Detector Cell Performance Tests and Determination of Polarisation
Characteristics for PoGO+
Author:
Linda Eliasson lindaeli@kth.se
Department of Physics
Royal Institute of Technology (KTH)
Supervisors:
Maxime Chauvin
Mark Pearce
October 23, 2016
Typeset in L A TEX
TRITA-FYS 2016:68 ISSN 0280-316X
ISRN KTH/FYS/– 16:68 –SE
©Linda Eliasson, 2016
Abstract
PoGO+ is a balloon-borne polarimeter that aims to measure the hard X-ray polarisa- tion properties of the Crab and Cygnus X-1. The instrument is an upgraded version of the PoGOLite Pathfinder and based on knowledge and experience from its maiden flight in 2013. It consists of 61 scintillator assemblies - detector cells - confined in an anticoincidence system and makes use of Compton scattering to measure the polarisation properties of the celestial targets.
Before the flight each detector cell is tested and calibrated followed by an evaluation of the polarimeter performance. An automated calibration system in LabVIEW was de- veloped for long time data acquisition with interspersed background measurements to account for a varying background spectrum. The system has been used to performance test the detector cells in PoGO+ and to estimate the measured modulation factor M for a 90 ◦ Compton scattered, highly polarised beam.
A figure-of-merit for performance tests is the detector cell sensitivity that measures the PMT generated number of photoelectrons per deposited keV in each cell. The perfor- mance tests on the assembled detector concluded that all detector cells functioned and previously measured detector cell sensitivities were updated due to relative PMT effi- ciency differences that had not been accounted for.
In order to estimate the neutron background rate, PoGO+ uses two LiCAF scintilla- tors. Function tests and calibrations were performed, concluding that these neutron scintillators could be used for flight.
Finally, the measured modulation factor was calculated when 90 ◦ Compton scattered
radiation from a Am-241 source irradiated the polarimeter. Fitting the modulation curve
resulted in M = (37.86 ± 0.89)% and a polarisation angle Ψ = (–1.53 ± 0.67) ◦ . Calculat-
ing M using Stokes parameters resulted in M = (37.80 ± 0.84)% and a polarisation angle
Ψ = (–2.01 ± 0.65) ◦ . The results show a 78% relative improvement from the detector
design flown in the PoGOLite Pathfinder mission in 2013.
Sammanfattning
PoGO+ ¨ ar en ballongburen polarimeter med m˚ alet att m¨ ata polarisationsegenskaperna hos h˚ ardr¨ ontgen fr˚ an Krabbnebulosan och Cygnus-X1. Instrumentet ¨ ar en uppgraderad version av PoGOLite Pathfinder och baseras p˚ a kunskap och erfarenhet som f¨ orv¨ arvats under dess f¨ orsta flygning ˚ ar 2013. Det best˚ ar av 61 scintillatorstrukturer - detektorceller - inneslutna i ett antikoinsidens-system och anv¨ ander sig av Comptonspridning f¨ or att m¨ ata polarisationsegenskaperna hos himlakropparna.
F¨ ore flygningen testas och kalibreras samtliga detektorceller, f¨ oljt av en utv¨ ardering av polarisationsegenskaperna. Ett automatisk kalibreringssystem i LabVIEW har utvecklats f¨ or att f¨ orv¨ arva l˚ angtidsdata varvat med bakgrundsm¨ atningar f¨ or att b¨ attre kunna upp- skatta ett varierande bakgrundsspektrum. Systemet har anv¨ ants f¨ or att m¨ ata prestandan hos detektorcellerna i PoGO+ samt best¨ amma den uppm¨ atta modulationsfaktorn M f¨ or 90 ◦ Comptonspridd str˚ alning.
Ett godhetstal som anv¨ ants i prestandatesterna ¨ ar detektorcellk¨ anslighet som m¨ ater det PMT-genererade antalet fotoelektroner per deponerad keV i varje detektorcell. Pre- standatesterna gjorda p˚ a polarimetern visade att samtliga detektorceller fungerade och tidigare uppm¨ atta detektorcellk¨ ansligheter uppdaterades p˚ a grund av relativa PMT- effektivitetsskillnader som tidigare ej betraktats.
F¨ or att kunna uppskatta neutronfl¨ odet i bakgrundsstr˚ alningen anv¨ ander PoGO+ tv˚ a LiCAF-scintillatorer. Efter att funktionstester och kalibreringar gjorts, drogs slutsatsen att neutrondetektorerna fungerade och kunde anv¨ andas f¨ or flygningen.
