cosmic rays and extensive air showers
TRANSCRIPT
Advanced lab course for bachelor students in physics
Cosmic rays and extensive air showers
December 2018
Prerequisites
• Cosmic rays
• Photomultipliers
• NIM-electronics
• Cerenkov effect
Goal of the experiment
• Setup of electronics
• Detector characterisation
• Extended coincident measurement
• Absorption measurement
• Angular measurement
Table of Contents
Table of Contents
2
1 Preface
The goal of the lab course is to measure cosmic rays by using the Cerenkov effect. In doing this, the han-dling of particle detectors and the accompanying measurement electronics should be learnt. Additionally,an understanding of the basics of cosmic rays and extensive air showers should be developed.
On the first day, students should get acquainted with the electronics and the methods of measurementand several calibration measurements should be performed. Following this overnight and the next day areseveral different measurements and scenarios, like e.g. the measurement of the relation between zenithangle and muon rate.
Fundamentally, this experiment fits in with the other experiments on particle physics as part of theadvanced lab course. However, it is currently the only one which, like the Pierre Auger Observatory inArgentina or Super-Kamiokande in Japan, uses the Cerenkov effect for the detection of particles, insteadof relying on expensive scintillation materials.
Of particular interest to this experiment is the measurement of cosmic muons. These constitute a rareoccasion, where the effects of special relativity are immediately apparent.
Limited by their short lifetime of τµ = 2.2µs, muons would classically decay before even travelling 700 m.It is relativistic time dilation which ensures that many muons fly for kilometres before decaying and canconsequently be measured on Earth’s surface.
Figure 1.1: Sketch of the secondary rays of an extensive air shower induced by a cosmic ray. Qualitatively,the shower components can be separated into an electromagnetic, a hadronic and a muoniccomponent [?].
3
Chapter 2. History
2 History
At the start of the 19th century, shortly after the discovery of radiation, numerous experiments exploringthe penetrating, ionising radiation were conducted on Earth. Using electrometers and cloud chambers,the radiation intensity could be quantified indirectly. Electrometers use for this the varying conductivityof air in the presence of ionising radiation of varying intensity. In cloud chambers, condensation nucleiform in an oversaturated gas mixture around molecules ionised by radiation, making the particle trackvisible. This allows to additionally draw quantitative conclusions about the particle type from the trail.
The prevalent idea was that radioactive particles in the Earth’s crust (and a few in the atmosphere) alonegenerated the radiation measured until then, which with increasing altitude, as tested by Rutherford withshielding materials, should be absorbed. At first, this assumption was confirmed qualitatively in 1910 bythe physicist Theodor Wulf. In an experiment on the Eiffel tower, he measured - using an electroscope -that the ionisation rate roughly halved going from the surface to the top of the tower (roughly 300 m).This absorption corresponded qualitatively to the expectation for radiation dominated by Earth, but infact a larger attenuation was expected. Two years later, in 1912, the Austrian physicist Viktor Hess,with electrometers for the measurement, flew in a hot air balloon to greater heights.
He ascended to 5000 m and starting at 1500 m he actually measured an increase in ionisation rate.From this increasing trend he concluded that the source of the radiation measured by him could not beterrestrial, and ”‘baptised”’ it ”‘cosmic radiation”’. For his discovery he was awarded the Nobel prize inphysics in 1936. In actuality, Hess measured the secondary radiation, ionising radiation from air showers,which are caused by the impact of high-energy cosmic rays on the atmosphere (compare fig. ??). Thisbecame apparent when in 1936, physicist Johann Pfotzer during balloon flights to extreme altitudes,could make out a radiation maximum at around 15 km. Seven years before that, Bothe and Kohlhorsterhad already attempted to determine the nature of the radiation using coincident measurements with leadand gold absorbers and found that the penetrating power was much higher than that of gamma radiation.So it must be another type of radiation. In fact, muons are charged particles of the lepton family andnot photons. They are mostly created in the decays of pions and kaons, which in turn are products ofthe interaction of high-energy primary cosmic rays with the atmosphere. The decays shown in fig. ?? areto be understood schematically, in reality large shower cascades with resulting air shower radii of severalkilometres are formed depending on the energy of the initiating primary particle.
During this time, A.H. Compton undertook several expeditions all around the globe to measure the cor-relations between the radiation intensity and coordinates. He found a relation between the equipotentiallines of the Earth’s magnetic field and the measured intensity, from which he concluded that the primaryradiation must consist of charged particles. In 1930, Anderson and Millikan discovered the positron usinga cloud chamber (for which Anderson was awarded the Nobel prize in 1936). Finally, in 1937, Andersonand Neddermayer discovered the muon.
4
3 Theory
3.1 Cosmic Rays
Cosmic Rays (CRs) are charged particles generated inside or also outside the Milky Way and acceleratedto high energies. Earth is permanently irradiated by these particles. When a high-energy CR enters theatmosphere, collisions with a nitrogen or oxygen atom create new particles, which due to the high initialenergy continue to move in the direction of the primary particle and in turn interact or decay, formingan extensive air shower. Some secondary particles reach the surface and can be detected there. Up untilthe second half of the 20th century, CRs were the only possibility to conduct high-energy particle physicsand discover new elementary particles.
Up to around 100 TeV, the primary rays can be measured directly using balloon and satellite experiments.Because the rate of particles decreased sharply, large surfaces and long measurement times are requiredbeyond this energy. This is realised by large, earthbound experiments, which measure the secondaryparticles to indirectly detect the CRs.
What can be found out by measuring the muons on Earth?
PeV EeV
ATIC
PROTON
Auger SD 2008
HiRes I
HiRes-MIA
Tibet Asg (SIBYLL 2.0)KASCADE-Grande (prel.)KASCADE (SIBYLL 2.0)KASCADE (QGSJET 01)
RUNJOB HiRes II
Equivalent c.m. energy (GeV)√spp
Energy (eV/particle)
HERA (γ - p)RHIC (p-p)
LHC (p-p)Tevatron (p-p)
1019
Sca
led
flux
E2.
5 J
(E)
(m
-2 s
ec-1 s
r-1 e
V1
.5)
1017
1018
1016
1015
1014
1013
1013
1014 1015 1016 1017 1018 1019 1020
102 103 104 105 106
1012
J(E)∝E−γ
TeV
whereby γ ≈ 2.7 – 3.0 galactic
extra-galactic
Knee1 particle
per m² & year
Ankle1 particle
per km² & year
Figure 3.1: The cosmic ray spectrum. The differential particle flux density as a function of the energy[?]. For a better presentation, the spectrum has been multiplied by E2.5.
5
Chapter 3. Theory
3.2 Atmospheric Showers
The interaction of a CR with the atomic nuclei of the atmosphere generates a particle cascade of amultitude of secondary particles, which can be divided into three components: hadronic, electromagneticand muonic. The shape and composition of the showers, as well as the number of secondary particles isof a stochastic nature, but the average depends on the energy and type of the primary particle, as wellas the density profile of the atmosphere. The project with the largest detection surface for the studyof the highest-energy CRs is the Pierre Auger Observatory, consisting of an array of water Cerenkovdetectors and fluorescence telescopes (for those who are interested: in the appendices ?? and ?? onecan find further explanation of how the Pierre Auger Observatory and the neutrino observatory IceCubedetect cosmic particles using the Cerenkov effect and why both of these experiments are so important forthe field of astroparticle physics).
3.2.1 Atmosphere
The first interaction partners of CRs on Earth are the atomic nuclei of the upper atmosphere. The densityof the atoms and correspondingly the interaction probability vary with altitude. The density profile forsmall heights can be approximated using the barometric formula as follows:
ρ(h) = ρ0 · exp
(− h
h0
), (3.1)
with ρ0 ' 1.35 kg/m3, h0 ' 7.25 km and h the elevation in km. For atmospheric showers, a relevantquantity is the so-called atmospheric depth X:
X(h) =
∞∫h
dh ρ(h) = ρ0h0 · exp
(− h
h0
)(3.2)
The atmosphere has an average depth of around 1030 g/ cm2. For homogeneous substances X = ρ · h, soca. 90 cm of lead and 10 m of water correspond to the same depth.The local atmospheric pressure can also be approximatively related to the atmospheric depth:p
hPa = Xg/ cm2 · g
m/ s2 · 0.1, with gravitational acceleration g ' 9.81 m/ s2.
3.2.2 Reaction with the Atmosphere
The particle showers are divided into hadronic, electromagnetic, muonic and neutrino components de-pending on the particle type and reaction mechanism, as shown in figure ??.
