦ 12 Telescope, 48 PMTs,
30°×360° FoV in each
station.
✦ If 127 stations are
installed with 20 km
spacing, a ground
coverage is ~ 40,000 km2
✦ Geometry: Radio, SD or
three coincidence of
FAST.
Segmented mirror telescope
Variable angles of elevation – steps.
15 deg 45 deg
Fluorescence detector Array of
Single-Pixel Telescopes (FAST)
16
56 EeV zenith 500
1
2
3
1
3 2
PhotonsatdiaphragmPhotonsatdiaphragm
Photonsatdiaphragm
Window of Opportunity at EUSO-TA
5
EUSO prototype
Telescope Array,
Utah, USA
Black Rock Mesa site
✦ Temporally borrow the EUSO-TA optics at the TA site.
✦ Two Fresnel lenses (+ 1 UV acrylic plate in front for protection)
✦ 1 m2 aperture, 14°×14° FoV ≒ FAST reference design.
✦ Installation in February 2014, test measurements in April and June 2014.
✦ Collaboration between Pierre Auger, Telescope Array and JEM-EUSO.
M. Casolino (RIKEN),
M. Bertaina, M. Marengo,
F. Borotto, B. Giraudo
(INFN-Torino)
EUSO-TA optics
Camera of FAST
6
Np.e./100ns
YAP
Signal
✦ PMT 8 inch R5912-03
✦ E7694-01(AC coupling)
✦ MUG6 UV band pass filter
✦ YAP (YAIO3: Ce) scintillator
with 241Am (50 Hz) to
monitor gain stability.
Anode & dynode
Signal
DAQ System
7
TAFD external
trigger, 3~5 Hz
Amplifiers
R979 CAEN
Signal×10
Camera of FAST
High Voltage power
supply, N1419 CAEN
Portable VME
Electronics
- Struck FADC 50 MHz
sampling, SIS3350
- GPS board, HytecGPS2092
15 MHz
low pass filter
All modules are
remotely controlled
through wireless
network.
777,Phillips scientific
Signal×50
Installation in February 2014
8
Start observation!!
1 2 3
4 5 6
7 8 9
Figure 4: Stability of the variance caused by night sky backgrounds every 5 minutes during
hours operation on April 30th 2014.
Figure 2: DAQ system of the prototype of FAST.
ure 3: Variances measured by the PMT under the shutter closing and opening. The
ance under shutter closing shows a noise of the electrics and that under opening shows
ht sky backgrounds.
9
Operation in Clear Night
12.7°C 4.6°C
YAP signal
7 hours data taking
+8%
Close Open
Electronic
noise level
Night sky
background
✦ Variance is proportional to PMT
current. Electronic noise is
negligible with regard to night sky
background.
✦ Good gain stability during data
taking, consistent with PMT
gain temperature dependence
of -1%/℃
Become quieter
background
gure 8: Observed signal from the vertical UV laser at a distance of 20.9 km from the
GPS Timing and CLF Signal
10
Average of
223 shots ✦ FAST-TAFD timing resolution,
100 ns. (20.9 µs is the TAFD
trigger processing time.)
✦ laser signal ~ 1019.5 eV at 21 km
✦ peak signal ~ 7 p.e. / 100 ns (σp.e.
= 12 p.e.) at the limit of
detectability
CHAPTER 3. TELESCOPE ARRAY EXPERIMENT
ure 3.28: The CLF system located at the center of TA (left) and the inside
ure of CLF (right).
