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A search for microwave emission from cosmic ray air showers

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THE UNIVERSITY OF CHICAGO
A SEARCH FOR MICROWAVE EMISSION FROM COSMIC RAY AIR SHOWERS
A DISSERTATION SUBMITTED TO
THE FACULTY OF THE DIVISION OF THE PHYSICAL SCIENCES
IN CANDIDACY FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
DEPARTMENT OF PHYSICS
BY
CHRISTOPHER LEE WILLIAMS
CHICAGO, ILLINOIS
AUGUST 2013
UMI Number: 3595993
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 3595993
Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author.
Microform Edition © ProQuest LLC.
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unauthorized copying under Title 17, United States Code
ProQuest LLC.
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c 2013 by Christopher Lee Williams
Copyright All rights reserved
For Bruce,
who taught me the value of pedantry.
TABLE OF CONTENTS
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vii
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xi
Part I Introduction
CHAPTER
1 ULTRA HIGH ENERGY COSMIC RAYS . . . . . . . .
1.1 The Extensive Air Shower as a Detection Tool . . .
1.2 The Pierre Auger Observatory . . . . . . . . . . . .
1.2.1 Surface Detector . . . . . . . . . . . . . . .
1.2.2 Fluorescence Detector . . . . . . . . . . . .
1.2.3 Fluorescence Detector Event Reconstruction
1.2.4 Fluorescence Detector Calibration . . . . . .
1.3 Ultra High Energy Cosmic Ray Astrophysics . . . .
1.3.1 GZK Secondaries . . . . . . . . . . . . . . .
1.4 Future Directions in Ultra High Energy Cosmic Ray
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Measurements
2 RADIO DETECTION OF EXTENSIVE AIR SHOWERS
2.1 History of Extensive Air Shower Radio Emission . . .
2.2 Isotropic Microwave Emission . . . . . . . . . . . . .
2.3 Previous Laboratory Measurements . . . . . . . . . .
2.4 EAS Radio Emission Toy Model . . . . . . . . . . . .
2.4.1 The Scaling Parameter, α . . . . . . . . . . .
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Part II The Microwave Detection of Air Showers Experiment
3 INSTRUMENT DESIGN . . . . . . . . . . . .
3.1 The Telescope Design . . . . . . . . . . . .
3.1.1 Reflector and receiver camera . . .
3.1.2 Analog electronics . . . . . . . . . .
3.1.3 Front-End electronics and digitizers
3.1.4 Trigger . . . . . . . . . . . . . . . .
3.2 Data acquisition, monitoring and operation
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3.3
3.4
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5 MIDAS AT AUGER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1 Telescope Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Auger Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
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3.5
EM simulation of telescope efficiency . . . . .
Telescope Calibration . . . . . . . . . . . . . .
3.4.1 Absolute calibration . . . . . . . . . .
3.4.2 Pixel calibration constants and timing
Data taking performance . . . . . . . . . . . .
4 CHICAGO DATASET ANALYSIS . .
4.1 EAS Microwave Signal Simulation
4.2 Data Sample and Event Selection
4.3 Limit . . . . . . . . . . . . . . . .
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Part III The Microwave Air Yield Beam Experiment
6 EXPERIMENTAL DESIGN . . . . . . . . .
6.1 Instrumentation, setup and DAQ . . .
6.1.1 Electron beam . . . . . . . . . .
6.1.2 Anechoic chamber and antennas
6.1.3 Data acquisition . . . . . . . . .
6.1.4 Simulations . . . . . . . . . . .
6.2 Data analysis . . . . . . . . . . . . . .
6.2.1 Oscilloscope traces . . . . . . .
6.2.2 Spectrum measurements . . . .
6.2.3 Flux calculation . . . . . . . .
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7 ANALYSIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.1.1 Proportionality with beam intensity . . . . . . . . .
7.1.2 Frequency power spectrum and absolute power flux
7.1.3 Flux systematics . . . . . . . . . . . . . . . . . . .
7.2 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . .
7.2.1 Interpretation . . . . . . . . . . . . . . . . . . . . .
7.2.2 ZHS Simulations . . . . . . . . . . . . . . . . . . .
7.2.3 Scaling to air showers . . . . . . . . . . . . . . . . .
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111
Part IV Conclusions
8 FUTURE DETECTOR DESIGN . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
8.1 Implications of Signal Measurements and EAS Limit . . . . . . . . . . . . . 115
8.1.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
v
8.2
Promise of Microwave Detectors . . . . . . . . . . . . . . . . . . . . . . . . . 118
References
123
vi
LIST OF FIGURES
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
1.10
1.11
1.12
1.13
1.14
Fluorescence Spectrum of Air . . . . . . . . . . . . .
Probability distribution functions of Xmax . . . . . .
The Pierre Auger Observatory . . . . . . . . . . . . .
Auger Surface Detector Calibration Fit . . . . . . . .
Schematic layout of Auger Fluorescence Detector . .
Geometry of shower detector plane . . . . . . . . . .
Auger Event Display . . . . . . . . . . . . . . . . . .
Auger fluorescence detector light-at-aperture . . . . .
Comparison of measurements of air fluorescence yield
Flux spectrum of ultra high energy cosmic rays . . .
Hillas diagram . . . . . . . . . . . . . . . . . . . . . .
Sky map of cosmic ray correlations . . . . . . . . . .
Measured values of hXmax i (Left) and RMS (Xmax ) .
Upper limits on ultra high energy secondaries . . . .
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2.1
2.2
2.3
Molecular scattering emission from a uniform slab of plasma . . . . . . . . .
Measurements of air plasma emission at SLAC . . . . . . . . . . . . . . . . .
Scaling relation of air plasma measurements at SLAC . . . . . . . . . . . . .
38
41
42
The MIDAS Telescope at the University of Chicago . . . . . . . . . . . . . .
The MIDAS focal plane . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Diagram of MIDAS analog electronics . . . . . . . . . . . . . . . . . . . . . .
Photograph of MIDAS analog electronics . . . . . . . . . . . . . . . . . . . .
Digital electronics board of the MIDAS experiment . . . . . . . . . . . . . .
Illustration of the MIDAS first level trigger . . . . . . . . . . . . . . . . . . .
Illustration of the MIDAS second level trigger . . . . . . . . . . . . . . . . .
Monitoring data of a single MIDAS pixel . . . . . . . . . . . . . . . . . . . .
Basic patterns of MIDAS second level trigger . . . . . . . . . . . . . . . . . .
Electromagnetic calculation of the MIDAS feed . . . . . . . . . . . . . . . .
Radiation pattern of single MIDAS pixels . . . . . . . . . . . . . . . . . . . .
Radiation pattern of the MIDAS focal plane . . . . . . . . . . . . . . . . . .
Example calibration of MIDAS telescope . . . . . . . . . . . . . . . . . . . .
Example of a measurement of the calibration constant k . . . . . . . . . . .
Distribution of the measured calibration constants k . . . . . . . . . . . . . .
Event display of an airplane altimeter noise event detected by the MIDAS
telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.17 Event display of an alternate airplane altimeter noise event detected by the
MIDAS telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.18 Event display of a candidate detected by the MIDAS telescope . . . . . . . .
3.19 Event display of a 4-pixel candidate detected by the MIDAS telescope . . . .
48
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Event display of a 3 × 1019 eV simulated EAS . . . . . . . . . . . . . . . . .
73
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
3.15
3.16
4.1
vii
69
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70
71
4.2
4.3
0
Expected number of triggered events per year for If,ref = If,ref
and α = 1 .
Exclusion limits on the microwave emission from UHECRs . . . . . . . . . .
75
78
5.1
5.2
The MIDAS telescope as it is installed at the Pierre Auger Observatory . . .
Distribution of time difference between matched MIDAS SLT event and Auger
SD event . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Daily trigger rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Preliminary exclusion sensitivity of the MIDAS detector operation in coincidence with the Auger observatory . . . . . . . . . . . . . . . . . . . . . . . .
80
83
84
6.1
6.2
6.3
6.4
6.5
6.6
Schematic of the Microwave Air Yield Beam Experiment .
Gains of the electronics chains in the MAYBE experiment
Average oscilloscope time traces . . . . . . . . . . . . . . .
Raw power spectrum of the MAYBE experiment . . . . . .
Results from Geant4 simulations . . . . . . . . . . . . . .
Power analysis of the MAYBE experiment . . . . . . . . .
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7.1
7.2
7.3
7.4
Measured power flux as a function of beam energy by MAYBE . . . . . . .
Frequency spectrum of the emission measured by MAYBE . . . . . . . . .
Fourier transform of the electric field as predicted with the ZHS simulation
Fitted relative gain of the MAYBE antenna . . . . . . . . . . . . . . . . .
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101
102
106
109
8.1
Expected number of triggered MIDAS events for If,ref = 8×10−16 W/m2 /Hz
and α = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Spectral dispersion plot of the RF signal from a CoREAS simulation . . . . . 120
Spatial distribution of the RF signal from a CoREAS simulation . . . . . . . 121
5.3
5.4
8.2
8.3
Auger
viii
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85
LIST OF TABLES
4.1
Table of cuts used in search program . . . . . . . . . . . . . . . . . . . . . .
7.1
Fν as obtained in ZHS simulations . . . . . . . . . . . . . . . . . . . . . . . 110
ix
74
ACKNOWLEDGMENTS
Foremost, I extend my eternal gratitude to Katelyn. Without her unwavering encouragement
and love, the final year of my studies would have been exponentially more difficult. I will
forever be able to look back on this time with the happiest of memories.
I would like to thank all of those who have supported me through the work leading
up to the completion of this thesis. Specifically, I would like to thank my thesis advisor
Paolo Privitera for his continued encouragement over 5 years of work and his hands-off
approach that gave me the freedom I needed to grow into an independent scientist. I would
like to thank the Auger group at University of Chicago, who always provided insightful
research discussions through my time in graduate school, the Auger Collaboration and the
collaborators that are involved in the Microwave Detector Task, and the members of the
AIRFLY collaboration, especially those who spent the many long hours at Fermilab with
me in the Test Beam Facility. I would like to thank my family and friends who have always
been supportive even when my ideas were less than clear.
I wish to thank the professors and mentors that have had a great impact on my development, without their continued support and guidance this work would not have been
possible: John Beacom, James Beatty, Juan Collar, James Cronin, Jennifer Johnson, Antoine Letessier-Selvon, Ralph Engel, Paul Martini, Robert Perry, Jonathan Rosner, the late
Simon Swordy, Todd Thompson, Donald Terndrup, and Scott Wakely.
I would like to extend my highest level of gratefulness to Angela Olinto and the late Bruce
Winstein, they are most responsible for keeping me focused on my goals and and helping me
find my path, I will forever be indebted for their support and encouragement.
x
ABSTRACT
At the highest energies, the sources of cosmic rays should be among the most powerful
extragalactic accelerators. Large observatories have revealed a flux suppression above a
few 1019 eV, similar to the expected effect of the interaction of ultrahigh energy cosmic
rays (UHECR) with the cosmic microwave background. The Pierre Auger Observatory has
measured the largest sample of cosmic ray induced extensive air showers (EAS) at the highest
energies leading to a precise measurement of the energy spectrum, hints of spatial anisotropy,
and a surprising change in the chemical composition at the highest energies. To answer the
question of the origin of UHECRs a larger sample of high quality data will be required to
reach a statistically significant result.
One of the possible techniques suggested to achieve this much larger data sample, in a
cost effective way, is ultra-wide field of view microwave telescopes which would operate in
an analogous way to the already successful fluorescence detection (FD) technique. Detecting
EAS in microwaves could be done with 100% duty cycle and essentially no atmospheric
effects. This presents many advantages over the FD which has a 10% duty cycle and requires
extensive atmospheric monitoring for calibration. We have pursued both prototype detector
designs and improved laboratory measurements, the results of which are reported herein,
and published in (Alvarez-Muñiz et al., 2013; Alvarez-Muñiz et al., 2012a; Williams et al.,
2013; Alvarez-Muñiz et al., 2013).
The Microwave Detection of Air Showers (MIDAS) experiment is the first ultra-wide field
of view imaging telescope deployed to detect isotropic microwave emission from EAS. With
61 days of livetime data operating on the University of Chicago campus we were able to
set new limits on isotropic microwave emission from extensive air showers. The new limits
rule out current laboratory air plasma measurements (Gorham et al., 2008) by more than
five sigma. The MIDAS experiment continues to take data installed in Argentina, operating
in coincidence with the Pierre Auger Observatory. Using the first 70 days of livetime data
xi
combined with a sample of EAS events from the Auger surface detector we are able to set a
preliminary limit which is even more stringent than that set with the Chicago data set.
Test beam efforts performed at Argonne National Lab, The Microwave Air Yield Beam
Experiment (MAYBE), have successfully measured a microwave signal which exhibits linear
scaling with energy deposit in a frequency range of 1 GHz to 15 GHz. This measurement
has produced strong upper limits on the isotropic emission of microwaves from air plasmas.
xii
Part I
Introduction
CHAPTER 1
ULTRA HIGH ENERGY COSMIC RAYS
While past years have brought about great understanding of ultra high energy cosmic
(UHECR)1 ray physics, pushing the energy frontier beyond 1020 eV and providing many
astrophysical insights, the origin and composition of UHECRs remain as outstanding questions. This is especially true at the highest energies where cosmic rays are expected to be
of extragalactic origin and accelerated in the most extreme environments in the universe.
Discovery of these interesting scientific results in UHECR physics have always followed the
development of new technologies that are able to push detections both to higher energies and
greater measurement precision. This was true from the very first detection of extensive air
showers (EAS) of particles induced by cosmic ray primaries in the end of the 1930s (Auger
et al., 1939), relying heavily on coincident timing precision in the particle detectors deployed,
and it continues to hold true for modern instruments. The goal of this work is to continue in
this tradition and seek new detector technology that will allow improved detections on the
highest energy and rarest events as a means of making new discoveries in UHECRs.
1.1
The Extensive Air Shower as a Detection Tool
Above energies of 1015 eV the flux of cosmic rays becomes too low to measure by direct
detection of the primary particle with experiments deployed either in space or on high altitude balloon payloads. At an energy 1015 eV the flux of cosmic rays on earth’s surface is
approximately 1 event/m2 /day (Antoni et al., 2005), and at ultra high energies, the focus
of this thesis, the cosmic ray events have become extremely rare with a steeply declining
flux and fewer than 1 event/km2 /century at the highest energies observed (Abraham et al.,
2010b). However, by utilizing the great volume of the atmosphere as a detector, it is possi1. For the purposes of this thesis, UHECR will be defined as all cosmic rays with primary energy greater
than 1018 eV.
2
ble to build large arrays which are capable of detecting UHECR events. When the primary
UHECR interacts with a nuclei in the upper atmosphere a large cascade of particles is initiated. This process was first described in a simple binary electromagnetic cascade by (Heitler,
1954) which contained only photons and electrons and positrons2 . In Heitler’s toy model of
the EAS electromagnetic cascade a primary particle with energy, E0 , travels an interaction
length, d = λr ln 2, where λr is the radiation length of the medium (λr = 37 g/cm2 for air).
At this point the particle interacts creating two particles, either through pair production
for a photon or a bremsstrahlung interaction in the case of an electron, with energy, E0 /2.
This cascade continues for each interaction length, d, branching into two particles half the
energy of the previous step until the particles fall below the critical energy for interaction,
Ec , (Ec ' 80 MeV for air). Therefore, the number of particles at the EAS maximum will be
Nmax = E0 /Ec
.
(1.1)
This maximum in particle development can be given as a physical location in the atmosphere
as well. The functional form of the depth of maximum, Xmax , is a function of the radiation
length of the medium and and primary energy, Xmax = λr ln (E0 /Ec ) + X0 , where X0 is
the depth of the primary interaction in g/cm2 . While Heitler’s model does not address the
energy loss of particles due to collisions or the decline of the shower particle number which
occurs after the shower has reached its maximum development, the toy model of the physics
is fundamentally correct for an electromagnetic cascade and can be used to estimate primary
particle parameters. This model can be extended to the hadronic component of EAS initiated
by hadron primaries as well by considering a similar pion to muon production interaction.
Further examination of the particle cascade is considered in (Stanev, 2010; Matthews, 2005)
as well as Monte Carlo (MC) simulations in (Alvarez-Muñiz et al., 2002).
Another feature of the EAS that is critically important as a tool for detecting UHECR
2. Considered as electrons for simplified discussion.
3
primaries is the lateral extent of the showers at ground level. The lateral spread in an electromagnetic cascade comes about because the secondary particles produced in the interactions
carry a transverse momentum that is on average the electron mass, me , also electrons undergo Coulomb scattering as they traverse the distance, d, of each interaction length. The
theory of this lateral distribution of electrons was developed by (Kamata & Nishimura, 1958;
Greisen, 1956) and the density of particles at a given distance from the EAS impact location
on the ground is given by the NKG formula,
C (s)
ρ (r, X) = Ne (X)
rr1
r s−1
r s−9/2
1+
r1
r1
,
(1.2)
where the density, ρ (r, X), of particles a distance r from the shower core is a function
of, r1 , the Molière length, s, a parameterization of the shower development, and, C (s),
√
a normalization factor where C (1) = 2π at shower maximum, (Stanev, 2010, pp. 180181). Once again, as with the Heitler model, the NKG formulation only applies to simple
electromagnetic cascades and must be modified to produced a parameterization for hadronic
EAS. This simple model however does highlight the key physics of interest to detector arrays.
From Equation 1.2 we see the lateral density distribution of particles grows linearly with
particle number, and thus if the information is included from Equation 1.1, it is simple to
infer that the lateral extent of the EAS, which is detectable with a given particle detector,
grows with primary energy. This fact was known to (Auger et al., 1939) in which the distance
between detectors was correctly used to estimate the primary particle energies up to 1015 eV.
At the highest energies the extent of the shower can be very large, with particles detectable at
few kilometers from the shower core. While UHECR events are rare, this large lateral extent
creates a large effective interaction area at ground level for a single event. This large effective
area of interaction is the key to building sparse arrays of particle detectors to sample the EAS
at ground level, from which the lateral distribution of the EAS can be reconstructed, which
is necessary for understanding the UHECR primary. It was this technique which (Linsley,
4
Figure 1.1: Measured fluorescence spectrum excited by 3 MeV electrons in dry air at 800 hPa
and 293 K. Reproduced from (Ave et al., 2007).
1963) used in the Volcano Ranch experiment outside Albuquerque, New Mexico to detect
the first cosmic ray with an energy of 1020 eV. In retrospect, this first observation was very
lucky as the Volcano Ranch array covered only an area of 9 km2 and we know now that the
flux of UHECR at 1020 eV is as few as 1 event/km2 /century.
As the EAS particles traverse the atmosphere 90% of the total primary energy is lost to
the air mass via ionization of the air molecules, while the remaining 10% is carried away by
the secondary particles which enter the ground as discussed above. Observation methods
which are able to observe the ionization energy can provide a calorimetric measurement of
the UHECR primary energy. Currently, the most successful method by which this ionization
is observed is that of the fluorescence detection (FD) method, (Arqueros et al., 2008). This
technique, pioneered in the early 1960s and first executed successfully in 1969 (Tanahashi,
1998), observes light produced when excited nitrogen molecules which are in the ionization
trail of the EAS de-excite, emitting a spectrum that is mostly in the UV spectral range,
Figure 1.1. For particles in the EAS, primarily electrons with energies between 1 GeV
5
and 30 MeV, energy is deposited as a function of atmospheric depth, dEdep /dX, with the
light yield for a single particle, Y (λ, P, T, u) (photons/MeV), dependent on the absolute
fluorescence yield, wavelength of emitted light, λ, atmospheric pressure, P , temperature,
T , and relative humidity, u. The fluorescence light yield is dependent only on the energy
deposit and not the individual particle energy, (Ave et al., 2008a). The number of photons
observed at a FD as a function of atmospheric depth can be written as an observable of the
total EAS energy deposit,
tot Z
dEdep
dNγ
=
Y (λ, P, T, u) · τ (λ, X) · εF D (X) dλ
dX
dX
.
(1.3)
In Equation 1.3, τ is the optical depth of the atmosphere through which the EAS is observed
and, εF D , the detector efficiency. The total energy deposit can be written as the integral of
the number of particle in the EAS,
tot Z
dEdep
dNe (X) dEdep
·
dE
dX
dX
dX
.
(1.4)
Using this definition in combination with Equation 1.3 we can see that a parametrization of
the EAS particle number as function of atmospheric depth will be proportional to the number
of photons received at the detector. The integral of this function with the proper normalization will give the calorimetric energy of the UHECR primary particle up to correction
factors for lost energy.
In the work of this thesis the simple four parameter longitudinal development parameterization of (Gaisser & Hillas, 1977) is used to describe development of the EAS, as is
relevant for describing ionizing particle number. This is the common parameterization used
by both the Auger and Telescope Array collaborations for reconstruction of FD events. The
Gaisser-Hillas (GH) parameterization describes the number of total electrons in the cascade
6
as a function of its longitudinal development,
Ne (X) = Ne,max
X − X0
Xmax − X0
Xmax −X0
λ
e
Xmax −X
λ
,
(1.5)
where, Ne (X), is the number of electrons in the cascade at a given slant depth, X, generally
measured in g/cm2 . Xmax is the depth of maximum development of the cascade, and Ne,max
is the number ionized electrons at that maximum value. X0 and λ are two additional fit
parameters which are dependent on the energy and mass of the primary, found with MC
simulations of hadronic interactions. The average depth of maximum development, hXmax i,
is dependent on the energy and composition of the primary (Heitler, 1954; Matthews, 2005),
hXmax i = α (ln E − hln Ai) + β
,
(1.6)
where hAi is the average of the logarithm of primary masses. The coefficients α and β
are dependent on the hadronic interactions (Wibig, 2009; Ionita, 2011). We see from the
equation for average depth of maximum that measuring UHECR primary composition using
Xmax can only be done statistically as this observable fluctuates on a shower by shower
basis. This is further illustrated in Figure 1.2 where we see that the probability distribution
functions of Xmax overlap significantly for different UHECR primaries.