Hadronic cascade
Most of the particles hitting Earth’s atmosphere are protons. They interact inelastically either in acollision with the air’s atomic nuclei, producing highly energetic nuclear fragments, pions, kaons, protons,neutrons and other baryonic secondary particles, or via ionisation processes. The primary particle losesthe majority of its energy to secondary particles in inelastic collisions. From this point onwards, thedevelopment of the shower depends on a number of processes. The stable particles continue to propagate,until they hit an interaction partner, the probability of which increases in the downwards ever denseratmosphere. The unstable particles, mostly kaons and pions, can also decay along the way.
6
3.2. Atmospheric Showers
Figure 3.2: The most important processes of particles in air showers. For neutrinos, the charge parity isneglected [?].
The most important decay processes are (νl− neutrino, νl+ antineutrino ):
π0 → γ + γ
π± →µ± + νµ∓
K± →µ± + νµ∓
µ± → e± + νe∓ + νµ±
On average ≈ 90% pions and ≈ 10% kaons are generated. Charged pions and kaons decay into muons andneutrinos, which practically do not contribute to the cascade. Neutral pions decay quasi-instantaneouslyinto photons and therefore contribute to the formation of the electromagnetic cascade considerably.
Electromagnetic cascade
The previously mentioned electrons of the cosmic radiation, as well as the electrons and positrons gener-ated in hadronic cascades, lose their energy in the atmosphere. The dominant processes are ionisation,annihilation of positrons and bremsstrahlung. The photons created in these processes carry over a largeportion of the energy. The high-energy photons interact above a few MeV mostly via pair production.In that process an electron and a positron are created, carrying equal amounts of the photon’s energy.
Both of these processes alternate and in this way form the electromagnetic cascade, as shown in figure??. It can be induced by an electron as well as a photon. In rare cases, a hard interaction with an atomicnucleus can again induce a hadronic subcascade.
Muons and Neutrinos
Unstable particles of the hadronic component – mostly pions – decay in thinner atmospheric layersbefore they can interact. In this way, muons and neutrinos are created at large altitudes, where theneutrinos leave the cascade process, since they can penetrate large material depths without interacting[?]. Compared to the other shower components, the muons rarely interact.
The composition and geometry of the shower changes with elevation. Even though of the particleswith energies smaller than 1 GeV the muons are the most common, particles from the hadronic andelectromagnetic components also reach the detectors [?], meaning that without a discrimination of theparticle type, the measured muon rate can be overestimated by a few percent. On arrival at the surface,
7
Chapter 3. Theory
Absorber (Air)
e-
e-e -
e+
e+e+
e+
e-
e-e-
e-
e+
e-e+
γ
γγ
γ
γ
γ
γ
γγ
e- e-γ
γ
Z(p+e-)
Cascade 1st 2nd 3rd 4th 5th
Figure 3.3: Schematic EM-cascade.
γ
γ
Ze+ e−
e−
e
γ
Ze+
e+
e−
eγ
Figure 3.4: Feynman graphs of (a) bremsstrahlung and (b) pair production in an EM-cascade.
the shower front possesses a very small thickness on the order of one metre and an energy-dependenthorizontal spread. For the highest energies of primary particles, this can be many hundreds of meters, asshown in figure ??.
Figure 3.5: Simulations of the incoming particles at the Pierre Auger Observatory. Shown are (a) particletracks and (b) the shower front. Single surface detectors are positioned on a triangular gridwith edge 1.5 km [?][?].
Muon Decay
From several GeV onwards, the radiation at sea level consists primarily of muons [?]. As discussed in??, a muon always decays into an electron or a positron and two neutrinos, via the Feynman diagramsshown in figure ??.
The average lifetime of muons is τµ ' 2.197 ·10−6 s, the distance travelled by light in this time span iscτ ' 659 m. That muons can penetrate several kilometres of atmosphere despite this, can be explainedrelativistically. Because of time dilation we have to scale the distance by the Lorentz factor γ for velocities
8
3.3. Acceptance and Rate
µ−
W −
µν
eνe− W + e+
eν
µν
µ +
Figure 3.6: Feynman graphs of the decays of (a) a negative and (b) a positive muon.
near c, e.g. v ' 0.998 · c.
s = v · τ · γ = v · τ · 1√1−
(vc
)2 ' 10.5 km ,
This way, the muon decays near the surface. By measuring the times of electron and positron signalscaused by muons stopped in the setup, the lifetime of the muon can be determined, which is done e.g. inexperiment 11 of the lab course of the master’s program.
3.3 Acceptance and Rate
The particularities of the geometry and the methods of the setup have to be taken into account in orderto get a satisfactory interpretation of the measurement results. Formulae for the geometrical acceptanceand the integral muon intensity in particular will be discussed.
3.3.1 Muon Flux at Sea Level
In experiments measuring atmospheric muons, the spectrum of the differential particle flux is often givenas the result [?],[?]. The flux is defined as
dφ
dp(p, θ) =
dn(p, θ)
dΩ dp dS dt,
with the particle momentum p(
[p] = GeVc
c:=1→ GeV)
, solid angle Ω ([Ω] = sr), surface area S ([S] = m2)
and time t ([t] = s ≡ Hz−1).
The muons that reach the surface are distributed according to a different momentum spectrum (fig. ??)than the primary particles. The spectrum of vertical muons is roughly constant near 1 GeV, decreasesbetween 10 GeV and 100 GeV in accordance with the primary proton spectrum (see section ??, fig. ??),and decreases even more strongly above 100 GeV, because the interactions of high-energy pions dominatecompared to the pion decay and so fewer muons are produced.
The integral intensity, which is important for detectors, can be calculated from the flux using eq. (??).To take into account the atmospheric depth X of the location of the measurement, the following equationis used [?]:
φlocal
φsea level= exp
(−X − 1030 g cm−2
630 g cm−2
)(3.3)
In the low-energy regime, the muon spectrum fluctuates strongly with the primary spectrum of CRs. Theprotons interact with the solar wind and the magnetic fields, so fewer primary particles are measuredduring strong solar activity. The magnetic field of the Earth also affects the CR flux, so the geomagneticlocation of the measurement must also be taken into account. On top of that, air pressure fluctuationsinfluence the shower development and the number of muons arriving at the surface. For high precision
9
Chapter 3. Theory
dϕ/d
p∙[m
2∙s
∙sr∙
GeV
]
1e-05
0.0001
0.001
0.01
0.1
1
10
p/[GeV]0.1 1 10 100 10001000
Hebbeker and Timmermans (2001) De, Ghosh and Das (1974)
Figure 3.7: The spectrum of muons at the surface. The differential particle flux density as a function ofthe energy. Combination of two fits of the low-energy [?] and the high-energy [?] regimes,which are compatible within the uncertainties.
measurements, these and many other confounding factors must be considered or the measurement rangepicked carefully.
When passing through matter, muons are slowed via ionisation and radiation processes. For muons ofenergies below several hundred GeV, the energy loss over a distance x in a material with density ρ canbe well approximated [?] by:
dE
dX=
dE
dx
1
ρ= 2.0
MeV cm2
g(3.4)
Fundamentally, a particle can only generate Cerenkov light, and therefore be detected by the detectorused, starting at a certain minimum momentum.To estimate the number of muons not stopped in the medium, the spectrum is cut off at the maximum de-posited energy, depending on the absorber thickness. For proper experiments, the spectrum is calculatedusing Monte-Carlo simulations (e.g. Geant4).
How does the fact that the Physics Centre is located about 200 m above sea level affect themuon flux?Are there other factors that influence the rate to be measured?
Canonical solid angle and acceptance
In general, the flux of muons at the surface depends strongly on the momentum and zenith angle θ [?].The zenith dependence [?] of φ for angles below 70 can be given as
dφ
dp(p, θ) =
dφ
dp(p) · cosn(θ) .
The rate of a detector with sensitive surface area S, geometrical (i.e. solid) acceptance A = Ω · S andminimum momentum threshold pmin can be calculated as
f =
∞∫pmin
dpdφ
dp(p)
︸ ︷︷ ︸φ⊥(0)
∫S
dS
∫Ω
dΩ cosn(θ)
︸ ︷︷ ︸=:Γ
, (3.5)
where φ⊥(0) is the integral vertical flux and Γ is the weighted geometrical acceptance. φ⊥(0) and Γ can
10
3.3. Acceptance and Rate
approximately be factorised and therefore be considered separately. So the measured rate of a detectorresults approximately from the product of the integral vertical muon flux and the weighted geometricalacceptance. The integral vertical muon flux is independent of the detector. The weighted geometricalacceptance depends on the setup and is examined next.