Additionally, the LIDAR system has been installed at CLF location in
tember 2010. When shooting the laser, the back-scattered photons are
ected at the ground. Thus, the telescope system same as LIDAR was set up
measure back scattered photons from CLF laser. Fig. 3.29 shows the image
LIDAR system and the typical result of VAOD measured by both LIDAR
tems located at BRM and CLF. While the LIDAR at BRM operates in the
e to start and finish every observation, CLF is shooting the laser every 30
utes. Since these results are consistent and complementary, we can use the
mospheric parameter with better time resolution in near future.
ure 3.29: The image of LIDAR system installed at the CLF location (left)
Central Laser Facility
Vertical UV laser shooting
every 30 minutes,
21 km from FAST,
10 Hz, 2.2 mJ, 300 shots
Histogram
Entries 28592
Mean 20.86
RMS 0.09781
s]µGPS timing difference (FAST - TAFD) [
19.5 20 20.5 21 21.5 22 22.5
Entries
0
500
1000
1500
2000
2500
3000
Histogram
Entries 28592
Mean 20.86
RMS 0.09781
Np.e./(100ns)
Time (20 ns / bin)
0 500 1000 1500 2000 2500 3000 3500 4000
p.e.N
0
1
2
3
4
5
6
7
Preliminary CLF Simulation
11
Raytracing
-7
0
+7
+14
-14
Laser length: 20 usec
Distance : L
1bin = 6.0e-3 km
t = 0
bin = 0
10,000 photons in the
a bin of laser length
8 inch 7 FOV
Simulation
Y. Takizawa (RIKEN)
Directional sensitivity
Efficiency
Np.e./(100ns)
e 8: Observed signal from the vertical UV laser at a distance of 20.9 km from the
prototype. As the signal is at the detection limit, 233 consecutive laser shot signals are
ged to increase the signal to noise ratio.
Data
Np.e./(100ns)
Figure 6: Stability of YAP signals during 7 hours operation on April 30th 2014.
ure 7: Observed waveform emitted from a single vertical UV laser from 6.1 km from the
ototype of FAST. The clear signal can be seen in the waveform.
11
Portable Laser Signal
12
Single laser shotFAST
FAST
FOV
Hit
Cloud
TAFD
✦ Vertical UV laser with same
energy of CLF (~1019.5 eV) at
6 km from FAST.
✦ Peak signal ~ 300 p.e. / 100
ns. All shots are detected.
✦ Expected signal TAFD/FAST:
(7 m2 aperture × 0.7 shadow ×
0.9 mirror) / (1 m2 aperture ×
0.43 optics efficiency) ~ 10
Operated by K. Yamazaki (OCU)
Np.e./(100ns)Np.e./(100ns)
Time (20 ns / bin)
0 500 1000 1500 2000 2500 3000 3500 4000
/p.e.N
0
1
2
3
4
5
6
Figure 11: CLF signal estimated using ray-tracing of the JEM-EUSO optics and knowledge
of the scattering processes in the air (without night sky background). This Figure can be
compared to the observed signal as shown in Figure 8.
Time (20 ns / bin)
0 500 1000 1500 2000 2500 3000 3500 4000
/(100ns)p.e.N
0
50
100
150
200
250
300
350
400
450
Figure 12: PLS signal estimated using ray-tracing of the JEM-EUSO optics and knowledge
of the scattering processes in the air (without night sky background). This Figure can be
compared with the observed signal as shown in Figure 9.
18
Simulation
Shower Signal Search
FAST
TAFD
FAST
FoV
✦ We searched for
FAST signals in
coincidence with
TAFD showers in
the FAST FoV.
✦ Data set: April and
June observation,
19 days, 83 hours.
✦ 16 candidates
found.
✦ Low energy showers
as expected.
log(E/eV)=18.0
Np.e./(100ns)
13
Example of Signal Candidates
14
FAST TAFD
log(E/eV)=18.3log(E/eV)=18.3
log(E/eV)=17.2
log(E/eV)=17.9
(a) Data: E = 1017.2 eV (b) Data: E = 1018.0 eV
Time (20 ns / bin)
0 500 1000 1500 2000 2500 3000 3500 4000
/(100ns)p.e.N
0
10
20
30
40
50
60
(c) Simulation: E = 1017.2 eV
Time (20 ns / bin)
0 500 1000 1500 2000 2500 3000 3500 4000
/(100ns)p.e.N
0
10
20
30
40
50
(d) Simulation: E = 1018.0 eV
Figure 15: Observed signals with the FAST prototype for shower candidates, (a) and (b), an
expected signals estimated from shower simulation using information reconstructed by the T
fluorescence detector, (c) and (d) respectively.