Unlike ground arrays which must sample the EAS particles in the forward region of the
shower, the light emitted in the FD process is isotropic which means EAS can be detected
off-axis and at large distances with a sensitive detector. This allows a single detector to
sample very large fiducial volumes with a very robust technique. However, because of the
nature of UV observation, the FD telescopes can only operate on clear moonless nights which
leads to a approximately 10% detector duty cycle, unlike the continuous operation of SD
arrays. As will be seen in § 1.2.2 the FD method is capable of producing the highest quality
measurements of the UHECR primary energy, composition, and direction reconstruction. It
7
Figure 1.2: Probability distribution functions Xmax simulated using SYBILL 2.1 for different
UHECR primaries at energy, E = 1019 eV. Reproduced from (Ionita, 2011).
is for this reason that the FD technique is our benchmark when evaluating new detector
technologies.
The quest for understanding of the UHECR spectrum has produced a rich history of
numerous experiments over the past 75 years, all of which have benefitted from the rise
of new technology to build better detectors. This rich history is covered in the reviews
of (Cronin, 1999; Nagano & Watson, 2000; Letessier-Selvon & Stanev, 2011). We will examine
in detail the current state of the art UHECR experiment, the Pierre Auger Observatory,
which combines both the FD technique with a large array of surface detectors (SD) in what
is known as a hybrid configuration. The combination of the two methods, FD and SD,
overcomes some of the negatives possessed by each individual technique and allows for the
largest collection aperture while maintaing a high level of data precision.
8
Figure 1.3: Figure of the Pierre Auger Observatory overlaid on a map of a section of the
Mendoza Province outside Malargüe, Argentina. The blue shaded region is the area of the
array with small blue dots marking the location of each water Cherenkov tank of the surface
detector. The green lines mark the individual field of view of each of the 24 fluorescence
telescopes of the FD which overlook the SD array.
1.2
The Pierre Auger Observatory
The Pierre Auger Observatory, originally conceived by J. W. Cronin and A. A. Watson in
the early 1990s, was designed through a series of workshops culminating with a final design
in 1995. The purpose of the design study was to develop a modern cosmic ray observatory
that would be have full sky coverage with sites in the Southern and Northern Hemispheres.
At each site, the techniques of the FD and SD would be be combined to give maximum
measurement precision over an instrumented area of 3000 km2 to measure a statistically
significant sample of UHECRs above 1019 eV at both sites (Abraham et al., 2004).
This extremely large area and excellent energy coverage was necessary to resolve the
discrepancy that existed between the AGASA and HiRes collaborations at the time. The
work of (Greisen, 1966; Zatsepin & Kuz’min, 1966) showed that for UHECR traversing the
9
intergalactic medium above an energy of 3 × 1019 eV, the cosmic ray primary will interact
with the photons of the cosmic microwave background by pion photoproduction through the
∆+ resonance3 , effectively attenuating the flux of cosmic rays arriving at earth from sources
beyond a few tens of Mpc. This attenuation of the flux is known as the GZK effect and should
appear as a sharp change in slope of the cosmic ray flux spectrum at this energy. As of the
early 2000s, the HiRes collaboration, which used a detector composed of multiple fluorescence
telescopes, reported seeing this flux suppression above an energy of 1019 eV (Abbasi et al.,
2005, 2004). At the same time, after collecting a decade of data with a SD array made up
of scintillation detectors, the AGASA collaboration reported seeing no flux suppression at
the highest energies (Takeda et al., 1998, 2003). Using the hybrid technique and the very
large collecting area, the Auger observatory was designed to answer this question as well as
explore the physics and astrophysics which was beyond the reach of previous detectors.
The joint requirements for a hybrid detector of this type included a relatively flat area
between 500 m and 1500 m above sea level. This ensures that EAS interacting with the
surface detector will be near the maximum of their development and the particles of the EAS
will be sampled relatively uniformly in shower development age. A flat site also provides
maximum line of sight for communications via radio links. Also, good sky conditions were
sought out to maximize the effectiveness of the FD’s UV telescopes. For the Southern site
a location in the province of Mendoza, Argentina was chosen near the city of Malargüe.
This site lies in the Pampa Amarilla covering a latitude of 35.1◦ − 35.5◦ S and longitude of
69.0◦ − 69.9◦ W. The altitude of the Pampa Amarilla site is between 1300 m and 1400 m
above sea level. The observatory was constructed and reached its completed size in 2008, as
seen in the map of Figure 1.3. A northern site of this original design, that would compliment
the Auger observatory in the south was never realized, although designs have continued for a
much larger array in the north (Blümer & the Pierre Auger Collaboration, 2010). Currently,
the Telescope Array collaboration, which is unassociated with the Auger Collaboration,
3. Baryon composed of uud quarks with an isospin of 3/2.
10
operates a smaller hybrid array near Delta, Utah which is a complimentary detector for
UHECRs (Kawai et al., 2008, 2009).
1.2.1 Surface Detector
The SD of the Auger array, as fully explained in (Abraham et al., 2004; Allekotte et al., 2008),
is composed of 1600 water Cherenkov detectors spaced on a 1.5 km triangular grid which
covers 3000 km2 . Each of the detectors is built with a rotomolded high-density polyethylene
water tank 3.6 m in diameter and 1.2 m in height which contains 12,000 liters of ultra pure
R liner instrumented with three 9 inch
water. Inside the tank is an internally reflective Tyvek
photomultiplier tubes (PMTs) spaced equally, 1.2 m from the center of the tank. The data
acquisition (DAQ) electronics, GPS timing system, and radio transceiver, which outfit each
detector, draw an average of 10 W of power, which is provided by a combination of solar
panels and back-up batteries. With this power system each detector operates autonomously
in the Argentine Pampas receiving necessary power 99% of the time and communicating
with the central data acquisition system (CDAS) via radio link. Water Cherenkov detectors
were chosen by the Auger collaboration for both their robustness and low cost. In the
original design the Cherenkov detectors operate as close to 100% duty cycle as possible for
20 years. This long term, continuous operation maximizes the integrated exposure at the
highest energies. Additionally, the large symmetric size of the Cherenkov detector gives each
station a rather uniform exposure up to large zenith angles, further increasing the exposure
of the array.
The signal recorded in each SD station is Cherenkov light from muons and electrons
within the EAS intersecting the water of the tank. As we can see from Equation 1.2 the
number of particles which pass through the detector is dependent on the distance from the
EAS core position. Near the shower core this can be many thousands of particles, while
for a shower of 1019 eV at 1000 m from the core the flux of muons is ∼ 1 m−2 . For the
11
Auger SD the signal from each PMT is measured in vertical equivalent muon (VEM) charge
peak
peak
distribution, QV EM , and signal peak intensity, IV EM , both of which are scaled to the signal
equivalent to that produced by a vertical muon passing through the detector (Bertou et al.,
2006).
The PMT signals of each detector station are digitized locally with a 40 MHz (25 ns time
bin) 10-bit flash analog-to-digital converter (FADC) and stored locally in a 10 s buffer. A
hierarchical trigger scheme has been developed with first (T1) and second (T2) level trigger
of the detector at each tank based on combination of over threshold triggers (T1: 1 bin
peak
peak
> 1.75 · IV EM , T2: 1 bin > 3.2 · IV EM ) and time over threshold triggers (T1 & T2: 13
peak
continuous bins > 0.2 · IV EM ). The third level trigger is performed on the array globally
over the CDAS by selecting tanks near one another with a positive level one or level two
trigger status. When a correct combination of tanks is found the event from the 10 s data
buffer is sent to a central processing facility. Additionally level 4 and level 5 triggers exist at
an event selection level to select physics events from the sample of recorded level 3 triggers.
A detailed explanation of this trigger is found in (Abraham et al., 2010c).
After accounting for the physics trigger, the SD becomes nearly 100% efficient for detection of EAS initiated by cosmic rays with a primary energy of 3 × 1018 eV. To reconstruct
the EAS energy the detected particle distribution is fit by a lateral distribution function,
S (r), such that a parameter has been defined, S (1000), to describe the signal strength the
EAS would have produced in a SD tank at a distance 1000 m from the EAS core. In the
case of Auger reconstruction, the LDF parameterization is chosen such that S (1000) is an
energy estimator (Newton et al., 2007). To account for various zenith angles which change
the geometry of the EAS the value of S (1000) is further parameterized to an energy estimator which is independent of zenith angle, S38 , which is the value of S (1000) the EAS would
have produced with a zenith angle θ = 38◦ . The value of S38 is cross-calibrated using high
b
quality events also observed with the fluorescence detector such that a fit of EFD = aS38
12
Figure 1.4: Correlation between S38 and E measured by the FD for the 839 selected hybrid
events used in the fit. The most energetic event has an energy of about 7.5 × 1019 eV.
Reproduced from (The Pierre Auger Collaboration, 2011a).
is found. The best fit value shown in Figure 1.4 produces a resulting SD statistical energy
resolution better than 16% for all energies greater than 3 × 1018 eV which is consistent with
the statistical uncertainties of the FD and SD whose quadratic sum is 18% (The Pierre Auger
Collaboration, 2011a).
Using the fit S (r), and the arrival times of the signal at each of the SD stations the
core position and and primary UHECR direction can be found by fitting the EAS particle
front. For EAS with energy between 3 × 1018 eV and 1019 eV the angular reconstruction
of arrival direction is better than 1.2◦ and the reconstruction is better than 0.9◦ for events
above 1019 eV (Bonifazi et al., 2008). The cross calibration provided by the FD is the great
benefit of a hybrid detector technique because the much more precise energy reconstruction
calibration from the FD can be transferred to the SD via common events. This gives the
best possible EAS reconstruction to the SD which has the advantage of a detector with 100%
duty cycle.
13
Figure 1.5: Left: Schematic layout of the FD building containing six telescopes. Right:
Schematic of the optical design of an FD telescope. Reproduced from (Abraham et al.,
2010a).
1.2.2 Fluorescence Detector
The FD of the Auger observatory is composed of 24 fluorescence telescopes overlooking the
central array of the SD, the full details of which are covered by (Abraham et al., 2010a).
These telescopes are split into four FD sites with six telescopes at each, seen in Figure 1.3.
Each of the FD sites is on a small elevation bordering the array, these small elevations are
typical of the area around the observatory. At a single site all six of the FD telescopes are
housed in a common building, Figure 1.5 (Left), that is climate controlled to reduce optical
aberrations induced by thermal-mechanical effects. The building of the FD site also houses
the electronics, communication systems, and a small mechanical workshop. Each of the 24
telescopes has a field of view of 30◦ × 30◦ in azimuth and elevation. This allows for full
coverage of the array such that the FD has 100% trigger efficiency for EAS above 1019 eV
over the total area instrumented by the SD. The hybrid coverage provided by the SD provides
detection flexibility as “stereo” detection (EAS being detected by two or more FD telescopes)
is not required for event reconstruction which can be done with a single telescope detection
and the EAS core impact position obtained from the SD.
The telescope design of the FD, a schematic is shown in Figure 1.5 (Right), is a modified
14
Schmidt camera design that uses a segmented spherical primary mirror 3.4 m in diameter
with a corrector ring that partially corrects spherical aberration and eliminates coma aberration. Additionally, the design employs an optical filter at the entrance of the telescope
made of Schott MUG-6 glass which transmits UV photons from ∼ 290 nm to ∼ 410 nm
while absorbing all visible light. This filter was chosen to be well-matched to the nitrogen
fluorescence spectrum, Figure 1.1. The FD telescope’s detector focal plane is made up of a
matrix of 440 PMTs with each pixel having a field of view of approximately 1.5◦ . Additionally, a mechanical shutter is located on the outside of the building to protect the telescope
from sun and moon light, and also from the heat of the day.
The signals from each of the PMTs in the telescope focal plane are passed to front-end
electronics that are arranged in progression of an Analog Board (AB), hardware first level
trigger (FLT) board, and second level trigger (SLT) board. For a single telescope there are 20
AB and FLT boards each serving 22 PMTs in a column of the camera. There is a single SLT
board serving the entire FD camera. The AB is responsible for conditioning and digitizing
the signals from the PMTs. The AB performs a differential to single-ended conversion on the
signal, adjusts channel gain, and applies an anti-aliasing filter. The signal is then adapted
from 15-bit dynamic range to 12-bit dynamic range. The signal digitization is done by the
FLT board using a 10 MHz ADC with 12-bit dynamic range. On a single card the signals
are digitized continuously for 22 PMTs in the column that the board serves. These digitized
signals are held in a circular ring buffer that is 100 µs in length. The digitized signals are
also sent to a field programmable gate array (FPGA) that performs the FLT on each pixel.
The FLT of the Auger FD uses a sliding “boxcar” sum and over threshold trigger. The digital
values from a fixed number of bins (6 ≤ nbins ≤ 16, 600 ns ≤ t ≤ 1.6 µs) trailing the current
time are summed and compared to a threshold which is regulated to hold the trigger rate of
a single pixel at 100 Hz. When a pixel trigger is found a retriggerable mono-flop is extended
to the pixel for 5-30 µs. The trigger values from the entire camera are passed to the SLT
15
board and into a second FPGA. Using the trigger values from each pixel the SLT board
searches the entire 440 pixel matrix for combinations of triggered pixels which match the
signal topology in the camera expected for EAS. The basic track structure that is searched for
are line elements of five pixels for which at least 4 of 5 pixels are triggered. This requirement
provides fault-tolerance against PMTs in the track which may not trigger due to signal-tonoise conditions or PMT defect. Each of these scans takes 1 µs to complete, once complete
and an SLT is issued, the data are read from the 100 µs buffers and housekeeping data are
passed to a dedicated computer, the MirrorPC (one serving each of the 24 telescopes), which
performs a third level trigger to reject lightning events. The third level trigger rejects 99%
of all lightning events and less than 0.7% of true EAS events. The event data is then stored
in the EyePC, which serves the FD site of the six telescopes where data is compiled by an
event builder, merging events in adjacent eyes. Externally triggered events from calibration
tests are flagged with a calibration status bit and sent directly to the EyePC.
The EyePC also sends a hybrid trigger, called T3, over the CDAS system which provides
an external trigger to the SD array. The purpose of this external trigger is to extend hybrid
events below and energy of 3 × 1018 eV where the SD trigger is not fully efficient. These
low energy events occur within 20 km of the FD buildings. The T3 algorithm performs a
fast reconstruction of the shower geometry and then collects the SD signals for the tanks
nearest the FD building at the calculated ground impact time. The FD and SD events are
then merged offline for hybrid analysis.
1.2.3 Fluorescence Detector Event Reconstruction
An EAS FD event appears as a track crossing the focal plane of the telescope on a time scale
of µs as is seen in the stereo event shown in Figure 1.7. To properly find the energy and
depth of maximum for an event the geometry of the EAS must be found. Using the track
geometry of an event, the EAS reconstruction becomes a two dimensional problem forming
16
Figure 1.6: Geometry of Shower Detector Plane reconstruction geometry illustrated for an
EAS. Reproduced from (Kuempel et al., 2008).
a plane which intersects the FD field of view known as the Shower Detector Plane (SDP).
The SDP has two geometric observables as seen in Figure 1.6, Rp , the distance of closest
approach between the track of the EAS and the telescope in the SDP and, χ0 , the angle of
incidence with the ground in the SDP. From this geometry we are able to write the arrival
time, ti , in the ith pixel of the FD telescope for photons emitted in the EAS ionization trail,
Rp
tan
ti = t0 +
c
χ0 − χi
2
,
(1.7)
where t0 is the time of emission of the fluorescence light, c is the speed of light in air, and χi is
the angle of the ith pixel line of sight in the SDP. For a given track through the camera which
produces a detectable signal in n pixels, the EAS parameters Rp , χ0 , and t0 can be found
using a χ2 -minimization procedure to find the best fit in the SDP. These values can then
be used to write the full three dimensional geometric reconstruction of the EAS including,
impact location and time at ground level, and the arrival azimuth and zenith angle of the
UHECR primary.
This reconstruction process using only a single FD telescope is known as a “monocular”
reconstruction and has a large degree of uncertainty due to degeneracies in the solution for
17
(a)
1.)
(c)
(b)
3.) Coihueco (a)
2.) SD LDF Fit
5.) Los Morados (c)
4.) Los Leones (b)
Figure 1.7: Stereo hybrid event with energy E = 3.3 × 1019 eV as seen in the Auger event
viewer for the SD and three FD telescopes. Panel 1 is the 3D reconstruction of the event.
Panel 2 the SD signals with an LDF fit. Panel 3, 4, and 5 are the signals (top) and GaisserHillas fit (bottom) in the respective FD telescopes.
18
shower geometry. These degeneracies are broken by observing an EAS event with more than
one FD telescope, the “stereo” observing mode, or as in the case of the Auger observatory
measuring the location of the EAS impact point on the ground breaks the reconstruction
degeneracy, the “hybrid” approach. The hybrid reconstruction method is highly desirable
because it allows for a much larger FD aperture than would be possible by requiring a
dataset with only stereo events. With the 100% duty cycle of the SD, nearly all events above
the SD trigger threshold are recorded by both detectors when the FD operates and can
be combined offline for analysis. Using the timing information provided by both detectors,
hybrid reconstruction resolution of the core location to 50 m is achievable. The reconstruction
resolution of the arrival direction of the UHECR primaries is typically 0.6◦ . The T3 external
trigger is issued to the SD by FD triggers because determining the ground impact point with
signal in at least one tank is sufficient to greatly improve geometric reconstruction. This
substantially increases the reconstruction robustness of the data set below the SD trigger
threshold.
With the geometry of the EAS known, the collected light profile can be fit by a GaisserHillas function, Equation 1.5, to determine the UHECR primary energy and Xmax . Because
the Gaisser-Hillas function describes the light emitted in the shower, to fit the EAS profile
with recorded data the emission amplitude received at the detector must account for numerous corrections. Beyond the detector efficiency, εF D , and the atmospheric optical depth, τ ,
additional corrections must be made for Cherenkov light from the EAS particle which reach
the shower either through direct observation or scattered light from Rayleigh and Mie scattering (Unger et al., 2008). There is also fluorescence light which undergoes multiple scatterings
in the atmosphere and then arrives at the detector. Without accounting for these additional
sources of light the fluorescence emission from an event will be overestimated. An example
measurement of the light at the aperture with a break down of additional components is
shown in Figure 1.8
19
Figure 1.8: Example of a light-at-aperture measurement (dots) and reconstructed light
sources (hatched areas). Reproduced from (Abraham et al., 2010a).
As we have seen in § 1.1, using the integral of the Gaisser-Hillas function to find the
UHECR primary energy only accounts for about 90% of the total energy. Additional corrections must be made for energy carried away by high energy muons and neutrinos. These
correction factors vary depending on the type of primary particle which initiated the EAS
and have been explored through detailed MC simulations (Pierog & Werner, 2009). After
the total reconstruction chain is taken into account, the FD of the Auger observatory has
statistical energy resolution of 8% (Dawson, 2007). The total systematic uncertainty for the
energy reconstruction is currently 22% for the Auger observatory and will be discussed in
full in § 1.2.4. Using a detailed simulation and a selection of 6744 EAS events above 1018 eV
the Auger observatory finds a reconstruction resolution of 20 g/cm2 when reconstruction
the shower depth of maximum from the hybrid dataset (The Pierre Auger Collaboration,
2011b).
20
1.2.4 Fluorescence Detector Calibration
Accurate reconstruction of EAS parameters with the FD relies on the calibration of the
telescopes and on atmospheric monitoring. These calibration and monitoring efforts combine
to produce a 22% systematic uncertainty on the energy scale of the FD reconstruction over
the entire spectrum above 1018 eV. Telescopes of the FD are calibrated with a variety of
methods, all of which are used to calculate the telescope photon efficiency, εF D , which takes
into account the effects of aperture, filter transmissivity, mirror reflectivity, pixel collection
efficiency and area, photocathode quantum efficiency, and gain. By placing a 2.5 m calibrated
light source in front of the telescope aperture these calibrations can be done in situ, finding
a detector response of 5 photons/ADC bin. Additionally, absolute calibration measurements
are made using vertical laser shots from a 337 nm laser placed in the telescope field of view at
a typical distance of 4 km. When done during good aerosol conditions, Rayleigh scattering
dominates the light which scatters into the camera and the traces recorded during these laser
shots can be used for calibration. Uncertainty in the calibration of the 2.5 m light source
dominates the calibration systematic uncertainty which totals 9.5%. The full details of these
calibration can be found in (Abraham et al., 2010a; Knapik et al., 2007).
Atmospheric effects on the light emission must also be taken into account to properly
reconstruct the EAS. At the current time, the Auger observatory uses a combination of lasers
and camera systems to monitor the atmosphere for aerosol content and cloud cover. The
primary system for measuring aerosol content is the use of two central laser facilities in the
center of the array, labeled on Figure 1.3 as CLF and XLF. The CLF uses a frequency tripled
Nd:YAG laser system to direct a steerable beam of 355 nm light into the night sky during
FD data taking runs. The CLF fires 50 vertical shots at a rate of 0.5 Hz every 15 minutes.
The scattered light from laser tracks is recorded using the same data acquisition as that used
for EAS measurements, with specific GPS timing used to separate the laser pulses from real
events. The CLF facility also records the direction, time, and relative energy of each laser
21
pulse fired which is matched to the FD data offline. Because the scattered laser light reaches
the FD through the same aerosol and cloud conditions as the fluorescence light of an EAS,
the known pulse energy can be used to infer the effect of atmospheric conditions on event
reconstruction (The Pierre Auger Collaboration, 2013). Additionally, each FD site contains
backscatter LIDARs which operate continuously outside the field of view of the FD telescopes
during data taking to monitor aerosol content and cloud cover. There are also infrared
cameras and robotic telescopes measuring the atmosphere’s optical depth (The Pierre Auger
Collaboration, 2012). On average 20% of the EAS event recorded by the FD require an energy
correction larger than 20%, but because of the extensive atmospheric monitoring efforts
the systematic uncertainty due to atmospheric effects on the total energy reconstruction is
4%. Reconstruction errors of the EAS account for a 10% systematic uncertainty and the
uncertainties associated with the energy carried away by muons and neutrinos in the EAS,
mostly due to hadronic models, contribute a 4% systematic uncertainty.