Slutligen uppskattades modulationsfaktorn n¨ ar ett 90 ◦ Comptonspritt str˚ alningsprov fr˚ am Am-241 bestr˚ alade polarimetern. Kurvanpassning av modulationskurvan resultera- de i M = (37.86±0.89)% och polarisationsvinkeln Ψ = (–1.53±0.67) ◦ . D˚ a polarisationse- genskaperna ber¨ aknades med Stokes parametrar drogs slutsatsen att M = (37.80±0.84)%
och polarisationsvinkeln Ψ = (–2.01 ± 0.65) ◦ . Resultaten inneb¨ ar en relativ f¨ orb¨ attring
med 78% j¨ amf¨ ort med tidigare detektordesign som fl¨ ogs med PoGOLite 2013.
Contents
1 Introduction 3
1.1 Introduction to X-ray Astrophysics . . . . 3
1.2 Outline of the Thesis . . . . 4
1.3 Author’s Contribution . . . . 4
2 X-ray Polarimetry in Astrophysics 5 2.1 Polarisation . . . . 5
2.1.1 Concept Description . . . . 5
2.1.2 Stokes Parameters . . . . 6
2.2 Astrophysical Processes . . . . 7
2.2.1 Compton Scattering and Inverse Compton Scattering . . . . 7
2.2.2 Cyclotron Radiation . . . . 8
2.2.3 Synchrotron Radiation . . . . 9
2.2.4 Curvature Radiation . . . . 10
2.3 X-ray Objects . . . . 10
2.3.1 Pulsars and Nebulae . . . . 10
2.3.2 X-ray Binaries . . . . 12
2.3.3 Gamma Ray Bursts - GRB . . . . 13
2.3.4 Active Galactic Nuclei - AGN . . . . 13
2.4 Detection Techniques . . . . 13
2.4.1 Interaction Processes in Compton Polarimeters . . . . 13
2.4.2 Scintillators . . . . 14
2.4.3 Photomultiplier Tubes - PMTs . . . . 16
2.4.4 Polarisation Measurements . . . . 17
3 PoGO+ 19 3.1 The Design of PoGO+ . . . . 19
3.1.1 SDC . . . . 20
3.1.2 Photomultiplier Tube . . . . 21
3.1.3 Shielding . . . . 22
3.1.4 Neutron Detectors . . . . 22
3.1.5 The Assembled Polarimeter . . . . 23
3.2 Data Selection and Polarisation Measurement . . . . 24
4 The Automated Calibration System 29 4.1 Introduction . . . . 29
4.2 Setup: Mechanical Test Frame and Automatic Calibration System . . . . 30
4.2.1 Improvements of the Automated Calibration System . . . . 31
5 Investigation of the Detector Cell Sensitivity 33 5.1 Introduction . . . . 33
5.2 Data Collection and Analysis Method . . . . 33
5.3 Analysis and Results . . . . 35
5.3.1 Waveform Selections . . . . 35
5.3.2 DCS Determination and Comparison . . . . 38
5.3.3 Investigation of PMT Efficiency Dependence on DCS Determination 39 5.4 Discussion and Conclusion . . . . 41
5.4.1 Additional Sources of Error . . . . 42
5.4.2 Statistical Error . . . . 42
5.4.3 Conclusion . . . . 42
6 Testing and Calibration of LiCAF Neutron Scintillators 45 6.1 Introduction . . . . 45
6.2 Data Collection and Analysis Method . . . . 46
6.3 Analysis and Results . . . . 48
6.3.1 New Fast and Slow Separation Estimate . . . . 48
6.3.2 Analysis and Results . . . . 49
6.4 Discussion and Conclusion . . . . 55
7 Polarisation Measurements 57 7.1 Introduction . . . . 57
7.2 Data Collection and Analysis Method . . . . 57
7.3 Analysis and Results . . . . 63
7.4 Discussion and Conclusion . . . . 68
7.4.1 Fast and Slow Separation . . . . 70
7.4.2 Statistics . . . . 71
7.4.3 Conclusion . . . . 71
8 Acknowledgments 72
A Polarisation Analysis 77
Bibliography 81
Chapter 1 Introduction
1.1 Introduction to X-ray Astrophysics
Throughout the centuries mankind has been fascinated by the sky and studied astronomi- cal objects visible from earth. During the last decades construction of airborne telescopes has given astronomers and astrophysicists the possibility to study radiation outside the optical, IR and radio energy ranges of the electromagnetic spectrum. This opened up the field of X-ray astronomy. In 1962 Riccardo Giacconi and his team discovered extrasolar X-rays from Scorpius-X1 [1]. About a decade later they found pulsating X-rays from Centaurus X-3, leading to the discovery of X-ray pulsars [2].