Comparison with simulated signal using
result reconstructed by TAFD
15
A signal location is fluctuated within the TAFD trigger frame of 12.8 µs.
log(E/eV)=17.2 log(E/eV)=18.0
(a) Data: E = 1017.2 eV (b) Data: E = 1018.0 eV
Simulation
Data
Simulation
Data
(E (eV))10
log
17 17.5 18 18.5 19 19.5 20
Impactparameter[km]
1
10
2
10
Preliminary
Detectable
Figure 14: Distribution of the impact parameter as a function of the primary energy recon-
structed by TA for shower candidates detected by the FAST prototype. The line indicates
the maximum detectable distance by the FAST prototype (not fitted).
20
Distance vs Energy (from TAFD) for Candidates
16
April+June RUN
FAST
FoV
Almost! log(E/eV)=19.1
Np.e./(100ns)
log(E/eV)=18.1
]2
[g/cmmaxReconstructed X
400 500 600 700 800 900 1000 1100 1200 1300 1400
Entries
0
100
200
300
400
500
600
eV19.5
10
f = 1.17
Proton EPOS
Iron EPOS
Simulation Study
17
Segmented mirror telescope
Variable angles of elevation – steps.
construction is still in development
15 deg 45 deg
Joint Laboratory of Optics Olomouc – March 2014
7
✦ Reconstruction efficiency
✦ FAST with 20 km spacing
✦ With smearing SD accuracy of
geometry, Xmax resolution of FAST is
30 g/cm2 at 1019.5 eV.
✦ 100% efficiency at 1019.5 eV
✦ Under implementing a reconstruction
by only FAST.
logE Proton Iron
18.5 0.65 0.56
19.0 0.88 0.89
19.5 0.99 1.00
Including
Xmax
resolution
✦ 4 PMTs Telescope
ProtonIron
Summary and Future Plans
✦ Promising results from the first field test of FAST
concept:
✦ very stable and simple operation
✦ robust behavior under night sky background (gain
stability, a single bright star does not matter when
integrating over the large FAST FOV)
✦ laser shots and shower candidates detected
✦ sensitivity is consistent with simulated expectation
✦ Very successful example of Auger, TA, JEM-EUSO
collaboration.
✦ Several improvements possible, e.g. high Q.E. PMT,
narrow UV pass filter, mirror design, reconstruction
method, etc.
✦ Next step: full 30°×30° prototype.
18
Segmented mirror telescope
Variable angles of elevation – steps.
15 deg 45 deg
(E (eV))10
log
17 17.5 18 18.5 19 19.5 20
Impactparameter[km]
1
10
2
10
Preliminary
Detectable
Figure 14: Distribution of the impact parameter as a function of the primary energy re
structed by TA for shower candidates detected by the FAST prototype. The line indic
the maximum detectable distance by the FAST prototype (not fitted).