The final uncertainties that make up the full 22% systematic are due to limitations in
our understanding of the air fluorescence mechanism both the absolute light yield and the
dependence of the light yield on atmospheric variables such as pressure, temperature, and
relative humidity. The Auger collaboration monitors the pressure, temperature and relative
humidity at the observatory site. This monitoring was originally done through a series of
dedicated weather balloon campaigns and is now done using data from the Global Data
Assimilation System, (Abreu et al., 2012b). With the weather data obtained, corrections
can be made to the EAS reconstruction using the fluorescence dependence measured by the
AIRFLY collaboration at accelerator test beams (Ave et al., 2007, 2008b). The effects of
pressure, temperature, and humidity on fluorescence yield contribute 7% uncertainty in the
Auger reconstruction.
The uncertainty in the absolute fluorescence yield is largest contribution to the energy
reconstruction uncertainty at 14% with absolute yield based on the work of (Nagano et al.,
22
Kakimoto et al. [5]
Nagano et al. [6]
FLASH Coll. [7]
AIRFLY Coll.
this measurement
MACFLY Coll. [8]
Lefeuvre et al. [9]
Waldenmaier et al. [10]
3
4
5
6
7
8
9
10
Y337 [photons/MeV]
Figure 1.9: Comparison of experimental results of absolute air fluorescence yield. Reproduced from (Ave et al., 2013).
2004). Measuring the absolute fluorescence yield is very difficult as it requires not only
precise understanding, but a large reduction in all systematic uncertainty for a test set-up
which measures signals at the single photon level. The AIRFLY collaboration developed
a novel method for this calibration procedure which uses captured Cherenkov light from
test beam particles as the calibration light source. Because the production of Cherenkov
light is well understood and the particles which produce it are the same as those producing
fluorescence light in the test set-up, this technique provides and absolute calibration in situ
with very limited systematic error.
We successfully completed the measurement of the absolute fluorescence yield through a
series of test beam measurements performed at the Test Beam Facility of the Fermi National
Accelerator Laboratory. This measurement used the innovative approach of passing single
120 GeV protons through the reflective cavity of an integrating sphere in which the exit port
had been modified such that it could be opened and closed. In the open configuration the
Cherenkov light produced by the proton exits the sphere and only fluorescence photons pro23
duced during the proton’s passage are captured. When the exit port is closed the Cherenkov
light is captured in the sphere. An identical port on top of the sphere is opened in this
configuration to maintain the geometry of the spherical reflector in which the throughput
efficiency is only dependent on the total surface area covered. The integrating sphere has
a PMT attached to a viewing port 90◦ off axis from the proton direction of travel. The
sphere is contained in a vacuum chamber to precisely control the pressure and purity of the
target gasses used in the measurement. Full experimental details can be found in (Ave et al.,
2013). Using the Cherenkov calibration system we find the total systematic uncertainty on
the measurement of 3.7%. Additionally, a second calibration system was developed which
measures the absolute light collection efficiency of the test set-up with a 337 nm nitrogen
gas laser. The light from the laser is measured with a NIST calibrated silicon probe and is
then passed through a calibrated integrating sphere and collimator which greatly attenuates
and completely depolarizes the laser light. This light is then passed into the integrating
sphere system used for measuring fluorescence light and the total collection efficiency is
found. The total systematic uncertainty of this calibration is 5.8% and is dominated by the
5% systematic uncertainty of the NIST calibrated probe. The advantage using two calibration methods is the uncommon systematic errors are reduced when the measurements are
combined. We report the absolute yield of fluorescence light in the 337 nm band in dry air
at 1013 hPa and 293 K is Y337 = 5.61 ± 0.06stat ± 0.22syst photons/MeV, with statistical and
systematic uncertainties listed separately. Figure 1.9 shows this result compared with other
measurements from the literature. We expect soon the community will adopt these new,
more precise results into their FD reconstructions. In the case of the Auger collaboration,
assuming all other values remain fixed, the total uncertainty on the energy reconstruction of
the FD becomes 17%.
24
Figure 1.10: Left: Energy spectrum derived from surface detector data calibrated with fluorescence detector measurements. The spectrum has been corrected for the energy resolution
of the detector. The number of events in each bin is indicated. Only statistical upper limits
are shown at 68% CL. Right: The combined energy spectrum fitted with two functions.
Only statistical uncertainties are shown. The systematic uncertainty in energy scale is 22%.
Reproduced from (The Pierre Auger Collaboration, 2011a).
1.3
Ultra High Energy Cosmic Ray Astrophysics
While the Auger collaboration has produced numerous scientific papers relating to the astrophysics of cosmic rays, this thesis will cover three main results that are the most relevant
to current developments in the field. These are measurement of the UHECR spectrum out
to the highest energies, measurements of Xmax , as it informs our understanding of the composition of the UHECR primaries, and the current status of anisotropy studies which are
attempting to associate the arrival direction of UHECRs with their sources. All of these are
examples of science that are intricately tied to the GZK cut-off, as discussed above.
The current spectrum of UHECR obtained by the SD of the Auger observatory is shown
in Figure 1.10 (Left). This is the largest data set collected to date, with more than 4,700
events above 1019 eV. In Figure 1.10 (Right) the combined energy spectrum, SD and FD,
is plotted as flux multiplied with energy cubed as function of energy. In this representation
the power law nature of the spectrum is flattened and spectral features, such as the “ankle”,
25
are clearly seen near 3 × 1018 eV. The origin of the “ankle” may arise from a transition
of the cosmic ray sources from primarily galactic to primarily extragalactic or it could be
due to source acceleration mechanism, discussed in depth in (Kotera & Olinto, 2011; Aloisio
et al., 2012). A sharp spectral suppression is also seen above 3 × 1019 eV, near the energy
predicted for the GZK effect, and is confirmed with high significance by both the Auger
Observatory (Abraham et al., 2008b) and HiRes Experiment (Abbasi et al., 2008). The
Auger measurement alone confirms the spectral suppression with more than 20 σ significance
putting to rest the AGASA HiRes discrepancy of the early 2000s. It also has ruled out several
“top-down models” which explained the origin of UHECRs as primordial heavy relics from
the Big Bang. The measurement of a flux suppression is not, however, a direct confirmation
of the GZK effect because the composition of the primary UHECRs is unknown. Also, it is
possible that a source cut-off may exist in the acceleration mechanism which would mimic the
effect of attenuation from photo-pion production and greatly reduce the number of particles
accelerated to the highest energies.
While the exact origin and acceleration mechanism remains unknown, we know that
the UHECR must be contained to the acceleration region as a minimum requirement to be
accelerated. This implies the Larmor radius sets a lower limit on the requirements of the
acceleration site to achieve a maximum energy, Emax . This maximum accessible energy by
the acceleration region is given by, Emax = eZBR, where R is the size of the accelerating
region, B is the magnitude of the field, Z is the atomic number of the nuclei, and, e, the
electric charge. As (Hillas, 1984) demonstrated, lines of constant Emax can be drawn in the
B − R phase space for astrophysical sites which are candidate accelerators. On the plot the
size of astrophysical objects can be overlaid with the appropriate magnetic field strength, an
updated version of the so called Hillas Plot is show in Figure 1.11. As is shown in the figure
the size scales of astrophysical objects spanning from km scale neutron stars to IGM shocks
on the scale of Mpc also span twenty-five orders of magnitude in magnetic field strengths,
26
neutron star
pr
ot
Fe
white
dwarf
on
10 2
0
eV
10 2
0
AGN
eV
AGN jets
GRB
hot spots
SNR
IGM shocks
Figure 1.11: Updated (Hillas, 1984) diagram. Above the blue (red) line protons (iron nuclei)
can be confined to a maximum energy of Emax = 1020 eV. The most powerful candidate
sources are shown with the uncertainties in their parameters. Abbreviations: AGN, Active
Galactic Nuclei; GRB, Gamma-Ray Burst; IGM, Intergalactic Medium; SNR, Supernova
Remnant. Reproduced from (Kotera & Olinto, 2011).
still with this great diversity of scales only a few objects reach up to the value required for
accelerating the highest energy particles, this is especially true for proton primaries where
the most likely candidate sources are neutron stars and active galactic nuclei (AGN). As
(Kotera & Olinto, 2011) point out, meeting the Hillas condition is necessary for UHECR
acceleration but it is not sufficient, the acceleration mechanisms proposed must also match
spectral shapes observed after propagation of UHECRs and the composition of the primary
particles (Allard, 2009).
At energies above the GZK cut-off only cosmic rays accelerated within a few tens of Mpc
will reach earth without being attenuated. It is with UHECRs of this energy that is possible
to do astronomical measurements, pointing back to the sources of UHECR acceleration,
assuming the UHECR primaries consist of protons which are bent by only small amounts
as they traverse the intergalactic medium. For UHECRs of higher charge, such as iron
nuclei, the bending in intergalactic magnetic fields can be as much as 20◦ , leaving little
27
Figure 1.12: Left: Black dots are arrival directions of 69 events above 5.5 × 1019 eV plotted
with the AGN of the Véron-Cetty and Véron (VCV) catalogue represented by the blue circles.
Each circle is 3.1◦ around the location of the AGN where color is an exposure weighting for
the Auger Observatory. Right: Arrival direction of same events as in (Left) overlaid with
flux weighted 2MRS galaxies with 5◦ smoothing. Reproduced from (Abreu et al., 2010),
further details in source paper.
hope for pointing back to the sources. In 2007 (The Pierre Auger Collaboration, 2007;
Abraham et al., 2008a) reported a strong correlation of the highest energy cosmic rays with
AGN of the Véron-Cetty and Véron (VCV) catalogue, finding 17 of 27 UHECR events
with E > 5.7 × 1019 eV and arrival directions within 3.1◦ of correlating VCV AGN, only
5.6 events were expected to correlate from an isotropic distribution producing a correlation
confidence greater than 99%. In (Abreu et al., 2010) an update of this correlation is given
finding that a much weaker correlation now exists with a larger dataset with 21 of 55 events
correlating with VCV AGN while 11.6 would be expected from an isotropic distribution. A
sky map of these events is shown in Figure 1.12 (Left). This much weaker 38% correlation
is less than 3 σ removed from the isotropic distribution implying a change of the data set or
that the original much stronger correlation was due to a statistical fluctuation. The Auger
collaboration also explores correlation with other catalogues, the Swift-BAT and 2MRS,
both catalogues are found have similar levels of correlation between 2 σ and 3 σ. 69 UHECR
events above 5.5 × 1019 eV are shown overlaid on the flux-weighted 2MRS galaxy catalogue
with 5◦ smoothing in Figure 1.12 (Right). From both panels in Figure 1.12, as well as the
correlations presented in (Abreu et al., 2010), we see that at the current time any astronomy
that is pursued with UHECR must be approached with caution as the small statistics and
28
Figure 1.13: hXmax i (Left) and RMS (Xmax ) (Right) plotted as a function of energy. Data
(points) are shown with the predictions for proton and iron for several hadronic interaction
models. The number of events in each bin is indicated. Systematic uncertainties are indicated
as a gray band. Reproduced from (The Pierre Auger Collaboration, 2011b).
direction reconstruction complications due to propagation through intergalactic fields make
reconstruction very difficult. This is especially true for any nuclei with Z > 1, where the
intergalactic magnetic fields have even greater effect. At this time, given the small statistics,
it can only be confirmed that the observed UHECRs are loosely correlated with the matter
distribution in the local universe, a result not surprising for a population that is expected to
be extra-galactic.
To fully understand the features seen in the UHECR spectrum and the UHECR correlation with regards to astrophysical sources, understanding the composition of UHECR
primary particles remains an interesting outstanding question. The main observables for the
measurement of UHECR primary composition of the Auger observatory are FD measurements of the average depth of maximum development of EAS, hXmax i, and the root mean
square of the Xmax distribution, RMS (Xmax ). As discussed in § 1.1 these estimators must
be used because determination of particle composition can only be done statistically for a
sample of EAS and not on a shower by shower basis because the average depth of maximum
distributions overlap for different primary UHECRs, this is especially true at higher ener29
gies. This statistics limited measurement is further hindered by the low duty cycle of the FD,
with only 10% observation time, the current data set does not contain an significant sample
of events above the spectral suppression feature near 3 × 1019 eV where UHECR astronomy becomes most interesting. Even with the limitations in the observables and detection
method, the Auger collaboration finds a surprising result in that the UHECR primaries are
trending toward higher mass nuclei above 1019 eV. This trend is seen in both hXmax i, Figure 1.13 (Left), and even more clearly in RMS (Xmax ), Figure 1.13 (Right), where the final
bin is consistent with model predictions for iron primaries shown in blue. If confirmed that
the UHECR are composed of iron nuclei, matching UHECRs to their sources will become
enormously difficult as the primaries will be bent to a large degree in magnetic field as they
traverse the intergalactic medium. Also, it remains a challenge to explain the origin of the
acceleration for these high energies, especially for rare heavy elements like iron, although
recent progress has been made on theories for acceleration in magnetars (Fang et al., 2012,
2013).
1.3.1 GZK Secondaries
The secondary products from the GZK mechanism arise from photo-pion production of
protons on CMB photons producing short lived pions which ultimately become neutrinos
and high energy gamma rays with characteristic energy of roughly 10% the primary UHECR
energy. This process follows:
p + γCMB → ∆+ → π 0 + p
→ π+ + n
ultimately followed by decays π + → µ+ + νµ and µ+ → e+ + νe + ν µ producing ultra high
energy neutrinos. High energy gamma rays are also produced by the decay π 0 → γγ. These
30
Figure 1.14: Left: Experimental limits on cosmogenic neutrinos shown with predicted fluxes
from various UHECR models. Dashed lines show sensitivity of planned experiments. See
source for model details. Reproduced from (Kotera & Olinto, 2011). Right: Current experimental limits on the flux of gamma rays at ultra high energies from the Auger Collaboration.
Dashed lines and shaded regions represent different emission models for gamma rays. Reproduced from (Abreu et al., 2011).
secondary particles are of great interest to the field of UHECRs as a detection would be
definitive proof of the GZK mechanism and a full sampling of the spectrum of secondary
particles would allow for analysis of source evolution which will answer questions about the
sources themselves. Secondary neutrinos can also exist from photo-disintegration of UHECR
nuclei by the CMB, however these produce neutrinos with a slightly lower energy peak and
significantly lower fluxes (Allard, 2012; Kotera et al., 2010).
Like the primary UHECRs, these ultra high energy neutrinos and photons will interact
with the atmosphere producing EAS with the distinguishing feature of having very large
Xmax , interacting very deep in the atmosphere due to their smaller cross sections. The
Auger collaboration has done a search for these highly inclined photon showers. To date no
detection has been made and this null result is used to set an upper limit on the flux of UHE
gamma rays (Abreu et al., 2011) as seen in Figure 1.14 (Right) which is just beginning to
reach the predictions for UHE gamma rays from the GZK mechanism and have ruled out
31
models which predict the production of UHE gamma rays from super heavy dark matter and
primordial big bang relics.
In the case of neutrinos the interaction length is so long in the atmosphere the neutrino
can reach the earth interacting in the surface. Looking for these particle cascades in the
Antarctic ice is the method of detection employed by the ANITA (Gorham et al., 2009,
2010) and IceCube (Halzen & Klein, 2010; Abbasi et al., 2010) experiments. The Auger
observatory has employed a technique to look for very inclined EAS which skim the Earth’s
atmosphere, producing extremely high values of Xmax . Also up-going EAS which originate
from the land around the detector. In this scenario an UHE neutrino would interact in the
Earth’s surface creating a τ particle which has a relatively long interaction length escaping the
Earth’s crust and creating an EAS. EAS arrays are most sensitive to this interaction channel
because it creates the largest effective detector volume. The details of these searches are
found in (Abreu et al., 2013) with current best combined limits shown in Figure 1.14 (Left).
To date there has been no detection of UHE neutrinos, but we see the upper limits presented
by Auger, IceCube, and ANITA are just beginning to reach the most optimistic theoretical
predictions. At the current time these measurements are statistics limited and will require
much larger exposures to dig into the many orders of phase space predicted by theories to
make a detection.
1.4
Future Directions in Ultra High Energy Cosmic Ray
Measurements
To answer the outstanding questions of UHECR composition and origin presented above, a
much larger sample of UHECR events will need to be collected. With the confirmation of
the strong suppression of UHECR flux above 1019 eV, it has become clear that the currently
operating experiments of the Pierre Auger Observatory and Telescope Array will not be
sufficient for this task. New UHECR experiments will need to instrument extremely large
32
areas in order to observe a statistically significant sample of events in the future. These
extremely large areas are also required for the field to reach new levels of sensitivity in
attempts to detect GZK secondary gamma rays and neutrinos which are severely exposure
limited because of their small production and interaction cross sections. This is especially
true in the case of UHECRs composed of heavy nuclei primaries in which the production of
secondaries is greatly suppressed.
While current techniques are very robust and able to collect extremely high quality data,
they are expensive and in the case of FD their detection duty cycle is limited. Simple extensions of current technology will not be cost effective for the next generation of detectors.
This necessitates exploration of new detection techniques in order to reach the large instrumented areas, while still maintaining the high quality data, required for the next generation
of UHECR detectors at an affordable cost. The results of our prototype detector R&D efforts and test beam measurements in the microwave regime are presented in this thesis, and
reported in (Alvarez-Muñiz et al., 2013; Alvarez-Muñiz et al., 2012a; Williams et al., 2013;
Alvarez-Muñiz et al., 2013).
33
CHAPTER 2
RADIO DETECTION OF EXTENSIVE AIR SHOWERS
2.1
History of Extensive Air Shower Radio Emission
In recent years, considerable interest has been placed on detecting EAS induced by UHECRs
using radio frequency techniques as a means of expanding to larger apertures. Radio detection techniques in both the MHz and GHz are an attractive solution for building extremely
large scale EAS detectors because the individual radio detector elements are low cost, require
little maintenance, and have nearly 100% detection duty cycle.
Radio emission associated with EAS had been measured by numerous groups in the late
1960s (Jelley et al., 1966; Allan & Jones, 1966; Porter et al., 1965; Barker et al., 1967; Prescott
et al., 1968; Fegan & Slevin, 1968), with most of this work being done between 20 MHz and
500 MHz measuring EAS in the forward region of the EAS very near the core of the shower,
with the particle detectors providing an external trigger for the radio detectors. At that
time, however, they lacked the fast timing electronics and low noise amplifiers required to
pursue a detailed analysis of detections and large scale detector prototypes, especially in
the GHz regime where an initial attempted detection by (Charman & Jelley, 1969) resulted
in upper limits on the forward emission at 3 GHz due to the high noise level of available
amplifiers. The theory of EAS radio emission was also incomplete at this time and when
combined with the difficulties associated with available electronics most research had ceased
by 1970.
In 2003 (Falcke & Gorham, 2003) renewed interest in detection of EAS using radio techniques because radio technology had progressed to a point where it was technically feasible
to build large scale arrays of radio elements for digital interferometry. To date much experimental activity (Falke, 2007; Huege & Falcke, 2005; Huege et al., 2012; Apel et al., 2012;
Abreu et al., 2012a; Acounis et al., 2012) and theoretical computation and modeling (Lud34
wig & Huege, 2011; James et al., 2011; Marin & Revenu, 2012; Alvarez-Muñiz et al., 2012;
Huege et al., 2013a) has been pursued to understand the radio emission produced by EAS.
From this large body of work a concordance model for the emission which exists in an air
shower has emerged (Huege, 2013). In an EAS initiated by a cosmic ray primary the emission
present can be considered to exist in two domains, the forward region of the EAS and the
ionization trail of the shower. The forward region of an EAS describes a geometry in which
the observer is at or near the core impact location of the incoming EAS. Generally, this
location is an observer line of sight that is within ∼ 10◦ of the vector which coincides with
the EAS path through the atmosphere. In this region the charge dynamics of the shower
front are responsible for the radio emission. These dynamics can be described as separate
mechanisms such as time-varying current in the geomagnetic field, charge separation between electrons and positrons, bulk charge excesses, etc., but as (Huege, 2013) points out
the emission received on the ground in both intensity and polarization of the electric field
will be a superposition of these emission mechanisms which are dependent on the geometry
of the EAS and the strength of the geomagnetic field. The main aspect of this emission
which is relevant for our study is that the radio emission in the forward regime is coherent
below a critical frequency which is dependent on the observer angle and, therefore, scales
quadratically with the number of emitting particles. In an EAS the forward radio emission
is the dominate source of emission, specifically below the frequency of ∼ 100 MHz where the
signal is coherent. Due to this strong signal, most experimental work has been carried out
in this region at MHz frequencies where the signal is strongest.
While these prototypes have had great success in making detections and understanding
of the EAS emission parameters, many hurdles must still be overcome to make this a viable
technology for a stand alone UHECR detector. Key problems which limit large detectors
of the forward emission include EAS parameter reconstruction, triggering, and detector
scaling. The high degeneracy in signal with respect to EAS geometry and geomagnetic
35
effects make matching observed emission to EAS parameters such as energy and shower
development a complicated task. Further complicating expansion strategies are large noise
backgrounds. The galactic background can be greater than 1000 K at MHz frequencies and
when combined with strong impulsive backgrounds from anthropogenic sources as well as
natural sources such as thunderstorms which are detectable at great distances (Apel et al.,
2011), the trigger rate at a single array element can become very great making data handling
and array triggering very complicated. The geometry of the emission itself is also a concern.