The Crab system consists of a pulsar and a pulsar wind nebula (PWN). Due to its brightness in a broad energy range from radio to gamma rays it is a natural system to study in the aim of learning more about the physical processes in a pulsar. Many telescopes such as Hubble, Chandra and Fermi have studied the Crab but there are still question marks left. One of the big issues to resolve is the emission processes of the high energy radiation. Where do the emitting particles accelerate? Several models about the acceleration processes taking place in both the pulsar and the nebula exist but so far observations haven’t been able to distinguish the models from each other. Polarisation measurements in the X-ray region give an additional variable to the models that therefore can be either rejected or eventually accepted. In addition, studying the polarised radia- tion can give more knowledge about magnetic fields in systems with a pulsar and a PWN.
In 2013, the balloon borne polarimeter PoGOLite Pathfinder studied the Crab system in a nearly circumpolar flight. The data collected during that flight was not enough to draw any conclusions and the main purpose was merely to test the polarimeter design.
Experience from the 2013 flight has been used to optimise the instrument from PoGO-
Lite to PoGO+ that plans to study the Crab system in the summer of 2016. The aim
with PoGO+ is to measure the polarisation fraction with 5σ significance. In addition
a secondary target - the X-ray binary Cygnus X-1 - will be studied if it is in the hard
state [3].
1.2 Outline of the Thesis
The following chapter, chapter 2, gives an introduction to astrophysical processes giv- ing rise to polarised X-rays together with a description of the basic concepts in X-ray polarimetry. Chapter 3 describes PoGO+ and gives an overview of the basic waveform selection principles. Chapter 4 gives a description of the automatic calibration system that was developed for this thesis. It was used to performance test the detector cells and to generate the longtime calibration measurements with interspersed background measurements required to be able to perform reproducible calibration measurements of the polarimeter. Chapter 5 describes the performance tests and analysis made on the detector cells using the comparable figure of merit detector cell sensitivity. In chapter 6 the performance tests on the neutron detectors are described and in chapter 7 the auto- mated calibration system was used to perform measurements to estimate the modulation factor measured by the polarimeter when irradiated by a 90 ◦ Compton scattered beam.
1.3 Author’s Contribution
The thesis was conducted with the PoGO collaboration, where existing software devel- oped by the members of the collaboration was accessible. Parts of that pre-existing software has been further developed and used to perform the analysis presented in chap- ters 5, 6 and 7. The author participated in data acquisition when the detector cell and neutron detector functional tests described in chapters 5 and 6 were performed.
LabVIEW software developed for earlier testing procedures has been modified and up-
graded with new operations suitable for the calibration conducted before the flight in
2016. In addition a simple electric circuit has been built to integrate software and me-
chanics in the test system.
Chapter 2
X-ray Polarimetry in Astrophysics
2.1 Polarisation
2.1.1 Concept Description
Consider a sinusoidal electromagnetic wave propagating in the ˆ x–direction and where the electric and magnetic fields are described by
E ¯ 1 (x , t ) = E · sin(ωt – kx + δ 1 )ˆ y (2.1) and
B ¯ 1 (x , t ) = B · sin(ωt – kx + δ 1 )ˆ z (2.2) The ¯ E–field direction, here the ˆ y–direction, is denoted the polarisation direction. Since the electric field is oscillating in only one direction it is said to be linearly polarised in the ˆ y–direction. Another wave with the same amplitude as the wave described above but linearly polarised in ˆ z–direction is described as:
E ¯ 2 (x , t ) = E · sin(ωt – kx + δ 2 )ˆ z (2.3) and
B ¯ 2 (x , t ) = B · sin(ωt – kx + δ 2 )ˆ y (2.4) Consider now a wave with the electric field ¯ E and magnetic field ¯ B, superimposed by the waves above. If δ 2 = δ 1 , the resulting wave is still linearly polarised but the direction of the resulting electric field is 45 ◦ from the y-axis, towards the z-axis. The direction of the field will not change with time, only the amplitude.
If on the other hand δ 2 = δ 1 + 90 ◦ the ¯ E–direction changes with time but its ampli- tude remains. The superimposed wave is now circularly polarised. A superimposed wave that has a phase shift 0 ◦ < δ < 90 ◦ is called elliptically polarised [4]. Like the majority of all polarimeters used in astrophysics [5], PoGOLite and PoGO+ can only measure linear polarisation. Therefore only linear polarisation will be considered in this thesis.