The solid angle is defined as the ratio of the surface area of a section and the square of the radius of asphere.
a
ΩdΩ = da
r2
Figure 3.8: Geometrical visualisation of the definition of the solid angle [?].
Since on the surface of a sphere da = dϕr dθ r sin θ the solid angle can be written in spherical coordinatesas:
dΩ := dϕ dθ sin θ (3.6)
Using this we can write the weighted geometrical acceptance as:
Γ =
∫S
dS
∫Ω
dΩ cosn (θ) (3.7)
Consider the simple case of a flat, circular detector with radius R, which observes with an opening angleω around the zenith. In this case we get:
Γ =πR2
2π∫0
dϕ
ω/2∫0
dθ sin (θ) cosn (θ) (3.8)
=πR2 · 2π · 1
n+ 1
[1− cosn+1
(ω2
)](3.9)
For such a detector, which covers the entire hemisphere (ω = 180), the rate per surface area is for muonsabove 1 GeV well approximated with φ⊥(0) ≈ 70 m−2 s−1 sr−1 and n = 2:
f
S=
φ⊥(0) · ΓS
=70 · 2π
3
1
s m2≈ 0.88
1
min cm2∼ O
(1
min cm2
)(3.10)
For general detector setups, especially for simultaneous measurements with multiple detectors, theweighted geometrical acceptance cannot be calculated trivially. Under the assumption that the cov-ered solid angle is small and the change of the muon flux within this range is negligible, the weightedacceptance can be simplified:
Γ (θ) = cosn (θ) ·∫S
dS
∫Ω
dΩ
︸ ︷︷ ︸=:A(θ)
(3.11)
Considering the other accuracies within the scope of this experiment, this approximation is permissi-ble. This integral is not soluble analytically for complex detector setups. In these cases, Monte-Carlosimulations are typically carried out to determine the geometrical acceptance A.
Shown in figure ?? is the result of one such Monte-Carlo simulation for cylindrical detectors with a heightof 15 cm, a radius of 6.5 cm and a vertical distance d in dependence of the zenith angle. The zenith angleis changed by moving one of the cylinders horizontally.
Also not included in the formulae are potential dependencies of the detector efficiencies on the angle ofincidence and position inside the detector. A consideration of these factors is not possible within thescope of this experiment.
11
Chapter 3. Theory
0 10 20 30 40 50 60 70
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
0.0012
2sr
d = 56.5cm d = 79.5cm
Zenith angle /
Acc
epta
nce
/ m
Figure 3.9: The zenith-angle-dependent geometrical acceptance for two cylinders of radius 6.5 cm, height15 cm placed above each other with the vertical distance of the centres of the cylinders d.
Which rate do you roughly expect for a 1 litre sphere of water? (cf. Sect. ??, eq. (??))
3.4 The Cerenkov Effect
When charged particles propagate in a medium at a velocity greater than the speed of light in thatmedium, the Cerenkov effect comes into play. The particle polarises the molecules of the medium andthereby induces the emission of light (fig. ??).
Figure 3.10: Polarisation of the molecules of the medium, destructive interference on the left, constructivesuperposition for velocities greater than the speed of light in the medium on the right, withv - particle’s speed, c0 - speed of light, n - refractive index of the medium [?].
For velocities smaller than the speed of light in the medium there is destructive interference on average,above this critical velocity a cone of Cerenkov light is created from constructively interfering waves (cf.Huygens construction in fig. ??).
The opening angle θ of this cone is called the Cerenkov angle and depends on v (and thus also on β - therelativistic velocity) and n:
cos(θ) =1
βn=c0vn
(3.12)
12
3.4. The Cerenkov Effect
0c tn
Cθ
v t⋅
γ
γ
µ +
Figure 3.11: Cerenkov cone for satisfied Cerenkov condition. The resulting wavefront (solid lines) is easilyconstructed geometrically.
Figure 3.12: Effectively detected photons for the employed water Cerenkov detectors.
And so the Cerenkov condition is :
β >1
n⇔ E >
mParticle√1− n−2
(3.13)
Is this condition fulfilled, then a particle emits photons per wavelength element dλ and distance dx (toa first approximation) according to the Frank-Tamm formula (figure ??, [?] - black curve):
dNγdxdλ
=2παz
λ2
(1− 1
(n(λ) · β)2
), (3.14)
where z is the absolute value of the charge of the particle in multiples of the elementary charge and αis Sommerfeld’s fine structure constant. Cerenkov radiation follows a continuous spectrum, where theintensity increases for higher frequencies (see black curve in fig. ??). Therefore, the typical wavelengthsrange from ultraviolet to blue (optical).
Why is water commonly used?In general, which properties of the particle can be determined using the Cerenkov effect?
In the wavelength range 300..600 nm – after taking into account all losses and efficiencies in the detectorsused in the experiment – effectively roughly 28 photons per cm of distance travelled through the waterby the particle are detected (integral of the shaded area in fig. ??) due to the Cerenkov effect.
Additional question: which initial energy does a muon need to penetrate 100 cm of concreteand generate Cerenkov light in water?
13
Chapter 4. Setups
4 Setups
For this lab course experiment, there are two setups: T20-1 and T20-2. Both setups are used to performthe same measurements, but the setups are not identical and therefore different aspects have to bepaid attention to both with regard to the measurement electronics and the analysis. The goal of thisexperiment is the measurement of atmospheric muons.
4.1 Overview
The basic setup of the experiment consists of two Cerenkov detectors, one standard NIM crate withevaluation electronics, one PC with a USB connection to the crate electronics and a standard 4-channeloscilloscope (see fig. ??). All components have been placed on a trolley which can be easily moved andpositioned by two people. Used as Cerenkov detector is a normal commercial coffee pot, which has beenfilled with distilled water and is read out with a light sensor - a photomultiplier.
Figure 4.1: The components of the setup
Figure 4.2: An experiment trolley with NIM crates, (and here 3) detectors, a PC and an oscilloscope.
14
4.2. Photomultipliers
4.2 Photomultipliers
For a long time, photomultipliers served as a substantial standard component of particle detectors in astro-and particle physics. Even though nowadays semiconductor detectors are increasingly used, classicalPMTs are still used in many places.
Figure 4.3: Greatly simplified schematic of the functionality of dynode stages as secondary electron mul-tipliers [?].
A PMT is an electron tube, consisting of a photocathode and dynode stages. When a photon hits thephotocathode, it knocks an electron out of the cathode material (photoelectric effect). These so-calledphotoelectrons are subsequently accelerated in the direction of the dynode, where they are multiplied(fig. ??), causing a measurable current pulse. PMTs are not only mechanically fragile (glass tube withpartially delicate dynode structures), but can also be damaged or destroyed (if an operating voltage isapplied) by large quantities of light – and therefore high currents.
The (quantum) efficiency of a PMT is significantly dependent on the wavelength of the irradiating lightand can be adapted to the required wavelength range by optimisation of the photocathode. A typicalmaterial for a photocathode, with sensitivity from the upper UV-range to the middle of the opticalspectrum, is a mixture of antimony and different alkali metals called a bialkali.“
As can be seen in figure ??, the quantum efficiency is only on the order of 20-30%, even in the mostsensitive range, so only about every third or fourth photon generates a secondary electron. In the lesssensitive ranges, the efficiency is even lower.
PMTs are not very efficient. Why are they suitable detectors despite this?
It is easily estimated that the current produced by the photoelectrons is tiny (for example on the orderof 1 nA, varies greatly with nPhotoelectrons and ∆t) and corresponding amplification is needed. This is thepurpose of the dynode stages. The photoelectrons from the cathode are accelerated towards a dynode,where they knock out more electrons. These are accelerated towards another dynode and there theyknock out even more electrons. This process is repeated until an electron cascade sufficiently large togenerate a stable signal pulse has formed. The amplification depends strongly on the number of dynodestages used. Typical are PMTs with 9 to 12 dynode stages (fig. ??). The photomultipliers used hereachieve amplifications of 105 to 106.
To make the electrons pass through the dynode stages as wanted, the latter have to be at ever higherelectric potentials. To achieve this, a high-voltage power source is connected to the PMT, which providesthe potentials for the dynodes over a voltage divider (line of resistors in fig. ??). The signal can be tappedfrom the anode and also, with a smaller amplification, from the last dynode. Because the amplificationdepends on the acceleration of the electrons (so the applied potential differences), too high voltages leadto the amplification of thermally excited electrons and thereby to amplified noise, saturation effects andpossibly the destruction of the PMT. Is the amplification too small, then the pulses can no longer bedistinguished from the noise. Accordingly, the operating voltage of the PMT in question must first bedetermined. Typical operating voltages for PMTs range from a few 100 V to several kV and depend a
15
Chapter 4. Setups
Figure 4.4: Typical quantum efficiency of a PMT with a bialkali cathode, according to [?].
lot on the model used.