Forward emission by its nature is highly beamed and only detectable over a small forward
solid angle relative to the EAS direction of travel. This emission is somewhat akin to a SD
radio analog in which a large number of individual elements in an array will be required to
detect an adequate number of UHECRs. Currently, the required spacing of radio elements in
the array necessary for stand alone detection and reconstruction of EAS is unknown, (Apel
et al., 2010). If this value is found to be much smaller than the array spacing in current SD,
∼ 1 km, the number of elements required for a comparable aperture may be prohibitively
large.
By contrast, radio emission produced in the ionization trail that follows the EAS front
through the atmosphere would be able to overcome the difficulties associated with the
beamed emission. If radio emission is produced in the air plasma left by the EAS it may be
possible to detect this emission at large angle relative to the EAS direction of travel assuming
the radio emission is isotropic like the fluorescence light seen by the FD. An off-axis detector
of this type can provide a direct radio analog to FDs, but with a greatly improved duty cycle
of nearly 100% because radio techniques can operate day and night, as well as during most
weather conditions. While this emission has not yet been observed at any frequency, the great
promise of this technique and the availability of cheap commercially sourced components,
especially in the microwave regime, make it worthwhile to pursue detector prototypes.
36
2.2
Isotropic Microwave Emission
The work by (Bekefi, 1966) on radiation in plasmas is the guiding theory for the prospect of
detecting isotropic microwave emission from EAS. Bekefi finds, for a weakly ionized plasma
with a Maxwellian velocity distribution, the emission from free electrons scattering with
neutral molecules will produce a flat spectrum in frequency space that is below the level
of black body emission. This emission is dictated by the emission, jω , and absorption, αω ,
coefficients of the plasma:
mωp2
Z ∞
ν(u) f (u) u4 du
6π 2 c3 0
Z
4π ωp2 ∞
∂f 3
αω = −
ν(u)
u du
2
3c ω 0
∂u
jω =
,
(2.1)
,
(2.2)
where ω is the emission frequency and ωp is the plasma frequency. f (u) is the electron
distribution as a function of velocity, u, and ν(u) is the collisional frequency of the plasma.
For a given volume of emitting plasma the emission along a ray towards an observer is given
by the differential equation,
dIω
= jω − αω Iω
ds
.
(2.3)
For clarity two definitional transformations are made, the source function, Sω , is defined
R
as is standard, Sω ≡ αjωω . The optical depth, τ , is defined such that τ = − αω ds, the
absorption coefficient integrated over the path length of a given ray, s. With these definitions
ω
Equation 2.3 becomes, dI
dτ = Iω − Sω . When solved over a single ray in a bounded emitting
volume we find the intensity at the observer is
37
Figure 2.1: Molecular scattering emission from a uniform slab of plasma presented in relative
units. Reproduced from (Bekefi, 1966).
Iω (B) = Iω
(A) e−τ (B,A)
Z τ (B,A)
+
0
Sω e−τ dτ 0
(2.4)
0
where the ray of emission runs from A to B. To obtain the total emission intensity from an
emitting volume at an observation point Equation 2.4 must be integrated over the volume of
the emitting region. This is done for a uniform slab of plasma in (Bekefi, 1966), reproduced
in Figure 2.1, and the emission found has the characteristic white frequency spectrum which
lies below the blackbody emission.
This result is very promising when considering detection of EAS because it implies the
existence of a broadband isotropic emission that is related to the number of individual
emitters present. However, the result is derived in the Maxwellian limit which is unlike that
of an EAS induced air plasma. This is especially true for the absorption parameter, αω ,
which is derived using detailed balance, a condition only true at equilibrium. What remains
unclear from this formal calculation of the emission is whether there exists bulk plasma effects
which would produce some level of coherence of the signal. This would greatly increase the
38
overall signal strength, as one expects coherent signals to be the phased sum of individual
emitters, scaling quadratically with emitter numbers. Even for very small volumes of order
the wavelength of emission this can have a large effect on the signal.
A more detailed simulation is required to fully understand the bulk emission mechanisms
and any coherence effects in the EAS plasma. This type of simulation would require a
prohibitively large amount of computation resources for the given problem. We find the
better option at this time is to pursue initial detections of the emission. Regardless of any
level of coherence, if isotropic microwave emission is observable in an EAS, a small prototype
detector system can be built and deployed quickly that can determine the feasibility of
detecting EAS using microwave emission on a large scale well before a detailed simulation
could be completed.
2.3
Previous Laboratory Measurements
The interest in detection of EAS plasma was renewed by beam tests carried out by (Gorham
et al., 2008) in 2003 and 2004, conducted at the Argonne Wakefield Accelerator (AWA)
and the Stanford Linear Accelerator Center (SLAC) respectively. The initial measurements
made at AWA were inconclusive given the high level of noise found to be associated with
the beam, but hints of a signal were present. It wasn’t until the SLAC tests in 2004 where
a signal detection was made. In the SLAC test, as was similarly set up at AWA, the target
consisted of a 1 m3 copper Faraday box lined internally with RF absorbing foam to produce
an anechoic chamber. Inside this box two antennas, sensitive to a frequency range of 1-8 GHz,
were placed which recorded orthogonal emission relative to the particle beam’s direction of
travel. An image of this chamber can be seen in Figure 6.1, as this is the same chamber that
we used to complete the MAYBE experiment, Part 5.2 of this thesis. The beam provided
by SLAC consisted of bunches of 28 GeV electrons with 1.2 × 107 electrons per bunch. This
gives a equivalent air shower energy of 3.36 × 1017 eV, defining the current reference shower
39
energy for the field of microwave detection of EAS. A radiator consisting of 90% Al2 O3 and
10% SiO2 was placed in front of the beam before the chamber to create an equivalent air
shower development, sampling 0 to 14 radiation lengths.
The results obtained varied greatly between polarizations. Using a broad bandwidth (1.56 GHz) the power in the antenna polarized along the beam axis, the copolarized direction,
was found to have a very strong prompt emission that coincided with the particle bunch’s
arrival at the chamber and decayed away quickly, in a characteristic time of approximately
10 ns. This prompt signal was followed by a signal with a longer decay time persisted
for an additional 20 − 30 ns until it is lost in the electronic noise floor of the oscilloscope
used, Figure 2.2 (Left). In the other antenna configuration, cross-polarized relative to the
beam’s direction of travel, no prompt emission is seen distinguishable for the more persistent
emission. In the case of the cross-polarized antenna, the persistent emission extends up to
60 ns after the passing of the electron beam until it is lost in the thermal noise floor,
Figure 2.2 (Right). It is believed the difference between polarizations may be from the strong
emission of radio Cherenkov emission by high energy electrons producing a noise signal in
the copolarized channel. Cherenkov emission is highly polarized at a right angle relative to
the direction of particle travel which appears in the polarization which is copolarized with
the particle beam, the emission is prompt and coherent. For a Cherenkov signal associated
with the bunch passing through the 1 m chamber, the observer expects a prompt coherent
emission with a given lifetime of order the chamber crossing time, less than 5 ns. It is
thought that with high enough degree of polarization isolation in the antennas and sufficient
absorption in the chamber, there should be no Cherenkov emission in the cross-polarized
channel.
In (Gorham et al., 2008) signal analysis was done using the cross-polarized channel from
15 to 30 ns after the beam passed. Using this time window, the emission measured is in
a high signal to noise regime and well separated from additional noise signals associated
40
Figure 2.2: Left: 100 beam average of measured copolarized emission measured in a band of
1.5-6 GHz at SLAC. Right: 100 beam average of measured cross-polarized emission. Pink
dashed lines in the right plot are calculations of suppressed and non-suppressed molecular
bremsstrahlung emission. Reproduced from (Gorham et al., 2008).
with the particle beam passing, such as Cherenkov leakage between polarizations due either
to an antenna effect or reflections inside the chamber. In order to measure the scaling of
the emission with beam energy, a critical component in understanding the detectability of
the emission in EAS, the power emitted in this time window is measured while varying
the number of electrons in the bunch which is equivalent to varying the total energy of
the beam pulse. In the SLAC test the beam energy was varied over approximately one
order of magnitude in total relative energy. From these measurements it is seen clearly,
Figure 2.3 (Right), that the integrated microwave signal energy measured scales quadratically
with the total beam energy, implying the signal measured is fully coherent. Additional tests
were made to understand the plasma’s behavior at different developmental depths in the
cascade. The emission was measured varying the radiator placed before chamber entrance,
probing cascade development between 4 and 14 radiation lengths. In these tests the air
plasma’s decay time was measured by fitting the 15-30 ns window of emission with an
exponential. At all cascade developments the time constant of the decay was found to
be consistent with ∼ 7 ns, Figure 2.3 (Left, Bottom). This time is consistent with the
41
Figure 2.3: Left: Integrated beam energy in a 15-30 ns time window from the cross-polarized
configuration plotted relative to cascade depth with plotted Gaisser-Hillas and Gaisser-Hillas
squared lines for comparison (Top). Measured exponential decay constant plotted relative to
cascade depth (Bottom). Right: Integrated microwave energy in a 15-30 ns time window from
the cross-polarized configuration plotted relative to beam energy and fit with a quadratic
function. Reproduced from (Gorham et al., 2008).
thermalization time expected for a tenuous air plasma and is the only measurement to date
of the thermalization constant in an air plasma.
Further analysis shows that when the integral of the microwave energy in the time bin
is plotted as a function of radiation length, Figure 2.3 (Left, Top), the measured values
follow a developmental function that does not match a Gaisser-Hillas parameterization nor
its square as would be expected from quadratic scaling of the emission with energy deposit.
The measured values lie between these two functions implying that the measurements can
not be fully consistent with the measured value of quadratic scaling which implies fully
coherent emission.
Even with these inconsistencies the measured flux value by (Gorham et al., 2008) gives a
0
reference flux density of If,ref
= 1.85 × 10−15 W/m2 /Hz at the developmental maximum of
an EAS with a primary energy of 3.36 × 1017 eV within the frequency range of 1.5-6 GHz.
This is a level of emission is very promising because it implies detectable values with even
a modest experimental set-up composed of commercially sourced components. In (Gorham
42
et al., 2008), the authors present results from a small radio telescope operated with four focal
plane receivers at the University of Hawaii campus in Honolulu, HI. This small prototype
system provides initial candidates of EAS detection. However, with only 4 receivers and an
urban environment which has a great deal of impulsive radio frequency noise, no definitive
detection could be made.
2.4
EAS Radio Emission Toy Model
Given the large uncertainties in the model of EAS plasma emission and the inconclusive
scaling results of (Gorham et al., 2008), we assume a generic form of the isotropic microwave
emission for the purposes of detector development in this work. At a given time, t, the
isotropic microwave flux at a detector is parameterized as,
ρ(t)
·
If (t) = If,ref ·
ρ0
2 N (t) α
d
·
R(t)
Nref
,
(2.5)
where If ref is the flux density at a distance d = 0.5 m from a reference shower of Eref =
3.36 × 1017 eV, R(t) is the distance between the detector and the emitting EAS segment, and
ρ(t)/(ρ0 ) is the atmospheric density at the altitude of the EAS segment relative to the density
at sea level. N (t), the number of EAS particle present at the time emission for the segment
of EAS derived from the Gaisser-Hillas function, Equation 1.5, and Nref is the average
number of shower particles at the maximum of the EAS development for a proton primary
of energy Eref . The parameter α characterizes phenomenologically the coherence scaling
relationship for the EAS microwave emission, with α = 2 (α = 1) corresponding to a fully
coherent (incoherent) emission. This notation has been adopted to provide a generic form
of describing the emission that can be used for comparison between experiments allowing us
to consider a large range of parameter emission space.
43
2.4.1 The Scaling Parameter, α
Coherent emission can occur when the superposition of emission wavefronts sums constructively. This is commonly caused when a group of individually emitting particles are distributed in a region smaller than the emission wavelength. The parameter α is an ad hoc
parametrization of the received flux or power describing the level of coherence in the microwave emission. In this work we have defined α as a scaling exponent on the collection of
individual emitters. The two extreme cases of this parameterization are:
Fully Coherent Ptot = Ne2 · P1
(2.6)
Fully Incoherent Ptot = Ne · P1
(2.7)
In Equation 2.6, the total received power, Ptot , is fully coherent, α = 2, scaling quadratically
with the number of EAS electrons, Ne . In Equation 2.7 the power received is fully incoherent,
α = 1, scaling linearly with Ne . In both Equation 2.6 and Equation 2.7, P1 is the microwave
emission power produced by a single emitting electron.
For a partially coherent collection of emitters we assume the collection of Ne electrons is
composed of M groups of µe coherent emitters,
Ne = M · µe
.
(2.8)
This assumption implies the total power goes as,
Ptot = M · µ2e · P1
,
(2.9)
the incoherent sum of M bunches of µe coherent emitters. After some manipulation of the
44
above equations we arrive at the parameterized power scaling,
Ptot = Neα · P1
,
(2.10)
.
(2.11)
where the scaling parameter is given by,
α=1+
log µe
log Ne
The number of emitters in a coherent bunch, µe , is defined by the coherent spatial properties
of the plasma. This number is dependent on various parameters of the plasma, such as plasma
temperature and density, and is also fundamentally linked to the emission wavelength. In
Maxwellian plasmas the Debye length or microwave emission wavelength are both natural
length scales to establish the coherent emitting volume required to define µe . Because these
parameters are unknown for non-Maxwellian EAS plasmas, we choose not to attempt an
in-depth description of the low energy EAS micro-physics. Instead we will use the ad hoc
scaling, α, as the coherence scaling parameterization in our toy model of isotropic EAS
microwave emission. We will allow α to run over the range 1 to 2 in all analyses, ensuring
the entire phase space for coherent emitting volumes is considered.
45
Part II
The Microwave Detection of Air Showers
Experiment
CHAPTER 3
INSTRUMENT DESIGN
In order to avoid the ambiguity associated with radio telescopes with single feeds, we sought
a design which would allow EAS imaging in the focal plane similar in style to the focal plane
of the FD. This required our initial prototype detector to have a large focal plane array. For
the prototype detector we employed as many commercially sourced components as possible
to keep the cost of construction low as this would translate well into scaled designs in the
event of a successful detection. Further, commercially sourced components, chosen mainly
for available communications components, are robust and able to operate continuously in
all weather conditions. This is an essential requirement for a detector design which has
maximized duty cycle over many years of operation.
3.1
The Telescope Design
The telescope of the Microwave Detection of Air Showers (MIDAS) experiment consists of a
large parabolic reflector with a multi-element receiver at its prime focus, installed on the roof
of the Kersten Physics Teaching Center at the University of Chicago (Figure 3.1). MIDAS
was commissioned and operated on the roof for approximately six months during a period of
testing and early data taking during 2011. The commissioning and operation of the MIDAS
experiment is published in (Alvarez-Muñiz et al., 2013).
3.1.1 Reflector and receiver camera
The parabolic reflector (Andrew), a legacy receiver obtained from the Department of Physics,
has 4.5 m diameter and a focal ratio of f /D = 0.34. The reflector is on a motorized altitudeazimuth mount allowing the telescope to move in a range of 90◦ in elevation and 120◦ in
azimuth. While not foreseen for the final design, the capability of pointing the telescope
47
Figure 3.1: The MIDAS telescope at the University of Chicago, with the 53-pixel camera at
the prime focus of the 4.5 m diameter parabolic dish reflector.
48
Figure 3.2: Photograph of the MIDAS focal plane
proved very useful for calibration purposes. During data taking for EAS detection, the
telescope is kept in a fixed position. The remote control of the telescope pointing (0.1◦
precision) is integrated in the data acquisition (DAQ) system (§ 3.2).
A 53-pixel receiver imaging camera is mounted on the prime focus of the dish, covering a
field of view approximately 20◦ × 10◦ . The microwave receivers are arranged in seven rows,
and staggered to maximize the sensitivity across the focal plane (Figure 3.2). Commercial
low noise block feed horns (LNBFs) operating in the extended C-band (3.4–4.2 GHz) were
chosen for the receiver. These feeds (WS International) are mass-produced as consumer
satellite television receivers and satisfy the requirements of being cheap and robust for continuous operation in all weather conditions. The LNBF integrates a feed horn, low noise
amplifier, and a frequency downconverter block. Each feed can receive two orthogonal linear
polarizations which are remotely selectable through the LNBF power voltage level setting.
A 5150 MHz local oscillator in the frequency downconverter block mixes the input RF signal
down to an output frequency interval of 950-1750 MHz, which is transmitted with minimal
loss through standard cable television coaxial cable. The receiver bandwidth, its gain Γ and
49
counting room
roof
+5 V
FEED
1 GHz
4 GHz
FILTER
BIAS-T
+18 V
IMPEDANCE
ADAPTER
Power
Detector
DC Pulse
To ADC
Figure 3.3: The analog electronics chain. See text for details of the components.
noise temperature were measured to be about 1 GHz, 65 dB and 20 K, respectively. Power
to the LNBF is provided through 30 meters of commercial quad-shielded RG-6 coaxial cable,
which also brings the RF signal, after amplification and downconversion, from the telescope
to the counting room.
3.1.2 Analog electronics
The analog electronics chain is summarized in Figure 3.3. The RF signal in the coaxial cable
is first passed through a custom 1.05–1.75 GHz bandpass filter (Soontai). The purpose of
the filter is to reject interference from radar altimeters of airplanes, which was identified
as a major source of background in the early stage of commissioning of the telescope. A
power inserter (commonly called bias-tee) provides the DC voltage to the LNBF over the
core of the RG-6 cable, while passing the AC-coupled RF signal to the power detector. An
impedance adapter matches the standard 75 Ohm impedance of the commercial satellite
TV components to the 50 Ohm impedance of the RF power detector (Mini-Circuits ZX4760-S+). The overall power loss L in the 30 m of cable and in the analog electronics was
measured to be 17 dB.
The power detector (input bandwidth ≈ 8 GHz) responds logarithmically to an RF
50
Figure 3.4: An analog electronics tray with eight channels. The bias tee (1), impedance
adapter (2), power detector (3), and DC voltage inputs (4) are visible.
51
power, P , in the range -55 dBm to 5 dBm, with a voltage output between 2.0 V and 0.5 V:
V = V0 − 10 a log(P )
,
(3.1)
with P in mW. The characteristics of the 53 power detectors were individually measured,
with typical values around V0 = 0.625 V and a = 0.025 V/dB. Also, their response time was
found to be about 100 ns, well suited for typical pulses of microseconds duration expected
from an EAS crossing the field of view of a pixel.
The analog electronics components are arranged in trays—8 channels per tray—for distribution of DC power and routing of the signals to the digital electronics (Figure 3.4).
3.1.3 Front-End electronics and digitizers
The signal from the power detector is digitized with 14-bit resolution (calibration constant
b = 7 ADC/mV) at a sampling rate of 20 MHz by custom-made flash analog-to-digital converter (FADC) boards (Figure 3.5). Up to 2048 samples are stored in a circular buffer and
processed by a first level trigger algorithm implemented in the on-board field programmable
gate array (FPGA). A standard VME interface allows for board control and data readout.
Four FADC boards, each with 16 channels, are used to digitize the entire receiver camera.
A Master Trigger Board, also equipped with FPGA logic and VME interface, provides the
global clock for the FADC synchronization and performs a high level trigger decision. Each
FADC board is connected to the Master Trigger board through Low Voltage Differential
Signaling (LVDS) lines carrying the clock and trigger signals.
A VME module equipped with a GPS receiver (Hytec 2092) tags the time of the triggered
events with 10 ns precision. Details of the MIDAS digital electronics can be found in (Bogdan
et al., 2011).
52
Figure 3.5: Digital electronics board with 16 Flash-ADC channels. The module includes an
FPGA for the First Level Trigger logic and a VME interface. The board was designed by
the Electronics Design Group at the Enrico Fermi Institute of the University of Chicago.
53
11400
ADC Counts
11200
11000
10800
10600
10400
10200
0
100
200
300
400
500
600
700
800
900
1000
Time (50 ns)
Figure 3.6: Illustration of the FLT. The digitized time trace for a 5 µs RF pulse from the
calibration antenna (see § 3.2), with the ADC running average of 20 consecutive time samples
superimposed as a gray histogram (red in the color version). An FLT is issued when the
running average falls below the threshold, indicated by the horizontal line.
Figure 3.7: Illustration of the SLT. The 4 highlighted pixels (top panel), located in three
different FADC boards, have an FLT occurring in the same 50 ns time sample. Each FADC
board sends through the LVDS lines the FLT status of its pixels to the Master Trigger
Board (bottom panel, left), where a matching SLT pattern is found. An SLT is then sent
back through the LVDS lines to the FADC boards (bottom panel, right) triggering the entire
camera for data readout.
54
Pixel 15
1600
11554
Entries
Mean
RMS
1400
11552
11550
21603
101
25
1200
11548
Entries
Threshold (ADC) Baseline (ADC)
Pixel 15
11556
11546
11544
11424
11422
1000
800
600
11420
400
11418
11416
200
11414
11412
11410
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0
0
Time (s)
50
100
150
200
250
300
350
400
FLT Rate (Hz)
Figure 3.8: Monitoring data from one pixel for a six-hour data taking run. On the left, the
ADC baseline averaged over 10 ms (upper panel) and the FLT threshold (bottom panel) as
a function of time. The threshold follows closely the variations of the baseline, keeping the
FLT rate during the run (right panel) around 100 Hz.
3.1.4 Trigger
MIDAS implements a multi-level trigger architecture, optimized for transient events with
topology and time structure compatible with signals from an EAS. The system is modeled
on the one successfully operating at the FD of the Pierre Auger Observatory (Abraham
et al., 2010a). For each channel, a First Level Trigger (FLT) algorithm identifies pulses
in the FADC trace. The FLT information from all channels is sent to the Master Trigger
Board where the Second Level Trigger (SLT) searches for patterns of FLTs compatible with
a cosmic ray track topologies in the camera.