Polarisation fraction and polarisation angle describe the polarisation in the radiation
coming from a source. The polarisation angle is the same as the angle to the electric
vector due to some reference direction and the polarisation fraction is a measure of the
(a) Polarisation ellipse (b) Poincar´ e Sphere
Figure 2.1: The polarisation ellipse and Poincar´ e sphere can be used to picture how the Stokes parameters are connected to the polarisation. The polarisation ellipse to the left shows that if χ = 0 ◦ the polarisation is linear: the angle Ψ is not changing with time. The right figure shows how the Poincar´ e sphere is spanned by the three Stokes parameters S 1 , S 2 and S 3 . S 0 represent the intensity I and the intensity fraction Ip gives the radius of the sphere. Adapted from [6].
amount of a photon beam that is polarised in that direction. It is worth to remind that all individual photons are 100% polarised, so if the polarisation fraction is zero the photons have an isotropically distributed polarisation.
2.1.2 Stokes Parameters
The Stokes parameters are four parameters, S 0 – S 3 , that can be used to describe the po- larisation characteristics of an electromagnetic wave. The parameters can be understood by studying figure 2.1 that shows a polarisation ellipse and a Poincar´ e sphere. The arrow in figure 2.1a pictures how the ¯ E–field changes with time. If χ = ±45 ◦ the polarisation ellipse becomes a perfect circle and the polarisation is circular, If on the other hand χ = 0 ◦ the ¯ E–field moves along the red line in the figure, without changing its direction.
The polarisation is in that case linear. In figure 2.1b S 1 – S 3 span the Poincar´ e sphere with the radius Ip, I being the intensity of the beam and p the polarisation fraction.
Using the variables in the figures, the Stokes parameters can be defined as:
S 0 S 1 S 2 S 3
=
I
Ip · cos (2Ψ) cos (2χ) Ip · sin (2Ψ) cos (2χ)
Ip · sin (2χ)
=
I Q U V
(2.5)
Since only linear polarisation is considered, χ = 0 ◦ in this thesis and the V term is neglected. The factor two in front of Ψ is due to symmetry: the polarisation angle Ψ can’t be distinguished from the angle Ψ + 180 ◦ , which is the polarisation ellipse rotated by 180 ◦ . From these parameters, the polarisation angle is given by
Ψ = 1
2 tan –1 U Q
(2.6) and the polarisation fraction
p =
p Q 2 + U 2
I (2.7)
2.2 Astrophysical Processes
The observed polarisation depends on the emission processes and the line-of-sight of the observer. Below follows a brief description of common astrophysical processes that produce polarised radiation.
2.2.1 Compton Scattering and Inverse Compton Scattering
Figure 2.2: Representation of the Compton scattering process: An incoming photon with energy E (red) and polarisation direction ¯ p (green) scatters off an electron with scattering angle θ, resulting in energy E’ (blue). φ is the azimuthal scattering angle with respect to ¯ p.
The probability that a polarised photon will Compton scatter is given by the Klein- Nishina differential cross section formula
dσ dΩ = r 2 0
2
E 0 E
2 E 0 E + E
E 0 – 2sin 2 θcos 2 φ
(2.8)
E 0
E = 1
1 + E
m e c 2 (1 – cosθ) (2.9)
where r 0 is the classical electron radius, m e is the electron rest mass, E and E 0 are the energies of the incident and the scattered photons, θ is the polar scattering angle and φ is the azimuthal scattering angle with respect to the polarisation vector [7]. A represen- tation is seen in figure 2.2.
Two conclusions can be drawn from equation 2.8. First, the scattering probability is
at its maximum when φ = 90 ◦ . In other words, Compton scattering favour the direc- tion perpendicular to the polarisation direction. Second, by scattering an unpolarised radiation by θ = 90 ◦ , the φ–dependence creates an anisotropy resulting in an almost completely polarised beam. In the same way a polarised beam can be less polarised by Compton scattering, causing a change in the polarisation fraction when the beam travels from an astrophysical source to a distant observer.
In inverse Compton scattering a low energy photon gains energy by scattering off a highly relativistic electron that subsequently loses energy in the process. With an addi- tion of a Doppler boost due to the relativistic kinematics, inverse Compton scattering resembles Compton scattering and the dependencies of the scattering angles θ and φ on the polarisation vector are therefore the same [8]. Due to the highly relativistic parti- cles originating from the astrophysical sources that are being studied, inverse Compton emission is the most common of the two processes mentioned. Synchrotron self Compton emission is when the relativistic particle in the process creates both inverse Compton emission and synchrotron radiation, something that can happen when there is a magnetic field present. Synchrotron radiation is described below.