Figure 4.5: Equivalent circuit of a PMT, where d1 through d12 are the 12 dynode stages, below whichthe resistors of the voltage divider, Zener diodes for voltage limitation and the capacitors forthe stabilisation of the dynode voltages are shown.
In the setup used, the PMT (photomultiplier tube) is screwed onto the pot and reaches into the upperpart of the pot’s interior (fig. ??, region 3), with its field of view in the direction of the water. On theother side, the base circuit board with the voltage divider (fig. ??, region 2) and a preamplifier (fig. ??,region 1) are located. The pot is completely filled with distilled water and the entire device is taped shut,to prevent surrounding light from entering. Additionally, there are dark boxes to minimise light leakageas much as possible. At the top of the PMT are the connections for the high-voltage power source andthe power source for the preamplifier, as well as the signal output with a LEMO 00- or BNC socket.
16
4.3. Amplification of the PMT Pulse
Figure 4.6: Cross section of the original detector[?]:1) Preamplifier2) Base circuit board3) Photomultiplier4) Pot interior
Figure 4.7: Schematic setup of adetector.blabblabblabblabblab
4.3 Amplification of the PMT Pulse
Even after the intrinsic amplification of the PMT, the generated pulses are too small for many applications.Because of this, additional amplifiers are often used (if they are built directly onto the PMT, they areoften referred to as preamplifiers“). Due to this amplification, the influence of noise contributions afterthe amplifier are reduced and the signal height is adapted to the dynamic range of the signal receivers(like discriminators) as well. Depending on the type, amplifiers can not only increase the signal amplitudelinearly, but also reverse the signal polarity and (whether desired or undesired) change the signal’s form.
The preamplifiers used in setup T20-1 generate both positive and very long (multiple µs) pulses. Sinceboth traits are unfavourable for the signal processing, additional CANBERRA amplifiers are employed,which invert the signal, shorten the pulses and increase their amplitude (set amplification & shaping timesensibly, observe on the oscilloscope), before the signal is forwarded.
The preamplifiers in the PMTs of setup T20-2 generate directly processable negative output pulses withamplitudes of several 100 mV and a pulse width of around 20− 40 ns.
4.4 NIM Components
The NIM (Nuclear Instrumentation Module) standard is the ”‘first and most simple standard in nuclearand high-energy physics”’ [?]. This standard defines module dimensions, operating voltages and connec-tors of so-called NIM modules, which can be operated in a NIM crate. There are a multitude of amplifiers,discriminators, voltage sources, coincidence counters, timers, etc., which adhere to this standard. Theprovided setups are made of different NIM modules as well, some of which were made at RWTH Aachen
17
Chapter 4. Setups
University, other were made by commercial manufacturers like Philips Scientific.
The NIM standard also defines connectors for coaxial cables (LEMO 00) and logic levels for digital signals.A fast NIM pulse (Fast-negative NIM Logic) is, as can be found in table ??, defined as a current pulseover 50 Ω. However, sometimes other common logic levels outside the NIM standard (e.g. (LV)TTL1: +3.3V/+5V, 0: 0V) are used, which often causes problems in the communication between differentmodules and requires the use of logic-level shifters.
Output current Voltage over 50 Ω
Logic 0 −1 mA to +1 mA 0 V
Logic 1 −14 mA to −18 mA −0.8 V
Table 4.1: Fast-negative NIM Logic.
Figure 4.8: Exemplar NIM pulse. Figure 4.9: Example of damping and dispersion ef-fects on a formerly rectangular NIMpulse.
Light sensor Amplifier Discriminator Counter
Detector
Figure 4.10: Simplified schematic of the signal route.
In this experiment, the analogue signal pulse is converted in a discriminator of type Philips Scientific
NIM Model 704 or NIM Model 715 into a binary NIM signal and from here on only digital signals willbe used. An arbitrary threshold between 10 mV and 1 V can be chosen using a screw. If an input signalof the discriminator rises above or falls below this level, a NIM pulse (-0.8V or -1.6 V if not properlyterminated using 50 Ω) with a so-called gate width τ of 2 ns to 100 ns is generated. This time τ mustbe measured and taken into account for the experiment. For setup T20-1, it is highly recommended tochoose the maximal gate width.The further signal path depends on the intended measurement. For example, for many measurements,the coincidence connection of multiple pots is required.
The setup of the crate electronics is shown below in fig. ?? and fig. ??.
18
4.5. Coincidence Circuit
The high-voltage module (HV module) is either available for each detector separately, or a dual HVmodule is provided. This is mostly because in general, the detectors posses different operating voltagesor operating plateaus. The electronics are cooled by an attached fan plate. It is important to ensure thatthe cooler is always turned on when the electronics are being used, or else a temperature build-up couldoccur inside the closely packed crate. The cooler should not be switched on or off during a measurement,since the resulting interference pulse in the vicinity of the crate could provoke false results.
4.5 Coincidence Circuit
For coincidence measurements, the discriminator signals of two or more sources are analysed together(cf. fig. ??). To this end, the NIM pulses of the discriminators are combined in a coincidence stage. Forthis purpose, a module developed at the RWTH is used. When two inputs are simultaneously active (inthis case two output pulses of the discriminators), a NIM pulse of predefined length is emitted from theoutput.
Figure 4.11: Simplified schematic of the signal path in a coincidence circuit.
If the coincidence window (gate τ) for the signal sources is chosen sufficiently small (in this case by pickingappropriate pulse lengths of the discriminators), both detectors have to signal practically simultaneouslyin order to generate an event. This is only the case when a fast particle passes through both pots one afterthe other, an interference pulse (either via the power grid or through the air) causes both discriminatorsto produce false pulses or two thermal electrons happen to induce an overlapping signal (proportionalto the gate length, single rate). Of course, only the first kind of events are wanted. If one succeeds insuppressing the others correspondingly, the measurement in coincidence allows for a much more reliabledetermination of the rate than a measurement with a single detector, since the probability for ”‘double”’false positives is much smaller. Analogously, it is possible to improve the quality of the measurementfurther by adding a third or fourth detector, provided these are available.
One disadvantage of this circuit is the limitation to a small solid angle when small, independent detec-tors are used (compare with a large detector, with several PMTs). This must be taken into account bya suitable calculation of the acceptance when determining the rate. For other measurements, like thedependence of the muon flux on the zenith angle or the absorption properties of matter w.r.t. the muonflux, this limitation to a set solid angle range smaller than 2π is desirable; here, the measurement incoincidence is practically the only possibility of realising the measurement. The signals measured sepa-rately or in coincidence are recorded by a counter (Canberra NIM Model 512). This counter possessestwo input channels, which can be used to e.g. monitor different discriminator thresholds or coincidencecascades of different heights.
How should the coincidence rate depend on the single rates qualitatively?How can one determine a relative efficiency of the detectors?
Interference
A small detector, like the pots used, which has no scintillator material and generates only Cerenkovphotons, creates comparatively small output pulses with a regular PMT. This means it is particularlychallenging to transfer the signal free from interference.But even if disturbances like cable damping and signal dispersion did not pose a problem, there is afundamental challenge with such an experimental setup: the coupling of electromagnetic disturbances.
19
Chapter 4. Setups
Essentially, this happens in two ways: electromagnetic waves, which induce voltages in antenna-like cableends in the setup, and fluctuations in the power supply of the setup.Interference pulses of this kind, caused for example by a switch being flipped in a neighbouring lab or bymobile devices, can sometimes exceed common discriminator thresholds and trigger false signals. Becauseof the comparatively low measurement rates, a measurement can easily be falsified in this way, since justturning on a nearby lamp produces up to 300 false events. For short measurements, these kind of jumpscan be recognised, but for long measurements this is practically impossible. Because of this, one shouldensure that no electronic devices like mobile phones are used right next to the crate.
Figure 4.12: Coupled disturbance (multiple triggering).
If the detectors receive an interference signal like in fig. ??, this can be identified and quantified afterthe measurement. To this end, the signal is recorded on a second, PC-based counter in addition to theNIM electronics. This counter provides the signals with a time stamp and displays them in individualtime bins. In this way, individual anomalies can be found.
What should be taken into account when handling analogue pulses?What could cause interference or false signals?