The FLT status bit of a given channel is activated whenever the ADC running sum of
20 consecutive time samples (1 µs) falls below a threshold (Figure 3.6). To compensate for
changes in the background noise level the FLT threshold is dynamically regulated, keeping
the FLT rate stable around a value of 100 Hz. Once triggered, the active status of the FLT
bit is extended for 10 µs. This trigger bit extension allows for coincident triggers between
camera channels to be implemented in the Master Trigger Board.
Every clock cycle (50 ns), each FADC board transmits 16 bits corresponding to the FLT
status of its 16 channels to the Master Trigger Board (Figure 3.7), where the SLT trigger
55
15
11
6
28
15
11
6
28
24
11
6
48
Figure 3.9: Basic patterns of which the 767 second level trigger patterns are composed.
algorithm searches for 4-pixel patterns of channels with FLT triggers overlapping in time.
There are 767 total patterns which are compatible with the topology of a cosmic ray shower in
the camera. These patterns are translations and rotations of the three basic trigger patterns
shown in Figure 3.9. When an SLT matching pattern is found, an event trigger signal is
distributed back to the FADC boards and to the GPS module. At this point, a block of
100 µs of ADC data (including 500 pre-trigger samples) is frozen in the memory buffer and
made available for read out via VME. All 53 channels, even those not participating to the
trigger decision, are readout and tagged with the GPS time.
Higher levels of trigger control have also been implemented. For example, the FLT
threshold regulation and data acquisition are inhibited whenever the SLT rate is higher than
a limit which can be set within the FPGA. This trigger veto is used to prevent excessive
dead time associated with writing event during periods of particularly high trigger rates.
The threshold is then automatically restored when the SLT rate returns to a normal level.
This trigger veto is controlled at the FADC board level allowing independent vetoing for all
four boards instrumenting the camera.
56
3.2
Data acquisition, monitoring and operation
A single board computer (GE Intelligent Platforms V7865) acting as VME master is used for
the data acquisition. The DAQ software monitors the relevant VME registers of the FADC
boards, and reads out through the VME bus the GPS time stamp and the data available in
the buffer after an event trigger. The event data are then assembled and written to disk in
ROOT format (Brun & Rademakers, 1997).
For monitoring purposes, the ADC baseline averaged over 10 ms (calculated in the FPGA
of the FADC board), the FLT rate, and the FLT threshold of each channel are readout and
recorded every second. An example of monitoring data collected during a six-hour data
taking run is presented in Figure 3.8.
Additional monitoring information is obtained from RF pulses periodically illuminating
the receiver camera. For this purpose, a patch antenna with a wide beam (HPBW=70◦ ) is
mounted at the center of the reflector dish. The antenna is driven by an RF signal generator
located in the counting room, which every 15 minutes produces a train of ten RF pulses of
10 µs width. These data provide monitoring information for all of the channels at the same
time, ensuring they are properly operating and that the trigger is working as designed.
Data runs last six hours and are automatically restarted, with data files backed up on
a server for offline analysis. Fully automatic and remote operation of the telescope was
achieved through slow control software for the antenna positioning, and for the status of
power supplies and of the VME crate.
3.3
EM simulation of telescope efficiency
The efficiency of the MIDAS telescope has a significant angular dependence, due to the large
field of view implemented in a parabolic reflector. For a proper calibration of the telescope
and an estimate of its sensitivity to EAS, the power pattern of each pixel—i.e the pixel
57
Figure 3.10: EM calculation of the feed for the dominant TE11 mode at 3.8 GHz. Left:
Normalized electric field radiation pattern for the MIDAS feed in polar coordinates. Both
the E-plane (φ = π/2) and H-plane are shown (φ = 0). Right: Electric field vector over the
feed aperture.
detection efficiency as a function of the direction (θ, φ) of the incident microwave radiation
with respect to the telescope boresight—must be determined. A full electromagnetic (EM)
simulation of the reflector and receiver camera has been developed for this purpose.
At radio and microwave wavelengths, it is convenient to simulate the antenna system
(reflector and feed) in emission mode, making use of the so-called Reciprocity Theorem
(Kraus & Marhefka, 2003; Orfanidis, 2010) to obtain its effective area Ai in a given direction:
Ai (θ, φ) =
λ2
G (θ, φ)
4π i
,
(3.2)
where λ is the wavelength of the radiation and Gi (θ, φ) is the gain of the antenna system for
pixel i, defined as the power emitted per unit solid angle in the direction (θ, φ) normalized
to the corresponding power emitted by an isotropic radiator. In practical terms, the antenna
effective area summarizes the dependence of the telescope gain on the dimensions of the
reflector, the frequency of the radiation, and overall illumination (i.e. taper) of the feed.
The feed is simulated as two cylindrical waveguides—the one corresponding to the feed
58
Figure 3.11: Left: Power radiation pattern for the central feed (pixel 15) of the MIDAS
camera. This feed presents the maximum antenna gain of the receiver camera, and a symmetrical pattern with very small side lobes. Right: Radiation pattern for a feed laterally
displaced by 16.5 cm (∼ 2λ) from the camera focus (pixel 13). Its gain is ∼50% smaller,
and presents a significant coma lobe.
aperture having a diameter d = 6.7 cm and the other having a diameter d = 5.5 cm—joined
by a small conical throat. The dominant propagating mode is the TE11 (electric field perpendicular to the feed axis) with a cutoff wavelength of 9.4 cm determined by the diameter
of the end section (λcT E = 1.71d) (Silver, 1965). The calculated radiation pattern of the
11
feed in polar coordinates for the E-plane (φ = π/2) and H-plane (φ = 0), and the direction
of the electric vector field over the feed aperture are shown in Figure 3.10.
To obtain the antenna effective area, the electromagnetic field distribution over the telescope aperture is calculated. For each feed, the telescope aperture is found by the intersection
of rays emitted by the feed with the plane perpendicular to the telescope axis and containing
the dish focal point. The paths of rays from the feed to the aperture plane are determined in
the optical limit using Fermat’s principle of least transit time. Spherical wave propagation is
assumed from feed to dish and plane wave propagation is assumed from dish to aperture. A
proper treatment of the optical paths is essential for MIDAS, since the lateral displacement
of the feeds with respect to the dish focal point produces significant differences in their gain.
Also, the shadow of the receiver camera, which increases the size of the side lobes, is included
59
in the simulation. The radiation field is then calculated in the far-field limit by the Fourier
transform of the aperture field distribution, and the power is obtained as the square of the
associated Poynting vector.
Equation 3.2 holds for an antenna system completely matched to its transmission line. In
practice, reflections at the feed entrance, at the throat between the cylindrical sections and
at the coupling between the feed and the coaxial line reduce the antenna effective area. Their
effect can be calculated introducing an equivalent transmission line model with impedance
mismatches which produce reflected power waves. Additional signal losses in the coaxial
cable and in the analog electronics are included in the simulation. Also, the reflector does
not collect all the power emitted by the feed, and part of it spills over, further reducing the
antenna total effective area.
The result of the EM simulation can be expressed as a relative power pattern for each
pixel i:
i (θ, φ) =
Gi (θ, φ)
G15 (0, 0)
,
(3.3)
where G15 (0, 0) is the calculated gain of the central pixel in the direction of boresight.
The pattern for the central feed (Figure 3.11, left) is symmetric around the boresight with
relatively small side lobes. Feeds away from the focal point (Figure 3.11, right) have smaller
gains and bigger, asymmetrical side lobes. From Equation 3.2, the effective area of the
antenna system to a microwave flux incident from a given direction is then given by:
Ai (θ, φ) = Aef f i (θ, φ)
,
(3.4)
2
λ G (0, 0) is the effective area of the dish.
where Aef f = 4π
15
The overall sensitivity of the camera can be calculated summing over the pixels: (θ, φ) =
P
i i (θ, φ),
and is presented in Figure 3.12. Even with the compact arrangement of the
MIDAS feeds over the focal plane, there is a region of reduced efficiency between adjacent
60
Figure 3.12: Radiation pattern of the MIDAS camera, calculated by summing over all pixels,
as function of the angle with respect to the antenna boresight.
61
feeds. Also, the efficiency at the borders of the field of view is as low as 20% of the efficiency
at the center. While not uniform over the camera, the telescope efficiency is reasonably high
in a large portion of its field of view, which is sufficient for the goals of this first low-cost
prototype for the MIDAS concept.
3.4
Telescope Calibration
Dedicated calibration measurements were performed during the commissioning of the telescope, which were followed up during data taking to verify the stability of the system.
The Sun, whose flux in the microwave range is measured daily by several solar radio
observatories around the world, was used as the primary source for the absolute calibration
of the MIDAS telescope. This calibration was cross-checked with other known astrophysical
sources. The monitoring patch antenna (§ 3.2) was also used for relative channel calibration.
3.4.1 Absolute calibration
An unpolarized microwave flux density, If , incident on the MIDAS reflector from a direction
(θ, φ) produces, at the input of the power detector of a given pixel i, a power Pi given by:
Pi =
Li · Γi · Bi · Aef f · i (θ, φ) · If
= αi · i (θ, φ) · If
2
,
(3.5)
where i (θ, φ) is the pixel relative power pattern, Aef f is the effective area of the dish, Bi
is the bandwidth of the electronics (given by the pixel bandpass filter), Γi is the gain of the
receiver, Li is the loss due to the 30 m cable and the analog electronics, and the factor 2
takes into account the fact that MIDAS measures a single polarized signal and thus detects
only half of the total power. The output voltage of the power detector (Equation 3.1) is
62
digitally sampled in the FADC board, yielding a signal ni in ADC counts:
ni = n0i − 10 ki log αi · i (θ, φ) · If
,
(3.6)
where n0i = bV0 , and ki = a b ' 175 ADC/dB with a, V0 and b as defined in § 3.1.2 and
3.1.3, respectively. The calibration constant ki is independently measured for each channel
(see § 3.4.2).
sys
We have defined a system power, Pi
sys
, with a corresponding signal ni
in ADC counts
to account for all additional background power. This power signal includes background
radiation from the sky in the main beam of the antenna, radiation from ground and adjacent
structures in the antenna side lobes, and electronics noise, dominated by the receiver noise
sys
sys
temperature. An equivalent flux density, If,i , is defined from Pi
sys
= αi If,i .
A measured signal ni can be converted into an absolutely calibrated flux density If by
deriving from Equation 3.6:
sys
ni = ni
− 10 ki log 1 +
i (θ, φ) · If
!
,
sys
If,i
sys
where i (θ, φ) is taken from the simulation described in § 3.3, and ni
(3.7)
and the corresponding
sys
If,i must be determined through calibration procedures.
Placing the telescope in a pointing in which the Sun transits through the field of view of
a given pixel allowed for calibration of both the absolute pixel gain and a test of how well the
side lobes of the pixel are modeled by the form given in Equation 3.3. The Sun was the ideal
source for this absolute calibration because it is bright, well monitored, and the emission in
C-Band is unpolarized and stable on the time scales of the transit. From Equation 3.7, the
63
55
0
Pixel 59
11000
10500
Elevation [°]
11500
Pixel 58
0
10500
45
40
35
30
10000
10000
1000
2000
3000
4000
5000
6000
7000
8000
ADC Counts
11500
Pixel 57
2000
3000
4000
5000
6000
7000
8000
0
Pixel 56
0
10500
10500
10000
10000
10000
11500
0
0
Pixel 42
0
Pixel 41
0
10500
10500
10500
10000
10000
10000
1000 2000 3000 4000 5000 6000 7000 8000
Pixel 43
0
10500
11000
Sun Trajectory
160 165 170 175 180 185 190 195 200
Azimuth [°]
1000
0
11000
59 58 57 56 43 42 41 40
50
1000 2000 3000 4000 5000 6000 7000 8000
Pixel 40
1000 2000 3000 4000 5000 6000 7000 8000
Time (s)
Figure 3.13: Example of a calibration measurement of the MIDAS telescope with a Sun transit. Top right inset: Sun trajectory in the top row of the camera pixels (azimuth measured
clockwise from North). The measured ADC signal (closed dots) for each pixel is shown in
the other panels, with the superimposed line representing the EM simulation for the best
sys
value of If,i (see text).
64
time evolution of the signal is given by:
sys
ni (t) = ni
sys
where ni
− 10ki log 1 +
i (θ(t), φ(t)) · If,
sys
If,i
!
,
(3.8)
is the ADC baseline measured before the Sun transits, (θ(t), φ(t)) is the sun
position in the sky at time t, and the solar flux density, If, , is taken from the daily measurements by the Nobeyama observatory (Nobeyama Radio Observatory, 2011). The value
sys
of If,i which best describe the calibration data is then obtained. An extensive measurement campaign was performed, with each Sun transit aiming to the calibration of a row of
pixels, with the end result being a full absolute calibration using the Sun for each of the
53-pixels in the Camera. An example of a Sun calibration run for the top row of pixels is
presented in Figure 3.13. These measurements not only provide an absolute calibration of
sys
each pixel through If,i , but also demonstrate the quality of the simulation of i (θ, φ). In
fact, simulations were found to describe very well the pixel power pattern in both the width
and the relative efficiency of the main power lobe as well as the side lobes, even for pixels
at the edges of the camera where strong aberrations are present. The agreement between
calibration data and simulation is consistent with an uncertainty of a few tenths of a degree
in the telescope pointing.
sys
As an example, several calibration measurements of the central pixel yielded a If,15 =
1.96 × 104 Jy1 , equivalent to a system temperature Tsys of:
sys
Tsys =
If,15 · Aef f
2kb
= 65 K
,
(3.9)
where kb is the Boltzmann constant, and Aef f = 9.1 m2 is the effective area (≈ 60% of
the geometric area) of the telescope as determined by simulations described in § 3.3. The
other pixels had a similar system temperature. The estimated systematic uncertainty on the
1. 1 Jy = 10−26 W/m2 /Hz
65
12000
k32 = 173 ± 1 ADC/dB
Signal (ADC counts)
11000
10000
9000
8000
7000
-40
-30
-20
-10
0
10
20
Ppulse (dBm)
Figure 3.14: Example of a measurement of the calibration constant k. Closed dots represent
the measured signal in pixel n. 32 for different powers of the calibration antenna pulses. The
line is the result of a fit to derive k32 . For Ppulse greater than 8 dBm, measurements are
affected by saturation of the LNBFs and were excluded from the fit.
sys
measurement of If,i is 15%, dominated by the uncertainty of the Nobeyama measurement
and of the telescope pointing.
Measurements of the Moon (If,M oon ' If, /100) and of the Crab Nebula (If,Crab '
If, /1000) were also performed, providing a cross-check of the absolute calibration. Using
the Sun calibration, the Moon temperature was found to be 245 K, consistent with the value
measured by (International Telecommunication Union, 2009) of 268 K (the measurement
was taken a day after the full moon). The flux density of the Crab Nebula was measured to
be 760 Jy, consistent with 718 ± 43 Jy measured by (Baars et al., 1977) at 3.38 GHz. Both
of these results agree to better than 10%, within the estimated systematic uncertainty of the
Sun calibration.
66
Entries
Mean
RMS
14
53
172.2
4.5
12
Entries
10
8
6
4
2
0
140
150
160
170
180
190
200
210
k (ADC/dB)
Figure 3.15: Distribution of the measured calibration constants k.
3.4.2 Pixel calibration constants and timing
The calibration constant ki in Equation 3.6 was measured by using the patch antenna
mounted at the center of the dish. The pulse power, Ppulse , of the RF signal generator
driving the patch antenna was changed over a wide range, and the corresponding signal,
pulse
ni
, was measured for each channel. From Equation 3.7, one expects:
pulse
ni
sys
where ni
=
sys
ni
− 10ki log 1 +
fi · Ppulse
!
,
sys
Pi
(3.10)
sys
is the signal measured when the RF signal generator is off, Pi
is the corre-
sponding power at the input of the power detector, and fi · Ppulse is the power induced by
the calibration pulse at the input of the power detector. The factor fi may change from
pixel to pixel, depending on the distance of the pixel from the patch antenna, on the relative
orientation of the linear polarizations of the emitter antenna and the receiver, and on the
sys
signal loss L. An example of a fit of Equation 3.10 , with ki , ni
sys
and fi /Pi
as free
parameters, to the calibration data for one channel is shown in Figure 3.14. The spread of
67
the distribution of the fitted calibration constants for the 53 channels (Figure 3.15) is 2.6%,
with an average of k = 172 ADC/dB.
The calibration pulses have a fast rise time (<1 ns) and illuminate all the camera receivers
simultaneously, allowing for a measurement of their time response and synchronization. The
time at which the amplitude of the measured pulse reaches 50% of its maximum value, t50 ,
was taken as an estimator. The distribution of t50 was found to have an RMS value of 25 ns,
more than adequate for the typical pulses of microseconds duration expected from an EAS
crossing the field of view of a pixel.
3.5
Data taking performance
The MIDAS telescope underwent an extensive period of commissioning during several months
in 2011 at the University of Chicago, which provided a validation of the overall design
and a test of the performance and duty cycle of the detector in a particularly challenging
environment for RF interference. Trigger rates were found to be significantly higher than
those expected from random fluctuations. The SLT rate due to combinatorial triggers, rbkg ,
is estimated to be 0.3 mHz:
rbkg = Npatt · npix · (rFLT )npix (τ )npix −1
,
(3.11)
where Npatt = 767 is the number of SLT patterns, npix = 53 is the number of pixels in the
MIDAS camera, rFLT = 100 Hz is the pixel FLT rate, and τ = 10 µs is the coincidence time
window.
The background rate of SLT events during data taking was well above the estimate of
Equation 3.11 and highly variable, ranging from 0.01 Hz to 2 kHz (averages calculated over
data taking runs of six hours). The major source of background was found to originate from
airplanes passing over the antenna on their way to the close-by Chicago Midway Interna68
Figure 3.16: Event display of an airplane altimeter noise event detected by the MIDAS
telescope. In the top left panel, pixels with an FLT are highlighted, with color coded by
arrival time. In the top right panel, ADC running averages of 20 consecutive time samples
for the selected pixels (identified by black dots and numbered accordingly in the left panel)
are shown. The running average of each pixel is referred to the threshold level (horizontal
line) for display purposes. The event shows only one pulse captured in the recorded trace of
100 µs.
Figure 3.17: Event display of an airplane altimeter noise event detected by the MIDAS
telescope. See caption of Figure 3.16 for a description of each panel. The event in the
bottom panel is a trace where the geometry of the airplane passing relative to the detector
allowed multiple altimeter pulses to be captured in a single recorded trace.
69
Figure 3.18: Event display of a candidate detected by the MIDAS telescope. See caption of
Figure 3.16 for a description of each panel. Although the timing characteristics of the event
are compatible with those of a cosmic ray shower, correlated signals in off-track pixels do
not allow for unambiguous identification.
tional Airport. Radar altimeters on board of these aircraft operate just above the C-Band
frequency, and, while suppressed by the MIDAS receiver bandwidth, their emissions are
strong enough to produce a sudden rise of the RF background in many neighboring channels
(or even in the whole camera), with a corresponding increase of the first and second level
trigger rates over several tens of seconds. An example of two separate events from distant
airplanes are shown in Figure 3.16 and 3.17 . Notice that all channels are illuminated simultaneously by a fast, strong RF pulse. In the case of Figure 3.17 the geometry of the airplane
crossing the telescope field of view is such that multiple pulses from the altimeter are captured in a single trace. We commonly see in the data events containing multiple pulses and
events containing only a single pulse in the 100 µs trace both of which are distinguished by
their fast, strong pulse illuminating multiple pixels simultaneously.
Most of the remaining background was characterized by very fast (<200 ns) transient
RF signals, which trigger simultaneously from a few pixels up to the entire camera. The
frequency of these events varied greatly during the data taking period, with no particular
correlation with day/night or week/weekend cycles. While their exact origin was not clear,
70
Figure 3.19: Event display of a 4-pixel candidate detected by the MIDAS telescope. See
caption of Figure 3.16 for a description of each panel. Several candidates with similar
characteristics—small signals and short tracks—were found in the data.
they were likely to have an anthropogenic origin in the vicinity of the detector.
Over the approximately six months of data taking operations in the urban environment
of the University of Chicago, the full MIDAS system achieved an effective duty cycle better
than 95%, a significant gain over the operation of an FD telescope. The MIDAS telescope
experienced very different weather conditions in Chicago. Through high temperatures during
summer, to heavy rain and storms, to snow and ice during the winter the detector operation
and data taking, as well as the telescope sensitivity, were found to be remarkably stable
during the entire period of commissioning. The commercially sourced components were all
within the design requirements and operated with minimal failure. The main objectives of
the MIDAS telescope at the University of Chicago—to validate the telescope design, and to
demonstrate of a large detector duty cycle—were successfully accomplished.
After operations in Chicago the camera and electronics of the MIDAS prototype detector
were unmounted and shipped to Malargüe, Argentina where they would be installed near
the Auger observatory. The installation and early analysis from data collected in Argentina
is discussed in Chapter 5.
71
CHAPTER 4
CHICAGO DATASET ANALYSIS
In addition to the successful testing of the components of the prototype telescope, the noise of
the urban environment was found to be manageable in such a way that a science analysis has
been conducted using data taken during the prototype commissioning phase of the MIDAS
detector.
4.1
EAS Microwave Signal Simulation
The sensitivity of the MIDAS telescope to microwave emission from EAS has been studied
with Monte Carlo simulations. The shower development in the atmosphere - i.e. the number
of charged particles N at any given atmospheric depth - is simulated with a Gaisser-Hillas
parameterization (Gaisser & Hillas, 1977), including proper fluctuations of the shower profile.
The shower arrival direction is isotropically distributed, with its landing point randomly
distributed over a large area around the telescope. For a given shower geometry, the number
of particles, N (t), along the shower profile is calculated, where t is the time in 50 ns samples
of the MIDAS digital electronics. The microwave flux density at the detector aperture is
then calculated, following the model as explained in § 2.4.