20

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Development of a prototype for Fluorescence detector Array of Single-pixel Telescopes (FAST)

  • 1. T. Fujii1,2, P. Privitera1, J. Jiang1, A. Matalon1, P. Motloch1, M. Casolino3, Y. Takizawa3, M. Bertaina4, J. N. Matthews5, K. Yamazaki6, B. Dawson7, M. Malacari7 1KICP University of Chicago, 2ICRR University of Tokyo, 3RIKEN, 4University of Torino, 5University of Utah, 6Osaka City University, 7University of Adelaide 2014/Oct/15, UHECR 2014 fujii@kicp.uchicago.edu Segmented mirror telescope Variable angles of elevation – steps. construction is still in development 15 deg 45 deg Joint Laboratory of Optics Olomouc – March 2014 7 Development of a prototype for Fluorescence detector Array of Single-pixel Telescopes (FAST)
  • 2. Physics Goal and Future Prospects 2 Origin and Nature of UHECRs Particle Interaction at the Highest Energies Exposure and full sky coverage TA×4 + Auger JEM-EUSO: Pioneer detection from space and sizable increase of exposure Detector R&D Radio, SiPM detector, FD or SD “Precision” measurement Auger Muon Upgrade Low energy enhancement (TALE+TA-muon+NICHE, Auger infill+HEAT+AMIGA) 5 - 10 years P. Privitera et al., KICP workshop, September, 2013 Next Generation Observatories In space (100×exposure) Ground (10×exposure with high quality events) 10 - 20 years
  • 3. Segmented mirror telescope Variable angles of elevation – steps. 15 deg 45 deg Fine pixelated camera (Auger, TA) Low cost single pixel telescope (FAST) ✦ Target : > 1019.5 eV, UHE nuclei and neutral particles ✦ Huge target volume ⇒ Fluorescence detector array Fluorescence detector Array of Single-Pixel Telescopes (FAST) Too expensive to cover a large area Shower profile reconstruction by given geometry
  • 4. 4 20 km ✦ Reference design: 1 m2 aperture, 15°×15° FoV per single PMT ✦ 12 Telescope, 48 PMTs, 30°×360° FoV in each station. ✦ If 127 stations are installed with 20 km spacing, a ground coverage is ~ 40,000 km2 ✦ Geometry: Radio, SD or three coincidence of FAST. Segmented mirror telescope Variable angles of elevation – steps. 15 deg 45 deg Fluorescence detector Array of Single-Pixel Telescopes (FAST) 16 56 EeV zenith 500 1 2 3 1 3 2 PhotonsatdiaphragmPhotonsatdiaphragm Photonsatdiaphragm
  • 5. Window of Opportunity at EUSO-TA 5 EUSO prototype Telescope Array, Utah, USA Black Rock Mesa site ✦ Temporally borrow the EUSO-TA optics at the TA site. ✦ Two Fresnel lenses (+ 1 UV acrylic plate in front for protection) ✦ 1 m2 aperture, 14°×14° FoV ≒ FAST reference design. ✦ Installation in February 2014, test measurements in April and June 2014. ✦ Collaboration between Pierre Auger, Telescope Array and JEM-EUSO. M. Casolino (RIKEN), M. Bertaina, M. Marengo, F. Borotto, B. Giraudo (INFN-Torino) EUSO-TA optics
  • 6. Camera of FAST 6 Np.e./100ns YAP Signal ✦ PMT 8 inch R5912-03 ✦ E7694-01(AC coupling) ✦ MUG6 UV band pass filter ✦ YAP (YAIO3: Ce) scintillator with 241Am (50 Hz) to monitor gain stability.
  • 7. Anode & dynode Signal DAQ System 7 TAFD external trigger, 3~5 Hz Amplifiers R979 CAEN Signal×10 Camera of FAST High Voltage power supply, N1419 CAEN Portable VME Electronics - Struck FADC 50 MHz sampling, SIS3350 - GPS board, HytecGPS2092 15 MHz low pass filter All modules are remotely controlled through wireless network. 777,Phillips scientific Signal×50
  • 8. Installation in February 2014 8 Start observation!! 1 2 3 4 5 6 7 8 9