4.6 USB DAQ
The setup has a PC connection via USB interface (fig. ??). The control program AKaDeMy bundles manyloading and readout functions (fig. ??).Firstly, multiple displays allow for the simultaneous readout and checking of discriminator thresholds ofthe individual pots , removing the need for a multimeter. Other devices without displays, like for examplea high-voltage power source, can be read out and logged in this way as well. A counter allows to recordthe binned rate and to log it in arbitrary time intervals, which enables a time-resolved measurement. Thecounter input of setup T20-2 expects a positive logic level, so a logic-level shifter must be used to convertthe NIM pulses.
20
4.7. Poisson Statistics
Figure 4.13: NI Data Acquisition Boxwith USB connectivity.
Figure 4.14: Screenshot of the LabVIEW interface.
During this experiment, we come across voltages on the order of mV, V and kV; whatcauses these differences and in which part of the experiment can we find which voltages?
4.7 Poisson Statistics
Using the USB-DAQ, precise statistics on the measured signals can be collected. The Poisson distributiondescribes rare, independent events for a constant time interval. The discrete distribution is given by thefollowing equation:
P (X = k) =λk
k!· e−λ , (4.1)
with the number of signals k, and the characteristic parameter λ. The mean of the distribution is µ = λ,the standard deviation is determined by σ2 = λ.
Which quantity follows a Poisson distribution? Why? Based on this, how can one statethe relative statistical error?
4.8 Crate Front View
By default, both setups contain one or more high-voltage modules for the operation of the PMTs and adiscriminator for the conversion of the signal pulse to a NIM pulse with simultaneous adjustment of thethreshold. There also is a coincidence stage, a dual counter and the USB-DAQ.
As a special feature, setup T20-1 (see fig. ?? and fig. ??) includes two amplifier modules by CANBERRA.These are used to invert and amplify the PMT pulse and adjust (shorten) its pulse. On top of this, theyalso supply low-voltage power to the preamplifier of the PMT. The gain must be set to an appropriatevalue before the experiment.
For setup T20-2 (see fig. ?? and fig. ??) no additional amplification is necessary, as the PMT’s signalalready is sufficiently amplified inside the PMT mount.
21
Chapter 4. Setups
USB-DAQ
inpu t
Cooler
Cou
nter
Coin
ciden
ce
Am
plifier
Am
plifier
Discrim
inator
2-ch
annel H
V p
ower su
pply
Figure 4.15: Photo and schematic of the hardware inside the crate of setup T20-1.
High voltage
High voltage
Light sensor
Light sensor Preamplifier
Preamplifier
Voltage 12 V
Voltage 12 V
Amplifier
Amplifier
Disciminator Coincidence
USB-DAQ
Counter
Figure 4.16: Schematic of the final circuit of setup T20-1.
22
4.8. Crate Front View
Figure 4.17: Photo and schematic of the hardware inside the crate of setup T20-2.
Voltage 6 V
Voltage 6 V
Discriminator Coincidence
USB-DAQ
Counter
Level shifter
High voltage
High voltage
Light sensor
Light sensor Preamplifier
Preamplifier
Figure 4.18: Schematic of the final circuit of setup T20-2.
23
Chapter 4. Setups
4.9 Handling the Oscilloscope
This section is a short reminder of the most important settings of an oscilloscope, which will hopefullyreduce the workload of this experiment.First, one should always know which pulse shape (height, width, ...) is being viewed. Second, the signalshould be terminated at the inputs with 50 Ohms, to achieve the best shape possible.
Now, the oscilloscope is adjusted to fit the expected signal.
Figure 4.19: 4-channel oscilloscope, displayed in channel 1 is a NIM pulse (height −0.8 V, width ∼ 75 ns).
• Adjusting individual channels:By pressing the channel menu, individual channels can be concealed or displayed.The offset of each channel can be shifted up or down.The displayed voltage must be adapted to the pulse height - the scale changes the voltage intervalrepresented on the display by the height of each box. In the photo, each box along the y-axisrepresents 500 mV.
24
4.9. Handling the Oscilloscope
• The time interval shown:The time interval shown must be adjusted to the pulse length - the scale changes the time intervalrepresented on the display by the width of each box. In the photo (fig. ??), each box along thex-axis represents 50 ns.
• Triggering:One triggers on one channel. If this channel triggers, all other displayed channels are read outsimultaneously as well. This way, coincidences can be viewed as well.Pick a channel used for triggering; set the threshold; set whether triggering occurs on a rising orfalling slope.The trigger time can, to some extent, be shifted so the signal some time before or after the triggercan be viewed (the actual trigger time must not always be visible). Always at the beginning:SetToZero.In the photo (fig. ??), the oscilloscope is triggered at the falling slope of channel 1, as soon as thepulse falls below the threshold of −200 mV.
• Afterglow:Helpful can be enabling afterglow under ’Display’. This controls for how long the trace is displayed.Setting a long afterglow time makes it is easier to view coincidences.
Warning!! Many are taught the trick to first press Autoset on the oscilloscope, to reset it to the defaultsettings. But for the 4-channel oscilloscope used, this activates an internal amplification of the voltageby a factor of 10, which often leads to confusion! Use this feature with caution.
25
Chapter 5. Procedure
5 Procedure
Premeasurements (sec. ??)
• High-voltage behaviour of PMTs and suitable discriminator thresholds
• Methodical determination of the suitable HV settings of the individual detectors and the associateddiscriminator settings
• Rate versus HV and corresponding rate versus discriminator voltage for all detectors used
• How does the rate depend on the voltage? What does the graph look like and why?
Coincidence Circuit and Flux Measurement (sec. ??)
• What is the measured flux? What is the expectation?
Zenith Angle Dependence of the Muon Flux (sec. ??)
• Measurement of the muon flux in coincidence versus the zenith angle.
Measurement of Muon Shielding (sec. ??)
• How strong is the shielding? What do you expect qualitatively?
For this experiment, a USB flash drive should be brought along for the measurement data!
5.1 Basic Setup
First, the experiment should be set up and connected correctly. Before you continue, the setup should bedisconnected from the power grid and the main power switches should be switched off. These are locatedon the power strip at the edge of the trolley, as well as at the bottom-right of the crates. All unnecessaryLEMO cables can be removed.
Each required detector pot is connected to a separate high-voltage power supply using a red HV cable,if this is not already the case.
ATTENTION:DO NOT OPERATE THE PMTS IN THE POTS IN SETUP T20-1 OVER 1.5 kV /
IN SETUP T20-2 OVER 2 kV.
It should be checked beforehand that no high-voltage unit is set too high and only then should the cablebe connected. An ”‘open-circuit”’ voltage of 1 − 1.5 kV is compatible with the detectors used and isunproblematic. Only connect or disconnect any power cables when the power is switched off.
THE PHOTOMULTIPLIERS USED IN THIS LAB COURSE ARE VERY UNUSUAL WITHRESPECT TO THE MAXIMUM VOLTAGE, OTHER PMTS CAN TOLERATE E.G. ONLY 400 V.
The preamplifier of the pots (T20-1) requires an additional low-voltage power supply of ±12 V. Theconnection for this is located on the back of the CANBERRA Amplifier (Model 2022).The preamplifier of the pots (T20-2) requires an additional low-voltage power supply of ±6 V. The cable
26
5.1. Basic Setup
for this has a quadrilateral three-pole connection to the pot (T20-2) and must be plugged into the littledistributor module, which is connected to the edge of the crate.
The signal is received from the detector at the respective LEMO or BNC connection. LEMO-BNCadapters are potentially required. Optimally, all detectors should be connected using signal cables ofequal length, to avoid systematic differences in transmission delays during the measurements that follow.
Now, the setup is connected to the power grid (power plug) and the main switch on the power strip isswitched on. The PC/monitor as well as the crates can now be turned on as well. Since the DUAL-counter will be needed often, it is recommended to set appropriate measurement parameters (in particularmeasurement time, the threshold for NIM pulses is set to -250 mV by default) and to save these as a”‘preset”’. The menu navigation is somewhat more complicated than the handling of the other modules,so a quick look at the manual is recommended: the most important settings to check are the correct unitof time (second/minute), the expected polarity (positive/negative) and the measurement time.
The measurement program AKaDeMy should be started on the PC. This LabVIEW-based interface allowsfor the readout of operating voltages etc., making it an extended control panel of the crate. The operationhas been kept intuitive; in case no data is output, it should be checked that the USB cable is connectedand whether the respective data source is connected to the USB module.
For the following experiments, the signal cables are connected to the preamplifier if necessary (onlynecessary for setup T20-1) and its output is passed on to the discriminator. Unused outputs should beterminated with 50-Ohm resistors to prevent cable reflections (see photo ??).
Figure 5.1: Example of terminating an unused output with a 50-Ohm resistor.