In order to convert the microwave flux density at the detector aperture into a signal in
ADC counts, the efficiency maps and calibration constants described in § 3.3 and § 3.4 were
implemented in the simulation. For each channel, the actual value of nsys and its fluctuation
were taken to be equal to their average values measured during several months of data taking,
providing a realistic simulation of the telescope sensitivity. The FLT and SLT algorithms
of § 3.1.4 were also implemented, and all simulated events fulfilling the SLT condition are
written to disk in the same format as the data. An example of an event simulated with
0
If,ref = If,ref
and α = 1 is shown in Figure 4.1.
72
Figure 4.1: Event display of a 3 × 1019 eV simulated EAS landing approximately 10 km from
the MIDAS telescope. See caption of Figure 3.16 for a description of each panel.
Simulations with different assumptions on the characteristics of the microwave emis0
sion from EAS were performed. For If,ref = If,ref
and α = 2, a rate of ∼450 triggered
events/year is expected, which reduces to ∼30 events/year for α = 1. The energy spectrum
of the triggered events is shown in Figure 4.2 for the latter case. In this case even with linear
scaling we see the simple MIDAS detector would be able to sample a significant number of
UHECR events above 1019 eV.
4.2
Data Sample and Event Selection
The MIDAS detector took data during several months in 2011, under various conditions of
anthropogenic noise and with several periods dedicated to calibration measurements. To
ensure quiet and stable data taking conditions, we limited the search for EAS candidates
to data runs with an average SLT rate less than 0.7 Hz. This requirement eliminates data
taking periods with particularly noisy conditions. The final data sample contains 1.1 × 106
SLT events collected during 61 days of live time.
We expect only ≈ 1600 SLT events from accidental coincidences of background fluctuations, indicating the data sample is likely dominated by anthropogenic noise. Simple event
73
Table 4.1: Table of cuts used in search program and their effect on selected data sample
Cut
Events Remaining After Cut
(1)
Less than 3 FLT pixels outside the SLT time window
625,012
(2)
All SLT patterns are time-ordered down-going
4,112
(3)
SLT pattern crossing time greater than 400 ns
1,432
(4)
Traces in triggered SLT patterns contain only 1 pulse > 5 σ
979
(5)
Pulses > 5 σ have a shape consistent with power detector’s time constant
924
(6)
FLT pixels matching a 5-pixel pattern topology with down-going time
order
21
(7)
Visual inspection of candidate events
0
selection criteria, based on timing and trigger information expected from EAS geometries
and laboratory measurements of detector electronics, were found to eliminate most of the
noise events. Table 4.1 summarizes the selection criteria, and the corresponding number of
selected events.
With cut (1), we require that no more than two FLT pixels in the event not participating
in any SLT pattern are triggered outside a time window defined by the smallest and the
largest FLT time amongst the pixels forming SLTs. This cut rejects a class of background
events characterized by a large number of camera pixels having a FLT, but distributed in
time outside the SLT window and having topologies that do not form a SLT pattern.
A large background rejection is obtained by asking that the time ordering of the FLT
pixels is consistent with a down-going track topology for triggered SLTs, as expected for
EAS (cut (2)). Also, we require the FLT time difference between the latest and the earliest
pixel of the SLT pattern to be larger than 400 ns (cut (3)), in order to reject a class of
background events with coincident pulses within the typical response time of the power
detector. Cut (3) will also eliminate cosmic ray events which produce fast signals, like those
74
2.5
Events/yr
2
1.5
1
0.5
0
17.5
18
18.5
19
19.5
20
log10(Energy [eV])
Figure 4.2: Expected number of triggered events per year as a function of energy, from a
simulation of the MIDAS telescope. A cosmic ray primary flux as measured in (Abraham
0
et al., 2010b) was assumed in the simulation. A microwave flux density If,ref = If,ref
and
a coherence parameter α = 1 were used to parameterize the EAS microwave emission in the
simulation.
with geometry pointing towards the telescope, which would be in any case very difficult to
distinguish from the overwhelming background of fast anthropogenic transients. In addition,
each pixel participating in the SLT must have recorded only one pulse > 5 σ (cut (4)), to
reject events with multiple pulses in the time trace, typical of noise induced by airplane
altimeters and communications. With cut (5), we ensure that the detected pulse in each
SLT pixel time trace is consistent with an RF pulse passing through the power detector a pulse with a fall time shorter than the 33 ns time constant of the power detector is likely
to be a random fluctuation or anthropogenic noise. Finally, we search the events for a 5pixel track topology with down-going time ordering (cut (6)). We expect 0.013 events from
accidental coincidences with such 5-pixel topology in 61 days of live time, which would make
any candidate event highly significant. Only 21 events survive this cut.
A visual inspection of the selected events was then performed (cut (7)). All were identified
as clear anthropogenic noise events, illuminating large portions of the camera with multiple
75
coincident pulses that fall below the 5 σ threshold in cut (4). Background events with similar
topology and a stronger signals are seen frequently in the data and are indeed rejected by
our selection criteria. The most likely explanation is that the residual background events
after cut (6) are produced by the same source of microwave radiation, but with a different
geometry relative to the detector. Notice that almost all of the 4-pixel events remaining after
cut (5) are background, as evident after a visual scan of the candidates. One example of a 4pixel event compatible with an EAS signal is shown in Fig. 3.19. However, the characteristics
of these events, which have signals close to the trigger threshold, are also compatible with a
tail of the overwhelming background noise. No strong conclusion can be drawn on the origin
of these kinds of events until a validation by a coincident detection at the Pierre Auger
Observatory is performed. Thus, we use the stronger 5-pixel selection, which yielded a null
result, to establish a limit on microwave emission from EAS. Notice that the large field of
view of the MIDAS telescope and our search criteria, based only on topology and timing of
the signals and with no requirement on the position of the maximum development of the
shower, makes the result of our search insensitive to the composition of UHECRs.
4.3
Limit
In order to establish a limit on the microwave emission from UHECR induced air showers
we simulated a large sample of Monte Carlo events spanning a range of coherence scaling parameter, α, values between one and two, and of reference power flux, If,ref , values between
2.3 × 10−16 W/m2 /Hz to 4.6 × 10−15 W/m2 /Hz (cf. Equation 2.5) for the MIDAS configuration operating at the University of Chicago campus. For each pair of {α, If,ref }, events are
simulated in discrete bins of primary energies between log10 E = 17.65 and log10 E = 20.05
in logarithmic steps of 0.1, sampled from an isotropic distribution. For each energy bin, the
simulation is run until 4000 SLTs or 4 × 106 simulated EAS are reached, whichever occurs
first. The result is then weighted with the UHECR energy spectrum of (Abraham et al.,
76
2010b) to produce a realistic energy spectrum of simulated SLT events.
The selection criteria (1) to (6) were applied to the simulated samples, and corresponding
number of expected events were derived. For example, for a fully coherent emission (α = 2)
0
and a reference power flux If,ref = If,ref
, we expect, in our 61 days of livetime, greater than
15 EAS candidate events above 2 × 1018 eV passing all our search criteria. This is excluded
at a greater than 5 σ level by our null detection result. To cover the full space of {α, If,ref },
we used a linear surface interpolation of the grid of simulated samples. The shaded gray
region in Fig. 4.3 is excluded with greater than 95% confidence. We exclude the reference
0
as measured by (Gorham et al., 2008), indicated by the solid horizontal
power flux If,ref
line in Fig. 4.3, over a large range of partial coherence emission hypotheses. An incoherent
emission for that reference power flux is not yet excluded by this measurement. The limits
reported herein have been published in (Alvarez-Muñiz et al., 2012a).
77
Figure 4.3: Exclusion limits on the microwave emission from UHECRs, obtained with 61 days
of live time measurements with the MIDAS detector. The power flux If,ref corresponds to a
reference shower of 3.36×1017 eV, and the α parameter characterizes the possible coherence of
the emission. The shaded area is excluded with greater than 95% confidence. The horizontal
line indicates the reference power flux suggested by laboratory measurements (Gorham et al.,
2008). The projected 95% CL sensitivity after collection of one year of coincident operation
data of the MIDAS detector at the Pierre Auger Observatory is represented by the dashed
line.
78
CHAPTER 5
MIDAS AT AUGER
5.1
Telescope Installation
In August of 2012 the MIDAS detector was installed near the LIDAR site (35.4967◦ S,
69.4497◦ W ) of the Los Leones FD of the Pierre Auger Observatory, see Figure 1.3. The
telescope is positioned such that its field of view is aligned with Bay 3 of the Los Leones FD,
pointing to an azimuth of 45◦ and an altitude of 20◦ , for data acquisition conditions. The
MIDAS detector at Auger uses the same camera and electronics from the prototype that was
deployed on the roof the Kersten Physics Teaching Center at the University of Chicago. A
new 5 m parabolic reflector was acquired for mounting of the camera at the prime focus, see
Figure 5.1. The reflector of the new set-up is mounted on an adjustable altitude-azimuth
mount that must be adjusted manually, as it is not motorized and calibrated for astronomical
pointing like the telescope in Chicago. The signals from the camera are passed through 30 m
of commercial quad-shielded RG-6 coaxial cable as in the original prototype. This cable is
run underground to the LIDAR building where the electronics for the telescope are housed.
The MIDAS detector operates remotely as was the case while prototyping at the University of Chicago site. Along with the VME crate controller, a dedicated PC is part of
the electronics which allows for autonomous operations and data logging. The PC is on the
local network of the Auger observatory and acts as a port of access to control the VME crate
and low voltage power supplies which are connected to a separate internal network. The
PC stores all data locally on hard drives at the site, daily data transfers to a central server
facility have been implemented as well. The MIDAS electronics have a battery back-up that
allows for approximately 3 hours of operation in the case of short term power failure at the
site. The LIDAR electronics container is temperature controlled to prevent overheating.
Data taking operation began on October 16, 2012 and has continued to the present time.
79
Figure 5.1: The MIDAS telescope as it is installed at the Pierre Auger Observatory, with
the 53-pixel camera mounted at the prime focus of the 5 m diameter parabolic dish reflector.
The telescope is pointing at an elevation greater than the nominal 20◦ in preparation for a
solar transit.
80
Before this date solar calibration runs were attempted for the central row of the camera, but
due to the difficulty in pointing a satisfactory calibration set has not been found and this is
a task the remains to be performed. During this period data taking has been intermittent
due to electrical problems with the back up power supply system and air conditioning unit
of the LIDAR container. When the telescope was operational we found a noise rate with the
average SLT rate per 24 hours ranging from 10−3 Hz to 1 Hz. This event rate is significantly
lower than what was found in the urban environment of the University of Chicago campus
and during data taking operation we find a detector duty cycle of approximately 95%.
5.2
Auger Analysis
The SLT rate is still higher than the expectation for thermal noise given by Equation 3.11. We
also see a strong bias in the number of SLT events on the side of the camera which is adjacent
to the LIDAR building and FD buildings, likely there is a correlation between operation of the
LIDAR or FD and these events, however, this has not yet been fully understood. Given these
problems pursuing a 4-pixel event search and comparing the rates to expected background
values is still rather difficult. The best analysis to pursue at this time is an event matching
search by comparing the time between MIDAS SLT events and events from the Auger SD.
This has much greater sensitivity than the blind search using cuts described § 4.2 which
is very conservative and inefficient in event selection. For the event matching analysis we
will assume the calibration of the MIDAS detector in Argentina is the same as that of the
MIDAS detector in Chicago because a full absolute calibration does not exist at this time
for the MIDAS camera as it operates at the Auger Observatory.
Using the dataset of the period from October 16, 2012 to April 26, 2013 we can perform
a preliminary event matching analysis. This period represents 70 days of live time data in
the MIDAS detector when considering all of the detector uptime and excluding periods of
SLT rate veto and dead time from writing events. This data is matched against a set of SD
81
data reconstructed for the the Auger array over the same time period.
To ensure high quality data we have used a process of event selection on the Auger SD
dataset. First, we require that all SD events reconstruct to meet the 6T5 condition, which
requires that all six SD tanks in a hexagon around at T5 triggered tank are active. Additional
cuts are made requiring that all event have an energy higher than 1018 eV. As we have seen
from MC with the MIDAS limit analysis from the Chicago dataset the MIDAS detector
should have very little sensitivity to events with energies below this cut in the flux-scaling
phase space that has yet to be excluded. To further reduce the SD data set prior to matching
we place a distance cut on the core impact location relative to the MIDAS telescope. For
events with 1018 eV ≤ E < 3 × 1018 eV the reconstructed core location must be within
16 km of the MIDAS detector (3 × 1018 eV ≤ E < 1019 eV, dmax < 30 km; E ≥ 1019 eV
there is no cut on the reconstructed core location). These distance cuts are based on results
seen in the MC of MIDAS sensitivity from the Chicago data set analysis. The distances are
conservatively chosen based on SLT event core reconstruction for MIDAS events simulated
with flux and scaling values in the excluded region of phase space.
To produce a clean sample of MIDAS SLT events which are free from bursts of anthropogenic noise, we require that all SLT events used for matching are isolated in time by at
least one second. This introduces an additional 4 days of detector dead time to the event
sample, bringing the total livetime to 66 days. For the event matching analysis, the selected
SLT sample is matched against the Auger SD dataset searching for events where the difference between SD event time and MIDAS SLT time is within the bounds of (−1, 1) second,
where negative time is when the MIDAS SLT event occurs before the Auger SD event. After
running this event search procedure, we found 110 events that were considered matched to
the Auger SD event dataset within this time bound. The SLT SD event time differences are
plotted in Figure 5.2 for the matched events, and their distribution appears very uniform in
the time window. Based on the uniform distribution of the time difference data, there is no
82
Figure 5.2: Distribution of time difference between matched MIDAS SLT event and Auger
SD event in a 2 second window. Negative times are events where the MIDAS event occurs
before the recorded time for the SD event.
reason to believe a sub-second time offset exists between the nanosecond time stamps of the
two experiments. We can further analyze this data set by looking at the average daily event
rates for both the Auger SD data sample and the MIDAS SLT event sample after event
selection. The histograms of these rates are plotted in Figure 5.3 and we find the Auger
data has a mean rate of, rA = 5.8 × 10−4 Hz, and the MIDAS data set has a mean rate of,
rM = 0.015 Hz. If we assume these data sets are uncorrelated and Poisson distributed the
probability for finding an accidental coincident event in a small time window of τ seconds is
given by,
Pc = PA · PM = rA rM τ 2 e−(rA +rM )τ
,
(5.1)
where PA is the probability of an Auger SD event and PM is the probability of a MIDAS SLT.
In the limit of a sufficiently small time window and event rates the probability for a coincident
83
Figure 5.3: Daily event rates for the Auger SD (Left) and MIDAS SLT (Right) after quality
cuts.
event becomes, Pc → rA rM τ 2 , with the coincident event rate given by rc = rA rM τ . For
the case of our event matching search the time window is τ = 2 seconds giving an event
rate of rc = 1.74 × 10−5 Hz, or 99.2 ± 9.96 coincident events in 66 days of live time. Our
finding of 110 matched events is consistent with the accidental coincidence rate from the
two distributions implying no excess. Further, the closest matched single event had a time
difference of 6.25 ms with an event core reconstructed to 2.54 km from the MIDAS detector.
This implies a light travel time of 8.5 µs making this a poor coincidence in the case of a
real event, this is further supported by the uniform distribution of matching event time
differences which suggests there is no global time offset on sub-second time scales. When
the 110 events are inspected by eye, there are no signs of characteristics expected for EAS
events crossing the field of view. The evidence suggests that with 66 days of livetime data
at the Auger Observatory the MIDAS detector has obtained a null result based on the veto
power of the Auger SD.
84
Figure 5.4: Preliminary exclusion sensitivity assuming Chicago calibration for 66 days of
livetime data taken with the MIDAS detector at the Pierre Auger Observatory (Red Dashed
Line). See text for details of exclusion analysis. See caption of Figure 4.3 for explanation of
shaded region and black line.
85
Using this null result as in § 4.3 we can set an exclusion limit in the {α, Ir,ref } parameter
space. As mentioned above we do not have a full optics calibration set for the camera of
the MIDAS detector at the Auger Observatory so we will use the solar calibration from the
Chicago data set to draw a preliminary 95% exclusion contour in this space. This line is
simulated using the same MC as that used for Chicago but the detector is now placed in the
configuration of the MIDAS detector at Auger with the correct elevation of 1400 m above
sea level. The preliminary 95% confidence exclusion line can be seen in Figure 5.4 which
has been updated to reflect the new values. As can be seen, even with this preliminary
exclusion and assumed calibration, the MIDAS detector has the sensitivity to fully rule out
0
the reference flux of (Gorham et al., 2008), Ir,ref
, with incoherent scaling, α = 1, at the level
of more than 4 σ. A full optics calibration will be required to make a definitive statement
about the exclusion of the references flux.
86
Part III
The Microwave Air Yield Beam
Experiment
CHAPTER 6
EXPERIMENTAL DESIGN
Due to the difficulty in quantifying analytically the expected emission and its dependence
on electron density, laboratory measurements under different ionization conditions must be
pursued. We have performed an accelerator-based experiment designed to characterize the
microwave emission from free electrons created through ionization using a 3 MeV electron
beam injected into a RF anechoic chamber of 1 m3 size. The measurements were carried
out at the Van de Graaff accelerator facility of the Chemistry Division at Argonne National
Laboratory. Other efforts using a higher energy beam are also being performed (AlvarezMuñiz et al., 2013).
6.1
Instrumentation, setup and DAQ
6.1.1 Electron beam
The beam created at the Van de Graaff accelerator consisted of bunches of 3 MeV electrons
with adjustable pulse width from 5 ns to 1 ms. The electron current and repetition rate
can also be adjusted to generate bunches containing typically from ∼1010 to 1013 electrons.
The bunch has a transverse size of 5 mm and passes through an exit window at the end of
the beam pipe which is made of a Duralumin foil 0.002 inches thick. The electron energy
is well below the threshold for Cherenkov production in air, this was chosen purposefully
because radio Cherenkov emission presented a major source of background radiation in the
previous laboratory measurements (Gorham et al., 2008), summarized in § 2.3. A pick-up
coil was placed at the exit window of the beam pipe for trigger purposes and to monitor
the beam current during data taking operations. This beam was also used by the AIRFLY
collaboration to measure the UV fluorescence spectrum and its pressure dependence, (Ave
et al., 2007), crucial for a proper determination of the energy scale in fluorescence-based
88
UHECRs detectors.
6.1.2 Anechoic chamber and antennas
The anechoic chamber of ∼ 1 m3 is the same chamber used by the experiment of (Gorham
et al., 2008), that has been instrumented with new receivers and electronics. The chamber
consists of three large modules assembled with RF shielding at the joints to prevent external
RF signals from interfering with internal measurements. The chamber stands on a heightadjustable cart that allows precise position adjustment in three dimensions. The inner surface
of the chamber is covered with RF pyramidal absorbers (AEMI AEP-8) that provide greater
than 30 dB attenuation of RF signals at normal incidence above a frequency of 1 GHz.
The chamber has a circular port of 3 cm diameter to allow the entry of the collimated 3
MeV electron beam that otherwise would be strongly attenuated and scattered in the 1 mm
copper front wall (the attenuation length of 3 MeV electrons in copper is ∼ 1.8 mm). Within
the anechoic chamber, ambient air at the ambient pressure form the target volume for the
experiment. In this configuration, transition radiation generated at the Duralumin window
and entering the chamber through this aperture can be a source of background that must
be considered.
Three radio receivers were mounted inside the chamber to characterize the microwave
emission in a broad frequency spectrum (see Figure 6.1). The main receiver was a Rohde
& Schwarz (R&S) HL050 Log-Periodic Antenna (LPA). Due to its extremely broadband
frequency range (0.85-26.5 GHz) this antenna is suitable to measure the microwave emission
over the full spectral range of interest for molecular bremsstrahlung radiation (MBR). The
nominal gain of the antenna is 8.5 dBi and the cross-polarization leakage is less than -30 dB
in the frequency range of interest. The LPA was connected to three different Miteq low noise
(0.4-0.9 dB) amplifiers with nominal frequency bands of 1-2 GHz, 4-8 GHz, and 8-12 GHz
and minimum amplification gains of 45 dB, 40 dB, and 51 dB respectively. The gain flatness
89
Figure 6.1: Left: layout of the antennas inside the chamber in a plane perpendicular to the
beam direction. Right: Picture of the central module of the chamber with the 3 installed
antennas. The external copper box on the left accommodates part of the electronics such as
the low noise amplifiers and the connectors to send the signal for acquisition.
within the nominal frequency band is 1.5 dB for all three amplifiers. The amplifier gains
have been tested in the lab and operate well outside their stated nominal frequency bands as
seen in Figure 6.2. The combination of the three amplifiers have been found to be suitable
to study the emission process in the frequency range from 1 up to 15 GHz.
Additionally, two commercially sourced low noise block feed horns (LNBF) were used for
cross-check measurements, C-band (3.4-4.2 GHz) and a Ku-band (12.2-12.7 GHz). These
receivers can measure two orthogonal polarizations selected via input voltage, left and right
circular polarization with the Ku-band LNBF (mixed with an internal heterodyne) and linear
polarizations with the C-band LNBF. Both LNBFs are equipped with low noise amplifiers
and frequency downconverters which output in the L-band frequency range (∼1-2 GHz). The
C-band LNBF has an amplification of 65 dB and a noise temperature of 30 K. The C-band
LNBF is identical to the type used in the MIDAS experiment. The Ku-band antenna has
an amplification gain of 50 dB and 48 K system temperature. These specifications were
measured in the laboratory and found to be in good agreement with the nominal values
expected for these devices.