  • 9. Figure 4: Stability of the variance caused by night sky backgrounds every 5 minutes during hours operation on April 30th 2014. Figure 2: DAQ system of the prototype of FAST. ure 3: Variances measured by the PMT under the shutter closing and opening. The ance under shutter closing shows a noise of the electrics and that under opening shows ht sky backgrounds. 9 Operation in Clear Night 12.7°C 4.6°C YAP signal 7 hours data taking +8% Close Open Electronic noise level Night sky background ✦ Variance is proportional to PMT current. Electronic noise is negligible with regard to night sky background. ✦ Good gain stability during data taking, consistent with PMT gain temperature dependence of -1%/℃ Become quieter background
  • 10. gure 8: Observed signal from the vertical UV laser at a distance of 20.9 km from the GPS Timing and CLF Signal 10 Average of 223 shots ✦ FAST-TAFD timing resolution, 100 ns. (20.9 µs is the TAFD trigger processing time.) ✦ laser signal ~ 1019.5 eV at 21 km ✦ peak signal ~ 7 p.e. / 100 ns (σp.e. = 12 p.e.) at the limit of detectability CHAPTER 3. TELESCOPE ARRAY EXPERIMENT ure 3.28: The CLF system located at the center of TA (left) and the inside ure of CLF (right). Additionally, the LIDAR system has been installed at CLF location in tember 2010. When shooting the laser, the back-scattered photons are ected at the ground. Thus, the telescope system same as LIDAR was set up measure back scattered photons from CLF laser. Fig. 3.29 shows the image LIDAR system and the typical result of VAOD measured by both LIDAR tems located at BRM and CLF. While the LIDAR at BRM operates in the e to start and finish every observation, CLF is shooting the laser every 30 utes. Since these results are consistent and complementary, we can use the mospheric parameter with better time resolution in near future. ure 3.29: The image of LIDAR system installed at the CLF location (left) Central Laser Facility Vertical UV laser shooting every 30 minutes, 21 km from FAST, 10 Hz, 2.2 mJ, 300 shots Histogram Entries 28592 Mean 20.86 RMS 0.09781 s]µGPS timing difference (FAST - TAFD) [ 19.5 20 20.5 21 21.5 22 22.5 Entries 0 500 1000 1500 2000 2500 3000 Histogram Entries 28592 Mean 20.86 RMS 0.09781 Np.e./(100ns)
  • 11. Time (20 ns / bin) 0 500 1000 1500 2000 2500 3000 3500 4000 p.e.N 0 1 2 3 4 5 6 7 Preliminary CLF Simulation 11 Raytracing -7 0 +7 +14 -14 Laser length: 20 usec Distance : L 1bin = 6.0e-3 km t = 0 bin = 0 10,000 photons in the a bin of laser length 8 inch 7 FOV Simulation Y. Takizawa (RIKEN) Directional sensitivity Efficiency Np.e./(100ns) e 8: Observed signal from the vertical UV laser at a distance of 20.9 km from the prototype. As the signal is at the detection limit, 233 consecutive laser shot signals are ged to increase the signal to noise ratio. Data Np.e./(100ns)
  • 12. Figure 6: Stability of YAP signals during 7 hours operation on April 30th 2014. ure 7: Observed waveform emitted from a single vertical UV laser from 6.1 km from the ototype of FAST. The clear signal can be seen in the waveform. 11 Portable Laser Signal 12 Single laser shotFAST FAST FOV Hit Cloud TAFD ✦ Vertical UV laser with same energy of CLF (~1019.5 eV) at 6 km from FAST. ✦ Peak signal ~ 300 p.e. / 100 ns. All shots are detected. ✦ Expected signal TAFD/FAST: (7 m2 aperture × 0.7 shadow × 0.9 mirror) / (1 m2 aperture × 0.43 optics efficiency) ~ 10 Operated by K. Yamazaki (OCU) Np.e./(100ns)Np.e./(100ns) Time (20 ns / bin) 0 500 1000 1500 2000 2500 3000 3500 4000 /p.e.N 0 1 2 3 4 5 6 Figure 11: CLF signal estimated using ray-tracing of the JEM-EUSO optics and knowledge of the scattering processes in the air (without night sky background). This Figure can be compared to the observed signal as shown in Figure 8. Time (20 ns / bin) 0 500 1000 1500 2000 2500 3000 3500 4000 /(100ns)p.e.N 0 50 100 150 200 250 300 350 400 450 Figure 12: PLS signal estimated using ray-tracing of the JEM-EUSO optics and knowledge of the scattering processes in the air (without night sky background). This Figure can be compared with the observed signal as shown in Figure 9. 18 Simulation