The amplified signals are connected to the discriminator via the ”‘IN”’-socket. The adjusting screws toits right can be used to set the threshold and the output pulse width. The outputs connected by a lineare coupled. It is best to use separate outputs and to terminate each connected one with 50 Ohms. Theoverlined outputs output an inverted signal.
The current configuration is found in most of the experiments that follow, since in principle the signal isalways discriminated as a NIM pulse. Nevertheless, is can be helpful for diagnostic purposes to connectthe (un)amplified signal directly to the input of the oscilloscope. It is important here as well to terminatethe signal with 50 Ohms or to configure the oscilloscope accordingly, to get the correct signal.
It is a good idea to vary the voltages and thresholds and observe the reaction on the oscilloscope, PCand crate before the experiment, to get a feeling for the behaviour of the devices.
Hints:
• T20-1: do not increase any HV over 1500 V, increase and decrease the HV slowly, (un)plug onlyafter turning the voltage down and generally be careful in handling high voltages.
• T20-2: do not increase any HV over 2000 V, increase and decrease the HV slowly, (un)plug onlyafter turning the voltage down and generally be careful in handling high voltages.
• T20-1: The operating range of the PMTs lies between 0.5− 1.2 kV.
27
Chapter 5. Procedure
• T20-2: The operating range of the PMTs lies between 1− 1.7 kV.
• Mind the comparability of the circuit configuration and the measurements!
• Open input channels of the amplifier should be terminated (50 Ohms).
• Y connectors are handy, but lead to reflections and signal attenuation.
• Do not amplify signals twice.
• Especially for coincidence: the signals are delayed by about 1 ns per 20 cm length of cable.
• Amplifiers and other modules delay the signal as well (if needed check with the oscilloscope).
• ”‘Presets”’ make handling the counter considerably easier when switching on and off a lot (ask atutor).
• The program AKaDeMy must by switched on using the double-arrow button. A measurement can berestarted quickly this way, among other things.
• Should the USB software crash (switching the cooler on or off can cause this), un- and repluggingthe USB connector can reset the system; a test panel window appears if the restart was successful.
• Do not set the high voltage to VMAX, since doing this might cause the maximum operating voltageof the detectors to be exceeded.
• For high-voltage power supplies with analogue displays, the HV can be read out using the measure-ment program AKaDeMy. For all other high voltages, the HV is read out using the respective digitaldisplay of the power supply module.
• Never open the pots yourself!
What to do when ... ? :
• T20-1: My PMT operating range is not within the norm.Check whether the set amplification (course gain) at the amplifier is suitably matched with yourdiscriminator threshold (check using the oscilloscope). If the amplification is chosen too small, thevoltage across the PMT must be turned up too high in order to get a signal. Is the pot darkenedproperly?
• T20-1: I am not getting any coincidences.Check whether the same cable lengths and gate times are used for both pots! Is the amplificationthe same? One after the other, take a look at all signals from the PMT, amplifier and discriminatorof both pots simultaneously with the oscilloscope. Where can you see coincidences? Do the pulseshapes look the same for both pots?
• T20-2: My PMT has no single rate.Is the pot darkened properly? Has the discriminator threshold been set suitably (compare withPMT pulse using the oscilloscope)?
• T20-2: I am not getting any coincidences.Check whether the same cable lengths and gate times are used for both pots! One after the other,take a look at all signals from the PMT, amplifier and discriminator of both pots simultaneouslywith the oscilloscope. Where can you see coincidences? Do the pulse shapes look the same for bothpots?
5.2 Premeasurements
The amplification of a photomultiplier depends greatly on the high voltage applied. Is the voltage too low,then the amplification is not large enough, the noise is low as well; is the voltage too high, then the noiseof the PMT dominates the measurement, but the sensitivity for small fluctuations of the discriminatorthreshold is reduced, which is especially advantageous for the measurement in coincidence with lowthresholds. As can be seen clearly in fig. ??, small deviations of the threshold can influence the signal
28
5.3. Coincident Measurement and Flux
rate massively if the threshold itself is low.
Figure 5.2: Exemplar curve of detector ratesversus high voltage for a fixedmeasurement threshold.
Figure 5.3: Example of the detector rates ver-sus discriminator threshold for afixed high voltage.
For the high-voltage setting, there is generally a linear plateau region (using appropriate axes), whichis suitable for measuring. When choosing a voltage, a compromise must be made between a lack ofsensitivity, noise and a strong threshold dependence. Depending on the measurement setup, there canbe different options for the setting; the plateau is, however, a good interval to start with (fig. ??). ThePMTs used here may under no circumstances be operated with voltages over 1500V (T20-1) /2000V (T20-2). Remember that this maximum voltage varies from device to device and can definitelydeviate a lot. In other experiments of the lab course, for example, photomultipliers are used, which shouldonly be operated with voltages of at most roughly 400 V. It is therefore imperative, that one familiarisesoneself with the operating parameters of the devices before trying different voltages.
Because of this, the first measurement comprises determining the voltage plateaus of both detectors.For this purpose, an appropriate discriminator threshold must be chosen; for the discriminator rangeof 10 − 1000 mV, 400 mV is a good option. This setting may of course not be changed during themeasurement.Because the measurement rate for a given discriminator threshold in turn depends on the chosen highvoltage, one should wonder beforehand, which high voltage and threshold interval are to be consideredfor the given setup. To this end, it is useful to have a look at the input pulse to the discriminator on theoscilloscope.Next, both parameters should be sampled iteratively. When suitable ranges have been found, bothmeasurement curves should be measured, so that in the end, you have a voltage plateau for eachdetector and a discriminator curve (rate versus threshold) for both detectors.
Based on the voltage plateaus, a suitable voltage can be picked for the individual pots (hint: measuringin the middle of the plateau stabilises the rate, because the HV-rate dependence (fig. ??) flattens out,however this increases the noise of the individual detectors slightly). The uncertainties can be estimatedas well.
All measurements are to be done with water. THE POTS MAY NOT BE SCREWED OPEN!The graphs for the report are to include, as above, the statistical and systematic uncertainties. Hint: thestatistical uncertainty depends strongly on the detection rate.
It should be checked that single events are independent and therefore follow a Poisson distribution. Todo this, a single detector and a coincidence circuit should be measured using the program AKaDeMy for ameaningful time interval.
The muon rate should be measured overnight with the detectors in a perpendicular arrange-ment and in coincidence (see section Coincident Measurement). Do not forget to start thismeasurement!
5.3 Coincident Measurement and Flux
By measuring in coincidence using two detectors, a large portion of the noise can be eliminated. Becauseof this, it is possible to pick a really low discriminator threshold for each pot, such that the rate is not
29
Chapter 5. Procedure
yet dominated by noise, but as high a single rate of the detector as possible can be achieved.
For different types of detectors, the coincidence rate can be put into proportion with the single rate ofeach detector. To do this, the discriminator threshold of one detector is varied in sensible intervals, thesingle rate of this detector is measured and subsequently, the threshold of a second detector (e.g. bymaking use of the preparatory measurement of the discriminators) is changed in such a way, that thesecond rate matches the first. It should be noted, that signals travel different wiring paths, so in theunfavourable case, two signals of one particle do not arrive in the coincidence stage simultaneously. Oneshould ensure using the delay modules (for T20-2) and an oscilloscope (for both setups), that the gateand delay times have been set sensibly.Only then can the coincidence rate be determined and analysed. For more information, see sectionTheory/Coincidence Circuit.
A coincidence rate versus single rate curve should be recorded and provided with errors.The shape of the measured curve should be explained qualitatively. It should be noted that the lab courseroom on the first floor is shielded by concrete because of structural conditions.
The rate of coincidental coincidences from two coincidental processes with average rates of frequencies f1
and f2 and gate times τ1 and τ2 is estimated as follows:
fcoincidental = (τ1 + τ2)f2f1. (5.1)
The setup of the actual coincidence circuit is really simple. The output signals of the discriminatorare plugged into a 3-fold unit of the pink coincidence stage. The green LED on the right shows, whichchannels are being processed. The output signal on the bottom-right is then again a NIM pulse, whichcan be handed over to the counter, just like pulses from the discriminator. The coincidence stage is easilydamaged by improper handling. To ensure it is functioning correctly, its functionality should be testedwith identical signals before starting the experiment.
Where does the formula for coincidental coincidences (??) come from? Starting from whichsingle rates do the coincidental coincidences contribute significantly to the true rate?