90
Figure 6.2: Plots of gains for the electronics chain from the LPA to the data acquisition
system. Electronics chain includes high frequency cable and Miteq low noise amplifiers. 12 GHz (Red), 4-8 GHz (Blue), 8-12 GHz (Green). All of the amplifiers were tested to work
well outside the factory specified range.
All the antennas are located in a central plane perpendicular to the beam direction and
pointing towards it so the distance from beam axis to the antenna is always ∼0.5 m. The
LPA is assembled in such a way that two polarizations, copolarized and cross-polarized
relative to the electron beam axis, can be recorded by rotating its orientation by 90 degrees.
Additionally, C-band, Ku-band LNBFs and a low frequency (0.7-2.4 GHz) antenna were also
located outside the chamber and close to the beam exit to monitor external radiation.
Down-converted L-band signals from C-band and Ku-band LNBFs were transmitted to
the control room through approximately 14 m of quad-shield RG-6 coaxial cable that have
an average loss of 0.3 dB per meter in the frequency range of the transmitting signal (∼1-2
GHz). The coaxial cable is also used to provide DC power to the feeds. A power inserter and
a 75 to 50 Ohm impedance adapter are connected to the end of the cable to allow the RF
signals from the antenna to pass to the data acquisition instrumentation. The LPA is directly
transmitted for readout trough a high-frequency co-axial cable suitable for transmission up
to 18 GHz. Losses from the cable, adapters and connectors were measured in the laboratory
91
Figure 6.3: Average of 100 traces as recorded with the oscilloscope from the C-band receiver
(left) and the LPA, the last one connected to the 4-8 GHz amplifier (right).
and used in the signal analysis as described in detail in § 6.2.3.
6.1.3 Data acquisition
RF signals from the antennas were recorded in the time domain using a Tektronix TDS6154C
oscilloscope (40 GSa/s and 20 GHz analog bandwidth) and in the frequency domain using
a R&S FSV30 spectrum analyzer (9 kHz-30 GHz frequency range). Figure 6.3 shows the
signal recorded in the C-band (left) and log-periodic (right) antennas for a 1 µs long pulse of
20 µA intensity, in this data the LPA is connected to the 4-8 GHz amplifier. A clear signal
(broader region in the figure) is measured in coincidence with the beam passing the volume
of the chamber in both receivers for the whole range of frequencies under study. For some
configurations, a prompt peak of signal was observed at the beginning of the trace (figure 6.3
(right panel)). This peak was found to be a very strong narrowband emission at 90 MHz
correlated with the electron pulse. The signal is so strong additional harmonic excitation in
the LPA appears. This signal is removed in the following analysis by always sampling data
well separated from the beginning of the pulse, see Figure 6.6.
Measurements with the spectrum analyzer were performed using the pick-up coil trigger
92
Figure 6.4: Power spectrum as measured when the beam was on and inside the chamber
(black line) and with no beam (red line)
to define a gate window on the beam pulse. An averaged power spectrum was measured
for several frequency bands in order to cover a broad frequency range from 1 to 7 GHz.
Measurements above 7 GHz were only possible with the oscilloscope because the time jitter in
the beam pulse arrival made it impossible to use the gated analysis above this frequency with
the spectrum analyzer. Simultaneous background spectra were also recorded for subtraction.
For all measurements the thermal noise floor from the amplifiers is well above the electronic
noise floor of either instrument.
6.1.4 Simulations
Geant4 (Allison et al., 2006) simulations reproducing the setup and running configurations
were performed in order to characterize the conditions inside the chamber. By simulating
the energy deposit in the chamber we are able to make a quantitative estimate of the number
of ionization electrons generated, as well as the density and spatial distribution of the energy
deposit. Figure 6.5 (left) shows the energy deposit in the chamber as a function of both
longitudinal, z, and transversal, y, directions relative to the beam axis (the distribution in
x is symmetrical to the one in y) for a typical configuration containing a total of 2.5 × 109
93
electrons inside the chamber. The area selected to integrate the energy deposit is 1 cm2 .
As it can be observed, the energy deposit is not uniformly distributed in the chamber but
denser in a conical region centered in the beam trajectory with a radius increasing from
a few mm to about 15 cm. The total energy deposit in the chamber for this particular
conditions is Edep = 5 × 1014 eV. Figure 6.5 (right) shows the integrated energy deposit as a
function of z and the corresponding density calculated in cylindrical slices of 1 cm thickness
and radius of 15 cm where most of the energy is deposited. This density, that increases fast
in the first portion of the chamber and then decreases up to about half of its maximum,
will be proportional to the ionization electron density. Assuming all the energy deposit is
invested in ionization, we obtain typical values for the ionization electron density of ∼108
electrons per cm3 (typical values for the different beam configurations range from 2 × 108 to
4 × 109 e/cm3 ).
The efficiency of the receivers depends on the angle of incidence of the incoming signal.
Therefore, any isotropic emission proportional to the energy deposit must be convolved with
the radiation pattern of the antenna. When quoting a reference flux value for the emission,
it will correspond to a certain reference distance, rref , for the signal distributed in a conical
region. The signal must also be corrected by an r2 factor to account for the different path
lengths for emitting regions. In consequence, when attributing a measured power flux for
the emission at the reference distance rref , the corresponding effective energy deposit,
eff =
Edep
ri2
i
Edep
2
rref
i
X
,
(6.1)
i
where,Edep
is the energy deposit in the chamber at a distance ri from the receiver. From
eff is approximately a factor 2 smaller than E
calculations based on simulations we find Edep
dep .
The total energy deposit inside the chamber calculated over the number of electrons
pulsed in 3.3 ns1 will vary for the different running conditions between 1014 and 1016 eV .
1. The signal measured comes from the contribution of electrons inside the chamber at a given instant in
94
Figure 6.5: Results from Geant4 simulations. Left: Energy deposit inside the 1 m3 chamber
as a function of both longitudinal z and transversal y directions for a configuration containing
a total of 2.5 × 109 electrons. Right: Integrated energy deposit and its density along the
beam axis. See text for more details.
This amount of energy deposit is comparable to the total energy deposit in a 1 m length
length at the depth of maximum development by an extensive air shower originated by a
cosmic ray of energy around 1018 -1020 eV.
6.2
Data analysis
The final goal of the experiment is to quantify the total flux density emitted by the air
plasma, the level of coherence, and its frequency dependence. In this section, the tools
developed to analyze data recorded from the oscilloscope and from the spectrum analyzer
are described.
A study of a possible exponential decay of the signal due to thermalization processes
would be also desirable, as it is a property described by (Gorham et al., 2008), but in the
current set-up the Van de Graaff pulse structure, specifically the time jitter of pulse arrive,
does not allow for this measurement.
time. For the 1 m anechoic chamber the electron crossing time is ∼ 3.3 ns, giving the time window for an
instantaneous distribution.
95
6.2.1 Oscilloscope traces
A first step in the analysis of the oscilloscope traces is to select only frequencies in the
amplified spectral range using a Fast Fourier Transform (FFT) algorithm. Figure 6.6 (left)
show one recorded trace (light blue line; LPA, copolarized) after selecting the frequency
range of interest ∆ν, in this case 4-8 GHz. The pick-up coil signal is also shown (dark blue
line). For this particular case the beam was pulsed with a rate of 10 Hz and 1 µs width. In
∆ν , from a possible beam
order to determine the power measured at the oscilloscope, Psignal
induced signal, the root-mean-square (RMS) of the recorded voltage over a defined time
window, VRMS , is calculated. Then the distribution of VRMS in the time range of interest
for all the recorded traces is obtained. The measured power is finally calculated as:
∆ν
Psignal
=
∆ν
Pbeam
∆ν
− Pbkg
=
hVRMS i2
hVRMS i2
−
R
R
beam
bkg
,
(6.2)
where the first term is calculated over a time period where the beam is active and stable
(region limited by dashed lines in figure 6.6 (left)), and the background contribution comes
from 300 bins at the beginning of the trace (region limited by solid lines). hVRMS i is the
mean of the VRMS distribution and R is input impedance of the electronics chain measured in
the lab using a white noise source. Figure 6.6 (right) shows the beam active and background
VRMS distributions for a set of 1000 traces recorded in the same conditions as the trace
shown on the left panel.
Because no RF signal was registered in the antennas when the beam was blocked with
a Faraday cup and the analysis time window is well separated from the prompt noise pulse,
no additional background subtraction due to emission coming from the accelerator itself is
needed. As we will see in § 7.1 the analysis of oscilloscope traces is used to determine the
total power in the amplified frequency band which is used to study the dependency of the
emission with beam intensity. Obtaining the power in smaller bins of frequency will allow
96
Figure 6.6: Left: recorded trace at the LPA with the 4-8 GHz amplifier connected (light
blue). The signal measured by the pick-up coil is also shown (dark blue line). Regions where
the analysis is performed are limited by solid and dashed lines (see text for more details).
Right: VRMS histograms obtained for 1000 traces.
also to obtain a spectrum in frequency that can be used to validate the results obtained
with the spectrum analyzer and also to extend the measurements to higher frequencies. The
total system temperature including the ambient and the system noise can be estimated from
∆ν / (k · ∆ν) and is between 500-700 K for the considered
the background power as Tsys = Pbkg
frequency range.
6.2.2 Spectrum measurements
In order to study the spectral characteristics of the emission in a broad range of frequencies
several measurements with the spectrum analyzer were performed. Spectra from the LPA
were taken for the ranges 0-3 GHz, 3-5 GHz and 5-7 GHz and for two different polarizations,
copolarized and cross-polarized with the beam direction. For this purpose different amplifiers
were used in order to optimize the signal amplification. The spectrum analyzer directly
provides the measured power in a certain frequency bandwidth ∆ν (previously selected
and maintained constant for all the measurements). Figure 6.4 shows the measured power
spectrum from 1 to 7 GHz obtained when the beam was inside the chamber. The presented
spectrum was obtained as an average of 25 frequency sweeps. To determine the measured
97
power due to a signal induced by the beam, a proper subtraction of the background is
∆ν
∆ν − P ∆ν ). The background spectrum recorded is shown as a red
required (Psignal
= Pbeam
bkg
line in figure 6.4.
6.2.3
Flux calculation
The flux recorded in the antenna F at a given frequency bandwidth ∆ν in units of W/m2 /Hz
can be obtained from the power measured at the acquisition devices as:
Fν =
∆ν − P ∆ν ) · 10−Gν /10
(Pbeam
bkg
Aνef f · ∆ν
(6.3)
where Gν is the absolute gain in dB for the reference frequency (we chose the central
frequency of the bandwidth interval ∆ν), Aef f is the effective area of the antenna and
∆ν is the selected frequency bandwidth. The estimate of the flux relies on an absolute
calibration of the total amplification affecting the signal Gν since the emission is recorded
at the receiver until it is measured in either the spectrum analyzer or the oscilloscope. This
end-to-end calibration includes, in the case of the LPA, the high-frequency cable and the
low-noise amplifier and, in the case of the C-band and Ku-band detectors, the coaxial cable,
impedance adapter and power inserter. This calibration was performed injecting a calibrated
signal from a signal generator into the cable connected to the receiver antenna and recording
it with the spectrum analyzer at the end of the electronic chain. Calibration curves of the
absolute gain G as a function of frequency were obtained for the three amplifiers and for
the C-band electronic channel. The effective area of the C-band antenna at 3.7 GHz, the
center frequency of the input bandwidth, is 6 × 10−3 m2 . For the LPA the effective area is
98
parameterized as
Aef f =
10GLPA c2
4πν 2
.
(6.4)
The nominal gain of the LPA is GLPA = 8.5 dBi. Fluctuations in this gain as a function of
frequency are at the level of 0.5 dBi (dependence provided by the manufacturer) and have
been properly included in the analysis.
99
CHAPTER 7
ANALYSIS
7.1
Results
7.1.1 Proportionality with beam intensity
One of the goals of the experiment is to measure the proportionality of the recorded signal
with beam energy. The analysis described in § 6.2.1 was applied to sets of 100 oscilloscope
traces measured with the LPA receiver for 1 µs width beam pulses with an intensities ranging
from ∼5 to 30 µA, corresponding beam current between 0.5 and 3 µC per pulse. Changing
the current results in variations in the instantaneous number of electrons and thus in the
energy deposit inside the chamber. Results of the power flux averaged over 100 traces are
shown in figure 7.1 for different frequency bands. The beam intensity value was obtained
by monitoring the signal in the pick-up coil. Both polarizations, copolarized (right panel)
and cross-polarized (left panel) with the beam direction, were analyzed. Lines with slopes
1 and 2, corresponding to linear and quadratic dependence with beam intensity, are shown
for comparison. These results indicate a clear linear dependence on beam energy of the
power emitted over the range of frequencies studied. The equal power flux observed in both
polarizations suggests an isotropic emission mechanism.
As was addressed in § 6.1.2, a possible background in this experiment given the opening
in the wall of the chamber is the transition radiation (TR) being created as the electron
beam exits the beam pipe through the Duralumin window. The unpolarized character of the
emission excludes a possible contamination of TR from the beam window which is expected
to be highly polarized. To study the existence of TR in more detail, we took measurements
with the chamber in a fixed location and we placed copper foil of varying thickness over the
port in the wall of the chamber. The thickness of the foil ranged from 3 mm to the open port
with no foil. There was no evidence for a change in in the level of microwave emission during
100
Figure 7.1: Measured power flux as a function of beam energy for different frequency bandwidths. Lines with slopes 1 and 2 are also shown for comparison. Left: cross-polarization.
Right:copolarization.
this test. Further, when the beam was block completely at the opening of the chamber with
5 cm of aluminum plate, there was no emission seen inside the chamber. This suggest the
microwave signal we have recorded is produced inside the chamber by the primary electron
beam.
7.1.2 Frequency power spectrum and absolute power flux
Figure 7.2 shows the frequency spectrum of the power flux of the observed emission. The
spectrum extends from 1 GHz up to 15 GHz and was measured for both polarizations. As
previously mentioned, the spectrum analyzer was used to measure the spectrum up to 7 GHz.
Above this frequency, and also at low frequency for cross-check, the spectrum was obtained
applying a FFT analysis to 1000 oscilloscope traces as described in § 6.2.1. The beam configuration changed for different data taking runs so in all cases the flux has been normalized
according to the intensity measured at the pick up coil. The results are in good agreement
for the different amplifiers and methods used. Small fluctuations and oscillations observed
are within the systematic uncertainties that will be detailed in next section. Compatible
results from both polarizations reflect the isotropic nature of the emission. Measurements
from the C and Ku band antennas are compatible with the presented results. The average
101
Figure 7.2: Frequency spectrum of the emission averaged in 500 MHz bins, corrected to
a beam condition with 8 × 1012 electrons per 2 µs pulse. Error bars are statistical plus
systematic error from background subtraction uncertainty due to phase error.
power flux for the presented spectrum ranges from ∼ 2 × 10−19 to ∼ 4 × 10−19 W/m2 /Hz.
The frequency spectrum was studied when the beam was well inside the chamber by placing
the signal gate well after the beginning of the pulse, excluding the first part with the prompt
peak of signal (see figure 6.3).
The LPA used for this measurements has an active radiating region with a location
dependent on the frequency. The phase center of the antenna will be further away from the
base of the antenna as frequency increases. Since the emission region is extended almost
over the whole chamber and the distance to the antenna-emission point (of the order of
tens of cm) is comparable to the dimension of the antenna, this effect must be taken into
account because the observed region will decrease as frequency increases as the active region
of the antenna becomes closer to the geometrical center of the chamber. The correction
was calculated using Geant4 simulations described in § 6.1.4. The response of the antenna
as a function of frequency was convolved with the energy deposit and an effective energy
eff for each frequency was obtained. The obtained power flux spectrum was then
deposit Edep
102
normalized according to the parameterization obtained. This correction assumes that the
signal scales linearly with the energy deposit as it has been consistently measured. Applying
this correction allows a measurement of the power flux spectrum for the same emission
conditions.
7.1.3 Flux systematics
In this section we detail the different sources of systematic uncertainties contributing to the
power flux. These systematic uncertainties can be separated into two different groups, those
directly affecting the measured power flux and those affecting the subsequent scaling, i.e.
modifying the assigned corresponding energy deposit. Reduction of the gain due to near field
effects: although the vast part of the emission comes from a region located in the far-field of
the antenna, some emission can be created very close to the antenna. In (Kraus & Marhefka,
2003) it is pointed out that in small measurement distances, the gain of the antenna can be
reduced by 0.16 dB. Another possible source of measurement uncertainty comes from the
miscalculation of the antenna gain pattern as it is taken from the data sheet. Even an error
as large as 1 dB will have a negligible effect on the recorded power given the high gain of the
LPA. The final source of measurement uncertainty is the creation of destructive standing
waves due to phase error in the cable connecting the LPA to the LNA used. This has
the effect of producing attenuation features in the spectrum at specific frequencies. These
features are seen in both the signal and background, but they can not be fully subtracted
due damage that was done to the cable post-data taking. We estimate an additional 10%
uncertainty after correction which is included within the error bars in Figure 7.2. We see no
evidence for any signal features in the spectrum that can be differentiated from this effect.
Uncertainty in the determination of the number of electrons inside the chamber is the
primary systematic uncertainty in scaling the measured radio emission to air showers. The
beam intensity was always measured at the beginning of each run. The measurement is
103
subject to a large uncertainty because in order to measure the current, the beam must be
stopped with a Faraday cup and is not measured in situ during the recording of microwave
emission. A conservative uncertainty of ±30% has been estimated. A second source of
measurement uncertainty is due to chamber-beam misalignment. A possible misalignment
of the beam with respect to the center of the chamber entrance hole can induce a decrease
in the total energy deposit inside the chamber because beam electrons can be absorbed or
scattered in the copper wall of the chamber. This will produce an overall underestimation in
the air shower scaling. This effect can be estimated using Geant4 simulations for different
alignments. Since the misalignment only induces a decrease in the total energy deposit, the
effect on the flux will always be a positive increase. A systematic uncertainty of +10% has
been calculated.
7.2
Discussion
Based on the isotropic nature of the observed radiation, a possible interpretation of the emission mechanism is bremsstrahlung radiation by the free electrons created through ionization
as they subsequently collide with the field of air molecules. We analyze next the consistency
of the measurements with theoretical predictions. Another possible interpretation is that the
signal measured is produced by the time varying electric field of the passing primary 3 MeV
electrons. Simulations of this signal has been done using the ZHS algorithm as described
in (Zas et al., 1992; Alvarez-Muñiz et al., 2009; Alvarez-Muñiz et al., 2010; García-Fernández
et al., 2013) and is discussed. We also propose a procedure to parameterize the emission,
comparing it with an extensive air shower from the obtained results.
7.2.1 Interpretation
Bremsstrahlung emission by a single electron produces a continuum spectrum that extends up
to photon energies comparable with the energy of the radiating electron. In the case under
104
study, the electron beam induces a certain degree of ionization in air creating a tenuous
plasma with electron densities ne = 108 − 199 electron/cm3 and typical plasma temperature
of Te ∼ 105 K. This plasma temperature is calculated assuming thermalization of the plasma
which is standard for derivations found in (Bekefi, 1966; Gorham et al., 2008) as explained
in § 2.2, however, it should be noted that this is not necessarily the case for neither the
air plasma created by the beam nor the air plasma created in a EAS. This plasma has a
characteristic frequency νp that ranges from 100 to 300 MHz for the different ionization
conditions recreated in our experiment. Below this frequency the plasma becomes opaque
to radiation and the emission is suppressed. Since our measurements are limited to the
frequency region well above the plasma frequency (ν > 1 GHz > νp ). The absorption of
light in the plasma is only calculated by (Bekefi, 1966) assuming detailed balance, a condition
only satisfied in a thermalized plasma. Additionally, there are enhancement and suppression
effects which must be taken into account, both of which are not well understood for nonthermalized plasma. To fully understand the strengths of emission and absorption effects
large scale simulations are required to understand multi-particle behavior at these very low
energies, but from estimates based on the extensions to the thermalized case (Gorham et al.,
2008) finds there exists at least 5 orders of magnitude in emission strength ranging from a
level of ∼ 10−15 W/m2 /Hz to ∼ 10−20 W/m2 /Hz for a reference air shower of 3.37×1017 eV.
This level is entirely consistent with the isotropic microwave emission we measured, however,
it is not possible to say conclusively the signal we measured is from MBR and not another
process due to the enormous uncertainties in the emission prediction.
7.2.2 ZHS Simulations
An alternative explanation for the signal received is the time varying electric field from
the 3 MeV primary electrons produces an RF signal in the antenna. This is in contrast
to the signal being produced by the secondary ionization electrons scattering with neutral
105
1e-16
1e-16
ZHS simulation - Copolarised antenna
ZHS simulation - Crosspolarised antenna
1e-17
|Ei|2 [V2 m-2 MHz-2]
|Ei|2 [V2 m-2 MHz-2]
1e-17
1e-18
1e-19
1e-20
5000
5010
5020
5030
Frequency [MHz]
5040
1e-20
5050
5050
5060
1e-16
ZHS simulation - Copolarised antenna
ZHS simulation - Crosspolarised antenna
5070
5080
Frequency [MHz]
5090
1e-18
1e-19
ZHS simulation - Copolarised antenna
ZHS simulation - Crosspolarised antenna
1e-18
1e-19
5110
1e-16
5120
5130
Frequency [MHz]
5140
5150
1e-20
5150
5160
5170
5180
Frequency [MHz]
5190
ZHS simulation - Copolarised antenna
ZHS simulation - Crosspolarised antenna
|Ei|2 [V2 m-2 MHz-2]
1e-17
1e-18
1e-19
1e-20
5200
5100
1e-17
|Ei|2 [V2 m-2 MHz-2]
1e-17
|Ei|2 [V2 m-2 MHz-2]
1e-18
1e-19
1e-16
1e-20
5100
ZHS simulation - Copolarised antenna
ZHS simulation - Crosspolarised antenna
5210
5220
5230
Frequency [MHz]
5240
5250
Figure 7.3: Module of the Fourier transform of the electric field in the copol (higher signals) and cross-pol polarizations (lower signals) as predicted with the ZHS simulation in 5
frequency subintervals between 5 and 5.25 GHz for a single pulse.