  • 13. Shower Signal Search FAST TAFD FAST FoV ✦ We searched for FAST signals in coincidence with TAFD showers in the FAST FoV. ✦ Data set: April and June observation, 19 days, 83 hours. ✦ 16 candidates found. ✦ Low energy showers as expected. log(E/eV)=18.0 Np.e./(100ns) 13
  • 14. Example of Signal Candidates 14 FAST TAFD log(E/eV)=18.3log(E/eV)=18.3 log(E/eV)=17.2 log(E/eV)=17.9
  • 15. (a) Data: E = 1017.2 eV (b) Data: E = 1018.0 eV Time (20 ns / bin) 0 500 1000 1500 2000 2500 3000 3500 4000 /(100ns)p.e.N 0 10 20 30 40 50 60 (c) Simulation: E = 1017.2 eV Time (20 ns / bin) 0 500 1000 1500 2000 2500 3000 3500 4000 /(100ns)p.e.N 0 10 20 30 40 50 (d) Simulation: E = 1018.0 eV Figure 15: Observed signals with the FAST prototype for shower candidates, (a) and (b), an expected signals estimated from shower simulation using information reconstructed by the T fluorescence detector, (c) and (d) respectively. Comparison with simulated signal using result reconstructed by TAFD 15 A signal location is fluctuated within the TAFD trigger frame of 12.8 µs. log(E/eV)=17.2 log(E/eV)=18.0 (a) Data: E = 1017.2 eV (b) Data: E = 1018.0 eV Simulation Data Simulation Data
  • 16. (E (eV))10 log 17 17.5 18 18.5 19 19.5 20 Impactparameter[km] 1 10 2 10 Preliminary Detectable Figure 14: Distribution of the impact parameter as a function of the primary energy recon- structed by TA for shower candidates detected by the FAST prototype. The line indicates the maximum detectable distance by the FAST prototype (not fitted). 20 Distance vs Energy (from TAFD) for Candidates 16 April+June RUN FAST FoV Almost! log(E/eV)=19.1 Np.e./(100ns) log(E/eV)=18.1
  • 17. ]2 [g/cmmaxReconstructed X 400 500 600 700 800 900 1000 1100 1200 1300 1400 Entries 0 100 200 300 400 500 600 eV19.5 10 f = 1.17 Proton EPOS Iron EPOS Simulation Study 17 Segmented mirror telescope Variable angles of elevation – steps. construction is still in development 15 deg 45 deg Joint Laboratory of Optics Olomouc – March 2014 7 ✦ Reconstruction efficiency ✦ FAST with 20 km spacing ✦ With smearing SD accuracy of geometry, Xmax resolution of FAST is 30 g/cm2 at 1019.5 eV. ✦ 100% efficiency at 1019.5 eV ✦ Under implementing a reconstruction by only FAST. logE Proton Iron 18.5 0.65 0.56 19.0 0.88 0.89 19.5 0.99 1.00 Including Xmax resolution ✦ 4 PMTs Telescope ProtonIron
  • 18. Summary and Future Plans ✦ Promising results from the first field test of FAST concept: ✦ very stable and simple operation ✦ robust behavior under night sky background (gain stability, a single bright star does not matter when integrating over the large FAST FOV) ✦ laser shots and shower candidates detected ✦ sensitivity is consistent with simulated expectation ✦ Very successful example of Auger, TA, JEM-EUSO collaboration. ✦ Several improvements possible, e.g. high Q.E. PMT, narrow UV pass filter, mirror design, reconstruction method, etc. ✦ Next step: full 30°×30° prototype. 18 Segmented mirror telescope Variable angles of elevation – steps. 15 deg 45 deg (E (eV))10 log 17 17.5 18 18.5 19 19.5 20 Impactparameter[km] 1 10 2 10 Preliminary Detectable Figure 14: Distribution of the impact parameter as a function of the primary energy re structed by TA for shower candidates detected by the FAST prototype. The line indic the maximum detectable distance by the FAST prototype (not fitted). 20