5.4 Measurement of the Angular Dependence
To determine the angular dependence of the muon flux, one of the two detectors, with a vertical distanceh, is moved horizontally by a distance of b and in this manner the coincidence rate for different zenithangles θ is measured (see fig. ??). The circuit of the setup does not change here either. The zenithangle dependence φ(p, θ) ' φ(p)⊥ · cos(θ)n is to be studied. The nightly measurement of the verticalflux can be used as well. One takes into account, that the distance between the two detectors changesfor different angles. The measurement should include at least four sampling points. It is recommendedto think beforehand or during the measurement about how much measurement time is needed, to get asensible compromise between statistical error and measurement duration.
5.5 Influence of Shielding
For the shielding measurement, the trolley is to be set up on several floors of tower 28 of the PhysicsCentre and the vertical coincidence rate measured. To do this, two pots are placed directly above eachother. In addition to this, the dimensions of the ceilings are to be determined. The density of concrete isroughly ρ ' 2.3 g
cm3 [?]. The measured rate should be plotted against the thickness of the concrete andthe material depth and discussed. The setup is essentially the same as for the coincidence measurement.It is important to note, where the field of view of the coupled detectors points. As can be seen in figure??, the detectors will ”‘look”’ into a solid concrete column if they are placed too close to load-bearingwalls. A compromise between distance to the walls and spatial requirements of the setup is to be made.Please do not obstruct the entire tower! It should also be ensured that others do not trip over the powercable.
30
5.6. Analysis of the Measured Data
Figure 5.4: Experimental setup for the measurement of the angular dependence (left). Schematic repre-sentation of the intersection of the view cone with the floors and a wall (right).
5.6 Analysis of the Measured Data
A USB flash drive should be brought along for the measured data. The analysis is done using a programof choice.
Measured values and results should be presented with both systematic and statistical uncertainties.
At least the following must be in the report:
• One graph of measured rate versus discriminator threshold for each detector used
• One graph of measured rate versus high voltage for each detector used
• Graph for the Poisson statistics of the single and coincidence rates
• Graph coincidence rate versus single rate
• Graph measured rate versus zenith angle including the expected curve
• Graph measured rate versus shielding including the expected curve
All graphs should include statistical and systematic uncertainties and the curves should be discussed. Thegraphs rate versus shielding and rate versus angle should additionally be compared with the theoreticallyexpected values. Any deviations from the expected curve should be discussed.
HINT: THE TWO SETUPS ARE NOT IDENTICAL AND THE MEASURED RATES CAN DIFFERGREATLY AS A RESULT OF THIS!
31
Appendix A. Pierre Auger Observatory
A Pierre Auger Observatory
A.1 Ultra-High-Energy Cosmic Radiation
The charged, low-energy particles of the cosmic radiation are deflected many times by magnetic fieldsalong their journey and therefore hit Earth isotropically, i.e. their sources cannot be deduced from theirdirection of incidence.
However, the detection of particles of the ultra-high-energy radiation (charged particles with energies ofover 1018 eV) would allow the direction of origin to be reconstructed. Together with the measurementof the elemental composition and the energy spectrum, conclusions can be drawn about the sources ofcosmic rays.
The highest-energy particle detected thus far had an energy of 1020 eV. Such a thing should not evenexist, according to conservative physical estimates, because no convincing sources are known to existin our cosmological neighbourhood and because the particles appear to arrive from all directions withroughly the same frequency, which suggests distant sources. There are several candidates for these - butparticles should not be able to reach us from such great distances with the measured 1020 eV. This isforbidden by a theoretical physical limit, the GZK-cutoff.
The existence of high-energy particles therefore raises several scientific questions (summary [?]):
• Where does this radiation come from and what is it made of?
• What are its sources and how are the elementary particles accelerated to such high energies?
• How do cosmic rays propagate through the interstellar medium towards Earth?
• Are the properties of the radiation changed as they propagate?
• What are the highest occurring energies in the cosmic radiation?
As the rate of cosmic rays that reach Earth with the highest energies is so low
1 Teilchen pro Jahrhundert und km2
giant detector fields are required on the surface of the Earth to achieve sufficient statistics.
Figure A.1: Is this a source of the highest-energy particles of the cosmic radiation? Stylisedimage of an active galactic core. Image by ESA/Christophe Carreau/ATG medialab.
32
A.2. The Pierre Auger Observatory
A.2 The Pierre Auger Observatory
The Pierre Auger Observatory is currently thelargest and most accurate experiment for themeasurement of cosmic rays.In a first, this installation employs a hybrid-technique to measure air showers, i.e. air show-ers are detected by a surface detector field (SD)as well as by optical telescopes (FD). The simul-taneous measurement of air showers using bothdetection methods greatly reduces the uncertain-ties of the measurement.With the 1600 surface detectors, 5 telescopebuildings and a surface area of approximately3000 m2 (fig. ??), measurements are possible upinto the range of the highest-energy cosmic rays.The experiment is stationed on the PampaAmarilla in Argentina, near the city of Malargue.Starting here, the net of surface detectors isspread out towards the north with gaps of 1.5 kmeach.
Figure A.2: Sketch of the Pierre Auger Observa-tory. The grey dots represent the indi-vidual tanks of the surface detector, thecoloured lines indicate the fields of viewof the optical telescopes.
The surface detector of the Pierre Auger Obser-vatory consists of a total of 1600 water Cerenkovtanks filled with ultrapure water (fig. ??, [?]).Every tank has a base area of 10 m2, is 120 cmtall and thus contains 12 tonnes of water. Sincethe speed of light is slower in water than invacuum, the penetrating particles can produceCerenkov light. To measure the Cerenkov light,two highly sensitive photomultipliers have beenplaced in each tank. All tanks are autonomousstations, which are powered by solar power andforward their signal via communication anten-nae.With the water Cerenkov tanks of the surfacedetector, the Pierre Auger Observatory possessesan instrument that allows it to measure nearly100% of the time.Basically, there are two modes, when the dataof the water Cerenkov tanks is saved. The firstis in hybrid mode together with the fluorescencedetector and the second is in standalone mode,when three different tanks in a smaller area see asignal. Both modes allow for an unusually goodreconstruction of the direction.
Figure A.3: Sketch of the water Cerenkov tanksused at the Pierre Auger Observatory.The Cerenkov light is detected by twophotomultipliers.
33
Appendix A. Pierre Auger Observatory
In five building on the edge of the detector field, a total of 27 fluorescence telescopes observe the sky overthe detector field during clear, dark nights (15% of the measuring time). While the particle distributionof air showers on the surface is measured using the tanks, the glowing trace can be used to reconstructthe evolution of the number of particles along the shower path through the atmosphere. This is possible,because the charged particles in the shower excite the nitrogen molecules in the air, causing them to emitultraviolet fluorescence light, which can subsequently be detected by the highly sensitive optics of thefluorescence telescopes. To this end, the incident light is collected using a large mirror surface of roughly12 square metres and bundled onto a camera made of 440 photomultipliers where it is detected. Theresults of the fluorescence telescopes allow for the best determination of the energy of an event and aretherefore used, among other things, to calibrate the entire experiment.
Knowing the fluorescence rate of air and the atmospheric conditions at the detector are very important forthe interpretation of the data. The data required for this are obtained through additional measurements.
A summary of the interplay of both complementary detection mechanisms is illustrated in figure ??.
The Pierre Auger Observatory has already obtained many important findings about the cosmic radiationusing this method of measuring extensive air showers [?]. The most important of these is the verificationof the theoretically predicted drop in the cosmic ray flux towards the highest energies (see figure ??).But additional knowledge about e.g. extra-galactic magnetic fields has also been gained and the modelshave been refined every time. As a result, many improvements have been made to simulations of particlepropagation from the source towards Earth, which is very important for the search for sources of cosmicrays.
Surface detector (SD)
1.5 km
Mirror
Camera
Fluorescence detector (FD)
Primary particle
Shower front
Shower axis
Θ
30°
several km
Fluorescence light (early)Fluorescence light (late)
Figure A.4: Detection principles at the Pierre Auger Observatory in Argentina. The surface detectorand the fluorescence detector already successfully measure air showers, which are induced bycosmic rays. The surface detector measures the particle distribution on the surface and thefluorescence detector measures the shower evolution through the atmosphere.
34
A.3. Planned Upgrade
Shown is figure ?? is shower event 201100102713of February 1, 2011. This is a hybrid event withan energy of E ' 6 · 1018 eV, which was seenby fluorescence telescopes in telescope buildingLoma Amarilla and seven tanks of the surfacedetector. The red (FD) and the blue (SD)lines indicate the reconstructed direction of theshower. The lines connected to the fluorescencetelescope show the evolution of arriving fluores-cence light over time. The size of the circles onthe surface represent how much energy was de-posited in the hit tanks of the surface detector.