106
5200
molecules. This emission is explored using simulations of the beam passing through air using
the ZHS algorithm.
What is measured in the lab is Fν , the mean power received per unit area and frequency.
A pulse lasts a time ∆t, the mean power per unit area is given by (Jackson, 1998)
Z t0 +∆t
Z t0 +∆t
dhP i
1
1 1
=
|E(t) × H(t)|dt =
|E(t)|2 dt
da
∆t t0
∆t Z0 t0
(7.1)
where Z0 is the impedance of free space 1 .
If the electric field exists only in the time interval ∆t, we can extend the integration
limits to infinity and then use Parseval’s theorem to introduce the Fourier transform of the
field:
Z ∞
Z ∞
1 1
1 1
dhP i
2
=
dt|E(t)| =
dν|E(ν)|2
da
∆t Z0 −∞
∆t Z0 −∞
(7.2)
We must take into account the different normalization due to the Fourier transform convention in the ZHS formula, namely E(ν) = EZHS /2, and we use that |E(ν)| = |E(−ν)| in
order to work with positive frequencies only (otherwise, we are getting only half the existing
power).
Z ∞
Z
1 1 1 ∞
1
1 1
dhP i
2
(ν)| =
=
dν |E
dν|EZHS (ν)|2
da
∆t Z0 −∞ 22 ZHS
∆t Z0 2 0
(7.3)
The mean power per unit frequency can be obtained by taking the derivative with respect
1. The last equality in Eq. (7.1) relies on the assumption that at all instants of time H(t) is perpendicular
and proportional to E(t). This is not true. However, for the field in time predicted by the ZHS formula, it
turns out that EZHS (t) and HZHS (t) are indeed orthogonal for all t (Alvarez-Muñiz et al., 2010). Since in
the frequency band of the MAYBE antenna EZHS (ν) is indeed a good approximation to the real field E(ν)
(as shown in (García-Fernández et al., 2013)), the antenna will not distinguish between the actual field and
the ZHS field in that frequency range which is what matters for detection. So for all practical purposes we
can assume that the last equality in Eq. (7.1) is valid.
107
to ν under the integral sign:
Fν =
d2 hP i
1
=
|E
(ν)|2
dadν
2Z0 ∆t ZHS
(7.4)
We have performed a simulation with 3 MeV electrons randomly distributed in time for
a time interval of 1 µs and laterally distributed using a Gaussian of standard deviation
σr = 0.25 cm. A total of 104 electrons are injected in constant density air and the electric
field in the frequency interval 5-5.25 GHz is computed. The field oscillates wildly in frequency
and we plot it in several frequency subintervals in Fig. 7.3. These oscillations do not appear
to be constant in time and when averaged over many beam pulses the emission produces a
flat spectrum.
The ZHS simulation yields for the mean of the field in frequency projected onto the copol
direction, parallel to z, and squared
h|Ez,ZHS (ν)|2 i = 6.0 · 10−18 V2 m−2 MHz−2 .
(7.5)
We have performed the simulations with 104 electrons. However, in a typical MAYBE run
the beam contains ' 8.3 × 1012 electrons in the entire 2 µs pulse and ' 1010 electrons
present in a given time window of 3.3 ns. Since the pulse is quite long compared to the
wavelengths of observation, we can safely assume it behaves incoherently, and therefore the
power increases linearly with the number of particles (this is confirmed in the simulations):
h|Ez (ν)|2 i =
1010
h|Ez,ZHS (ν)|2 i = 6 · 10−12 V2 m−2 MHz−2
104
(7.6)
In MAYBE, the electron beam lasts for 1 − 2 µs, but we assume once primary electrons cross
108
the chamber they are absorbed in the copper wall, therefore
∆t = 3.3 · 10−9 s = 3.3 · 10−3 MHz−1
(7.7)
Taking the impedance of free space
Z0 ≈ 377 Ω
(7.8)
and substituting in Eq. (7.4) gives an estimated Fν :
Fν ∼ 2.4 · 10−18 W m−2 Hz−1 (copol channel at 5.0 GHz)
(7.9)
The calculations above have been performed for a dipole-like effective length, but we
know the MAYBE antenna has a different pattern. In Fig. 7.4 the fit to the antenna relative
gain is shown. The angle in this plot is such that θ = 0◦ corresponds to the polar axis of the
antenna which is parallel to the beam axis.
1
Log antenna
Dipole antenna
Gain(e)/Gain(//2)
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
Angle (degrees)
60
70
80
90
Figure 7.4: Fitted relative gain of the MAYBE antenna obtained from the data sheet and
comparison with a dipole gain. The angle in this plot is such that 0◦ corresponds to the
polar axis of the antenna which is parallel to the beam axis.
Knowing the antenna pattern, a modification to the formula for Fν in Eq. (7.4) is needed
to take the gain into account. Assuming that the effective length of the antenna is parallel
109
Fν units of 10−18 W m−2 Hz−1 - 1013 electrons
Band
1.5 - 1.75 GHz 5 - 5.25 GHz 8 - 8.25 GHz
copol
0.76
0.77
0.78
Cross-pol
0.25
0.25
0.26
Table 7.1: Fν in units of 10−18 W m−2 Hz−1 , as obtained in ZHS simulations in different
frequency ranges and in the copol and Cross-pol channels, scaled to 1013 electrons in the
beam.
to θ̂ (E-plane), and since the field is calculated adding the fields of a number of small tracks,
accounting for the antenna gain yields the following expression for Fν :
s
2 +
*
X
G(θ
)
1
i
ZHS
Eθ (θi )
Fν =
2Z0 ∆t G(π/2) (7.10)
i
Here EθZHS (θi ) is the θ̂-component of the field due to an electron subtrack i as predicted by
the ZHS MC. θi is the angle between the line joining the center of the electron subtrack and
the polar axis of the antenna (parallel to the beam axis). G(θi )/G(π/2) is ratio of the gains
at an arbitrary direction θi and at θ = π/2 which is plotted in Fig. 7.4. By performing an
adequate rotation of the antenna frame we can also compute the cross-pol component of the
field. The results for Fν in the copol and cross-pol channels are given in Table 7.1 for several
frequencies. Fν is approximately the same in the three frequency bandwidths, indicating a
incoherent behavior of the field. Also it can be seen that the value of Fν in the cross-pol
channel is ∼ 1/3 smaller than in the copol channel.
As with the understanding of the molecular bremsstrahlung prediction uncertainties exist
in the simulation of the beam used in the ZHS MC, but the result obtained is consistent
with the emission we measured in the test beam, within systematic errors, to better than a
factor of 3. Although there is no conclusive understanding, the ZHS MC result implies that
the measured emission could be entirely due to the time variable E-field associated with the
passing of the primary 3 MeV electrons. At this time, these interpretations can only lead us
110
to set an upper limit on the MBR emission in air shower plasmas.
7.2.3 Scaling to air showers
With the assumption that the signal measured is produced entirely by the MBR process, one
open question about the interpretation of the measurements is how the measured power flux
translates to a reference value to parameterize the emission in an extensive air shower. This
scaling is far from obvious because it relies on the assumption that the undergoing process
in both the shower and the lab has a common emission mechanism and behavior. There
are indeed some known differences that could contribute to induce different conditions and
possibly different signals (from now on, comparisons with an air shower will always refer to
the conditions at the stage of maximum shower development).
While in the experiment performed in the lab all primary electrons have an energy of
3 MeV, the energy spectrum of electrons generated in an air shower follow a power-law
distribution covering a broad range of energies (from a few MeV to several GeV). (Indeed
the energy distribution is not homogeneous, high energy electrons tend to remain close to the
shower axis). Even though the difference seems quite drastic because the emission process
scales linearly with the energy deposit, as has been measured in the lab, both situations
converge to a similar scenario. As mentioned in § 6.1.4, the number of electrons and also
the total energy deposit is very similar in the lab chamber and in a shower at maximum
development. In consequence, the distribution of free electrons created through ionization
in the range of interest for the process (a few eV) will be almost identical. The emission
independence of air fluorescence, a related linear process, has been tested by (Ave et al.,
2013) confirming the emission independence of the ionizing particles. This, of course, is only
true for an emission which has no bulk plasma effects.
As already pointed out in § 6.1.4, the total energy deposit inside the chamber is comparable to the energy deposit in a 0.6 m segment of an EAS apart from the difference in the
111
deposition volumes. In the chamber the energy is deposited in a 1 m3 volume. At heights
of about 5 km,where the air density has decreased about 20% with respect to the one at sea
level, the Molière radius is about 100 m so the ionization electron density can be significantly
smaller. In this experiment, the signal has been studied in a large range of densities, covering
about 1 order of magnitude, with no evidence of change in the characteristics of the emission.
Another dissimilarity arises from the difference in the time distribution of the primary
electrons. While in the 3 MeV beam particles are homogeneously distributed along the pulse
width, in an air shower the time spread of particles depends on the distance to the shower
core. Particles close to the shower core travel with time delays of the order of tenths of
nanoseconds while at distances of about one Molière radius the spread of particles is at the
level of tens of ns. Along one pulse, no significant changes in power as a function of time
have been observed although the presence of the strong peak at the beginning of the trace
makes it difficult to study the signal as the beam initially enters the chamber.
Keeping in mind these discrepancies that could give rise to differences in the emission
and a possible alternative explanation for the observed emission which is unrelated to MBR
we will assume in the following analysis that the measured microwave flux is an upper bound
on the possible MBR signal. The power flux reported in § 7.1.2 F = 3 × 10−19 W/m2 /Hz
was obtained for a beam configuration where 1010 electrons where injected in the chamber
in a time window of 3.3 ns. Geant4 simulations reproducing the data taking conditions
eff in the 1 m3 chamber of 1.25 × 1015 eV. Using
give a total effective energy deposit Eref
a Gaisser-Hillas parameterization of the air shower development (Gaisser & Hillas, 1977)
the energy deposit in 0.6 m length path observed by the LPA at a distance of 0.5 m, at
the atmospheric depth of maximum development can be estimated. It is obtained that a
shower of 1.2 × 1019 eV deposits an energy equivalent to the total energy deposited inside
the anechoic chamber.
Results reported in (Gorham et al., 2008) suggest a flux of If,ref = 1.85×10−15 W/m2 /Hz
112
for the emission at the shower maximum of a reference shower of primary energy Eref =
3.36 × 1017 eV at a distance of 0.5 m from the receiver. For this energy reference, an extrapolation of the obtained linear scaling from the MAYBE result gives a reference power flux
MAYBE = 10−20 W/m2 /Hz to be
for an EAS with energy, Eref , which must be less than If,ref
consistent with our understanding of the measured microwave signal.
113
Part IV
Conclusions
CHAPTER 8
FUTURE DETECTOR DESIGN
8.1
Implications of Signal Measurements and EAS Limit
With the described MIDAS and MAYBE experiments we have set the strongest limits to
date on isotropic microwave emission from air plasmas induced by both EAS and in test
beams. At this time our experiments have only produced upper limits on the emission,
and while strong, there is still phase space which remains unexplored. The existence of
isotropic microwave emission remains an outstanding question that can only be answered by
continued exploration and testing. Further, we also would like to understand the feasibility
of the microwave technique in general and at what level it is not longer viable as a detector
for UHECRs.
8.1.1 Sensitivity
To estimate the sensitivity required of future designs let us take two values as guiding
limits. For both values we assume the flux is incoherent, α = 1, as there has been no
evidence in our measurement for coherence that would greatly enhance the signal. The
optimist scenario leaves us in a state where the reference flux value is just out of reach
of the sensitivity of the MIDAS detector and the results of the MAYBE experiment are
invalid. In this scenario we would have a reference flux from the MIDAS limit at Auger of
Auger
If,ref = 8×10−16 W/m2 /Hz. With our preliminary limit from the operations at Auger this
value is ruled out with 90% confidence, but for our thought exercise this is a suitable upper
limit. A simulated spectrum in events per year is shown in Figure 8.1, with an integrated
total of ∼ 13 events/yr. While this number of events is suitable for a prototype detector
making a first detection of microwave emission, a higher event rate is desirable in the case
of a full scale detector. At this reference flux value the telescope records only a few events
115
per year above 1019 eV with nearly 100% duty cycle, by comparison the Auger FD has
recorded a few hundred events during its roughly 5 years of operation at 10% duty cycle.
To exceed this rate of events, at least two orders of magnitude increase must be achieved
in data collection. One possibility is simply to deploy an array of 100 detectors, however,
the more interesting possibility is to make each detector itself more sensitive. In the current
design with the sensitivity of MIDAS using a the 4.5 m reflector most shower cores for events
with energy, E = 1019 eV for showers triggered in the MC fall within 10 km of the detector.
Increasing this distance by building a more sensitive detector would greatly increase the
integrated aperture of a microwave telescope as number of events grows linearly with the
instrumented area. If we recall from the work of (Kraus & Marhefka, 2003) the minimum
detectable change in flux, ∆If , for a microwave receiver is given by,
∆If =
kB · Tsys
√
Aef f ∆ν∆t
,
(8.1)
where kB is the Boltzmann constant, Tsys is the detector system temperature, Aef f it the
telescope effective area, ∆ν is the observation bandwidth, and ∆t is the time window of
integration.
Based on the timing structure of the signal and nature of the emission the MIDAS detector
is already nearly optimized in both ∆ν and ∆t. Also, at a Tsys = 65 K it is hard to imagine
an improvement greater than a factor of two on the minimum detectable change in flux due
to an improvement in system temperature. Modifying the size of the collection element of
the receiver is the one clear place where large gains in sensitivity can still be made. To
achieve a factor of 100 increase in sensitivity this requires increasing the size of the collection
element to an effective diameter of 50 m. While, this is very large and likely not feasible
on a scale necessary to instrument large areas, reflectors up to a size of 20 m are obtainable
commercially. At 20 m the sensitivity of a single detector increases by roughly a factor 16
0
which would return MIDAS to it’s original sensitivity assuming the case of If,ref
and α = 2
116
Figure 8.1: Expected number of triggered events per year as a function of energy, from a
simulation of the MIDAS telescope at the Auger Observatory using the Chicago calibration
data set. A cosmic ray primary flux as measured in (Abraham et al., 2010b) was assumed
Auger
in the simulation. A microwave flux density If,ref = 8 × 10−16 W/m2 /Hz and a coherence
parameter α = 1 were used to parameterize the EAS microwave emission in the simulation.
to be true. It should be noted that increasing the size of the collecting area also necessitates
more pixel to achieve the same field of view which is strictly necessary in order to increase
the size of the aperture. This then adds further complications in triggering, reconstruction,
and electronics. If the signal were to exist at this level, likely all of these difficulties could
be overcome to produce a full scale UHECR detector in the microwave.
In the pessimistic and yet more likely scenario the limit of the MAYBE experiment is
MAYBE < 10−20 W/m2 /Hz is our upper limit. At nearly
correct, and the reference value If,ref
five orders of magnitude below the nominal range of sensitivity for the MIDAS experiment,
the detector sensitivity required to perform measurements of EAS events at even the highest
energies imply this technique is no longer viable as a means of detecting UHECRs. However,
due to the caveats that have been discussed and the large uncertainties associated with the
MAYBE measurement, a final determination of the level of microwave emission can only be
117
made by placing microwave detectors in coincidence with large cosmic ray detectors as we
have done with MIDAS detector at Auger. Additionally, two other microwave prototypes
have been designed and deployed at the Pierre Auger Observatory. Within the next year we
will have a definitive answer on the feasibility of using microwave detectors as a means of
detecting isotropic radiation from ultra high energy EAS.
8.2
Promise of Microwave Detectors
While the feasibility of building detectors for isotropic microwave emission remains tenuous,
microwave detectors in general have advantages over working in the MHz regime and there
may still exist a place for these detectors in particle astrophysics. In February 2012, serendipitous detections of microwave emission from EAS were announced, having been made using
GHz radio receivers triggered by cosmic ray air shower surface detectors. These detections
were made separately by the CROME experiment which operates in coincidence with the
KASKADE-Grande array (Šmída, R. et al., 2013) and the EASIER experiment operating
passively on a small number of SD tanks at the Auger Observatory (Facal San Luis & The
Pierre Auger Collaboration, 2013). Both of these experiments use similar extended C-band
LNBFs, like that of the MIDAS experiment, instrumented with power detectors. In the case
of CROME a 9-pixel array is instrumented on a 3.4 m parabolic reflector pointed at zenith
with event triggers coming externally from the KASCADE-Grande data acquisition. For the
EASIER experiment, at the time of detection 7 SD tanks were instrumented with a single
LNBF which are oriented to point to zenith with no reflector. The signal from the LNBFs
are digitized and read out by an extra channel on the SD data acquisition. The LNBFs
of EASIER operate passively and only record signal traces when the SD tank triggers and
event with its internal PMTs. Both of these experiments have measured strong, fast signals
which are coincident with an EAS triggering the detector and have a pulse width consistent
with the time constant of the power detector, ∼ 10 ns. For both experiments the geometry
118
of the events was such that the detectors are in the forward regime as outlined in § 2.1 and
inconsistent with a measurement of isotropic microwave emission.
The ANITA collaboration has also reported on detection of a sample of events which are
thought to come from UHECRs (Hoover et al., 2010). The signals in the case of ANITA
are thought to be forward emission which is reflected off the Antarctic ice and up to the
balloon payload where the emission is detected in a RF band of 200 MHz to 1200 MHz.
The ANITA signals are also very fast, have a characteristic pulse width of ∼ 5 ns. The
key evidence for reflected events in the case of ANITA is the polarization of the signal.
All of the events arrive at the balloon payload horizontally polarized which is consistent
with reflection and inconsistent with the vertically polarized signal expected from an UHE
neutrino event in the Antarctic ice sheet. Further, two events were observed above the
horizon with inverted horizontal polarity, strengthening the case for reflected EAS events.
While at surprisingly high frequencies, these measurements are all consistent with forward
radio emission originating from geomagnetic and Askaryan mechanism. Only very recently
have simulations been extended up to these high frequencies where work is on-going to
understand the spectral cut-offs associated with these emission phenomena (Alvarez-Muñiz
et al., 2012b; Huege et al., 2013b).
We have begun using the CoREAS simulation of (Huege et al., 2013b) to explore the high
frequency spectra and test spatial distributions of the emission at ground level for observers
of forward EAS events. These studies have revealed that there is indeed a region of coherent
emission extending to high frequency near the Cherenkov angle for EAS events. This is seen
in the spectral dispersion plot of Figure 8.2, for a distance of 100 m from the core of the
simulated EAS the emission spectra extends up beyond 1 GHz. In local coordinates on the
ground, Figure 8.3, we see that the signal produces a ring pattern as one would expect from
the Askaryan mechanisms for EAS (Askaryan, 1962, 1965; Saltzberg et al., 2001). We have
also confirmed that the high frequency microwave emission is coherent, microwave power
119
Figure 8.2: Spectral dispersion plot of the RF signal at ground level for a CoREAS simulated
PeV proton induced EAS.
flux scaling quadratically with EAS energy, as has been confirmed at low frequency.
As with the search for isotropic microwave emission, which was motivated by the search
for a 100% detector duty cycle analog for FD telescopes, coherent microwave emission in
the forward EAS regime presents itself for interesting detector possibilities. Because of the
coherent, broadband nature of the emission the signals themselves should be very unique at
the detector level. This is especially true in the case of microwave frequencies where, as we
have shown, it is possible to construct telescopes with imaging focal planes which further
benefit from event topology in triggering. One can imaging such a telescope, or array of
telescopes, which have sensitivity below 1 PeV. Given the proper trigger algorithms and
120
Figure 8.3: Spatial distribution in meters east and west of the total electric field strength
in µV/m for a CoREAS simulated 100 TeV proton induced EAS. The event event has been
filtered using a RF band of 100 MHz to 5 GHz. Small black lines originating from the center
of each bin are projected angle of the electric field vector at each point of the observer plane.
The time parameter, t = 7 ns is time relative to when the EAS impacts the ground. In this
geometry the peak of the emission arrives seven ns after impact.
121
data acquisition, it may be possible to construct a microwave analogue to the currently very
successful very high energy (VHE) gamma ray observatories operating in the UV such as,
VERITAS, HESS, and MAGIC (Hinton & Hofmann, 2009). As with FD telescopes, VHE
gamma ray telescopes are limited by their detector duty cycle and the possibility recording
events in microwaves with 100% duty cycle represents a substantial increase in sensitivity.
Beyond the primary difficulty of simply building detectors with large enough effective
areas to detect EAS below 1 PeV, there remains a great deal of difficulty in discerning the
small sample of gamma ray events within the much larger sample of cosmic ray primaries,
which have been well studied by SD experiments. Our hope is that through simulations we
will be able to show that primary composition is discernible through observable parameters
such as spatial distribution of signals in the detector focal plane and spectral information
from the RF signal, as is done for primary separation in UV VHE observatories.
The difficulty for radio telescopes in measuring these observables is due to the high
bandwidth nature of the Cherenkov signals. Because the signals extend over 1 GHz of
analog bandwidth the data acquisition time scales required to detect these signals will need
to be ∼ 1 ns in order and in the RF domain to have resolving power on the pulse structure.
This implies sub-ns RF sampling of at least 1 GHz of analog bandwidth for likely hundreds
of pixels. At the current time the electronics to complete this measurement do not exist on
the scale needed for many hundred pixel detector planes, a serious R&D effort will need to be
pursued before prototype telescopes can be constructed. Currently, we have begun this R&D
effort at the University of Chicago. Assuming these technical challenges can be overcome in
a cost effective way, the prospect for microwave imaging telescopes to make a large impact
in the sensitivity of future particle astrophysics experiments remains encouraging.
122
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