Figure A.5: Shower event at the Pierre AugerObservatory.
A.3 Planned Upgrade
To achieve an even better examination of the air shower, the Pierre Auger Observatory is working toadditionally determine the muonic component separately. In the future, with the planned upgrade ofthe installation, the scientists at the Pierre Auger Observatory want to determine the precise number ofmuons. The installation of an additional muon detector would permit determining the properties of theprimary particle for every single shower: for example a heavy or a light atomic nucleus, a proton or agamma quantum. Today, such a statement can only be made based on statistics.
This would enable the study of arrival direction and energy of each type of particle separately. Thedecline in the number of incoming particles of the cosmic radiation towards high energies can thereforealso be considered for each type of particle separately:There are several models, which are predicted by elementary particle physics and can explain this decrease.The two generally favoured theories are the GZK-cutoff, i.e. the interaction of cosmic rays with thecosmic microwave background, and the reaching of the maximum energy, that the accelerators of thecosmic radiation can muster.
After the upgrade, these models can be verified efficiently and tested for the predictions of fundamentalphysics, which will be inaccessible using accelerators on Earth for a long time. If this is successful, wegain valuable information about the acceleration mechanisms and sources of the cosmic radiation.
35
Appendix B. IceCube
B IceCube
In this chapter, the principal detection method for neutrinos, as well as the setup and functionality ofthe neutrino detector IceCube are briefly explained.
B.1 Detection of Neutrinos
Neutrinos are electrically neutral elementary particles and belong to the family of leptons. There arethree neutrino flavours in the standard model of particle physics: the electron, muon and tau neutrino.They only interact via the weak force1 and have a very small cross section. Because of this, they passthrough matter almost unimpeded. This is why they are excellent messengers of the most energetic eventsin the universe, since unlike light, they can escape effortlessly from extremely dense environments, likethe innards of cosmic particle accelerators, and are not deflected by magnetic fields along their journeytowards Earth.
When neutrinos interact with matter, with a nucleus N to be precise, this happens via one of twofundamental processes:
On the one hand, a neutrino can interact via the neutral current with the nucleus, this means a Z0
gauge boson is exchanged in the reaction and the neutrino remains. A hadronic cascade X is created asa reaction product of this interaction:
ν +N → ν +X (B.1)
On the other hand, a neutrino can be converted into a lepton l of the same flavour by exchanging a W±
gauge boson. This reaction via the charged current also produces a hadronic cascade:
ν +N → l +X (B.2)
Detecting the charged lepton is possible using Cerenkov radiation, which is emitted by the lepton duringits flight through the detector material.From the detection of Cerenkov photons with optical sensors, the energy and direction of the lepton canbe reconstructed. At high energies, the direction of the charged lepton is correlated with that of theneutrino. Thus, the detection of the lepton allows for conclusions on the original neutrino properties tobe drawn.
In principle, all three lepton flavours can be used for detection, but muons are particularly suitablefor a good direction or track reconstruction. Muons create long tracks in the detector (see figures ??,??), because they have a relatively large mass and a long life time. Electrons, on the other hand, arereabsorbed almost immediately, because they interact with the atoms much more strongly (see figures??, ??). Tau leptons generate very bright, but also very short cascades. They decay quickly because oftheir high mass and therefore only leave a short track (see figures ??, ??).
Not only the charged lepton, but also the cascades produce Cerenkov light. They look like point lights,though, and no longer contain any directional information. For this reason, the primary focus of aneutrino detector is the detection of the produced lepton.
1Gravity can be neglected because of the tiny masses of the neutrinos.
36
B.1. Detection of Neutrinos
Figure B.1: Signature of a muon neutrino, whichinteracts outside of the detector [?].The created muon leaves behind a cleartrack through the detector. The greypoints represent optical modules.
Figure B.2: Signature of a 3 PeV muon neutrino inIceCube [?]. The produced muon orig-inally has an energy of 1.6 PeV and inthe middle of the detector still has anenergy of 300 TeV. The colours indicatethe order in time of the hit modules (red- early, blue - late).
Figure B.3: Signature of an electron neutrino [?].The created electron is reabsorbed im-mediately and produces a hadronic(yellow) as well as an electromagnetic(blue) cascade. The grey points repre-sent optical modules.
Figure B.4: Signature of a 3 PeV electron in Ice-Cube [?]. The colours indicate the or-der in time of the hit modules (red -early, blue - late). The grey points rep-resent the other optical modules.
37
Appendix B. IceCube
Figure B.5: Signature of a tau neutrino [?]. Theproduced tau decays immediately andproduces a hadronic (yellow) cascade.
Figure B.6: Simulated signature of a 583 TeV tauneutrino in IceCube [?]. The eventdemonstrates the characteristic “doublebang” structure. The colours indicatethe order in time of the hit modules(red - early, blue - late). The grey cir-cles represent the hadronic interactionpoints.
B.2 IceCube Neutrino Observatory
Figure B.7: Sketch of an optical module ofIceCube.
The IceCube neutrino observatory is located at thegeographic south pole and uses the mostly clearAntarctic ice as detector material. It is currentlythe largest neutrino telescope and possesses an in-strumented volume of roughly 1 km3.Located inside this volume are 5160 optical sensors,the so-called digital optical modules (DOMs, seesketch in figure ??), at a depth of 1450 m to 3450 m.These are attached to 86 vertical strings with avertical separation of 17 m. The distance betweenthe strings is approximately 120 m. All opticalsensors contain a photomultiplier, whose data isrecorded and read out via a DAQ (data acquisition).The holes needed for the strings were drilled intothe 3-kilometre-thick ice sheet with the help of 80
to 90 water.
With this setup (see figure ??), IceCube collects information on astrophysical neutrinos in an energyrange from ' 100 GeV up to several PeV. The detection depends on the quality of the ice, though, and sois affected by the so-called dust layer, a layer of dust located about 2100 m below the surface. Cerenkovlight is absorbed by the dust layer and can therefore no longer be used for the detection, i.e. informationis lost.
The largest background source for the detector are atmospheric muons, which are not created by aneutrino interaction, but in cosmic showers (see section ??). To reduce this background, one can use
38
B.2. IceCube Neutrino Observatory
the fact that neutrinos only interact weakly. Because of this, they can, unlike other particles, penetratethe Earth unhindered in greater numbers. The Earth serves as a filter for atmospheric muons from thenorthern hemisphere. When neutrinos interact with a nucleus in the detector volume, the muon trackspoint in almost the same direction as the original neutrino. All optical modules on the strings thereforelook towards the centre of the Earth. This method is used, among other things, to look for extraterrestrialneutrino sources in the northern hemisphere.
To be able to distinguish the signal and background muon events from the southern hemisphere, additionalcriteria are required. For the detection of extraterrestrial neutrinos, IceCube therefore requires a signalevent to start inside the detector and be highly energetic. Atmospheric neutrinos would always leavetracks that already existed before entering the detector.
Figure B.8: Schematic side view of the IceCube neutrino observatory. Indicated are IceTop (detector forair showers), the IceCube detector and DeepCore (a low-energy extension of IceCube). Imageby the IceCube Collaboration.
39
Appendix B. IceCube
B.3 Detection of Extraterrestrial Neutrinos
The first proof for extraterrestrial high-energy neutrinos was provided in April 2012 by the discovery ofthe two at that time most energetic neutrino events: Ernie and Bert.The deeper search, the results of which have been presented recently ([?], [?]), revealed another 26 eventswith energies above 30 TeV - significantly more than what is expected for neutrinos produced in theEarth’s atmosphere.
In figure ??, the data is compared with the expectations of all backgrounds, e.g. of atmospheric muons.A deviation from the expected background towards high energies is clearly visible. So these must beextraterrestrial neutrino events.
A spatial or temporal accumulation of the 28 events, which would point at a specific cosmic source, couldnot be determined thus far, as the number of events is still too small (see figure ??). But increasedstatistics in the years to come and a joint analysis with experiments of cosmic radiation, like e.g. thePierre Auger Observatory, will more strongly narrow down the selection of source candidates.
Figure B.9: Shown is the deposited energy of allhighest-energy neutrino events mea-sured by IceCube over 622 days [?]. Thenumber of events are compared withthe theoretical predictions for the back-ground. Apparent is a deviation fromthe background towards higher ener-gies: proof of extraterrestrial neutrinos.
Figure B.10: Sky map of the most energetic de-tected neutrino events in equatorialcoordinates [?]. The plus signs (+)indicate cascade events, the crosses(x) muon track events. The greycurve indicates the position of thegalactic plane.
40
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