2.2.2 Cyclotron Radiation
Figure 2.3: A dipole profile (red) sketch of cyclotron radiation emitted by a charged particle, here an electron, with the non-relativistic velocity ¯ v accelerated by a magnetic field ¯ B. For a distant observer the maximum polarisation fraction is when ¯ B is perpendicular to the line- of-sight, since the acceleration ¯ a will appear to have a constant direction and only change in magnitude as the dipole sweeps past the observer.
The source of cyclotron radiation is a charged particle traversing non-relativistic in a mag-
netic field. The Lorentz force will make the particle move in a circular manner around a
magnetic field ¯ B, which means that the acceleration vector ¯ a is pointed inwards. Radi-
ation loss is proportional to 1/m 2 and therefore more prominent for light particles such
as electrons and positrons. The polarisation vector of the emitted cyclotron radiation is in a plane parallel to its acceleration vector and perpendicular to the magnetic field [9].
The distribution of the photon emission is dipolar, as seen in figure 2.3 and the polar- isation depend on the field of view of an observer. For a distant observer, the highest polarisation fraction will be seen when ¯ B is perpendicular to the line-of-sight. This is because ¯ a will appear to have a constant direction and only vary in magnitude. Hence the electric field doesn’t change direction either but only vary in magnitude as the dipole distribution sweeps past the line-of-sight.
2.2.3 Synchrotron Radiation
Figure 2.4: Dipole profile sketch of synchrotron radiation emitted by a charged particle traveling at the relativistic velocity ¯ v resulting in a boost in the direction of ¯ v. Just as in cyclotron radiation, a distant observer will find the highest polarisation fraction when the line- of-sight is in the plane spanned by ¯ v and acceleration ¯ a.
Synchrotron radiation is the same as cyclotron radiation with the difference that the charged particle is travelling in the magnetic field at relativistic velocities. This results in a boost of radiation in the same direction as the particle is travelling. The radiation is only visible for an observer if the trajectory of the charged particle lies within the angle of 1/γ of the line-of-sight, where γ is the Lorentz factor
γ = 1
p 1 – v 2 /c 2 (2.10)
Figure 2.4 shows the dipole profile of the emitted synchrotron radiation. Just as in
cyclotron emission, the polarisation ¯ p is in the plane perpendicular to the ¯ B-field, spanned
by the acceleration ¯ a and velocity ¯ v. For an observer the polarisation fraction is at its
maximum when the line-of-sight is in that plane [9].
2.2.4 Curvature Radiation
Curvature radiation is related to cyclotron and synchrotron radiation since it involves charged particles that move in a magnetic field. However, in curvature radiation the magnetic field is strongly curved, resulting in the particle moving with the magnetic field lines instead of perpendicular to it. Just as for synchrotron/cyclotron radiation the emitted radiation is polarised in a plane spanned by the acceleration ¯ a and velocity ¯ v vectors but since the velocity is in the direction of the magnetic field, the polarisation will be parallel to the magnetic field [10].
2.3 X-ray Objects
This section describes some of the extrasolar objects that emit X-rays and an overview of some models related to polarisation characteristics from pulsars and nebulae. The Crab system and Cygnus X-1, the two main targets for PoGOLite and PoGO+, are also briefly described.
2.3.1 Pulsars and Nebulae
Neutron stars are remnants of supernovae and contain predominantly neutrons even though a small population of protons, electrons and heavier nuclei appears. Free neu- trons have a mean lifetime of about 886 s, but the number of electrons and protons is small enough for the Pauli principle to prevent them from decaying [11].
When a star collapses into a supernova, the outer layers of nuclear elements are bounced outward in a shockwave when they hit the inner degenerated core of neutrons. At the same time, the magnetic flux of the star is conserved as the surface area rapidly com- presses and the radius decreases from about r i ≈ 10 5 km to r f ≈ 10 km. This leads to a magnification of the magnetic field with the ratio of the initial and final cross sectional area, or
B f ≈ r 2 i
r 2 f B i (2.11)
Neutron stars can therefore have a magnetic field in the order of at least 10 8 T compared with the sun’s 10 –4 T.
Since angular momentum is conserved when the radius decreases, the neutron star rotates more rapid than its progenitor. As a comparison, the sun has a rotation period of about 24 days, while the period of the Crab pulsar is 33 ms. When a neutron star rotates and emits radiation in the line-of-sight of an observer, it is called a pulsar. The radiation is seen in short and regular intervals as it sweeps through the line-of-sight.
Nebulae are interstellar dust clouds that can be formed by supernova remnants (SNR).
In a pulsar wind nebula (PWN), a special class that includes the Crab nebula, the rel-
ativistic wind from the pulsar interacts with the cold matter in the SNR that slows it
down in a termination shock. The SNR is heated in the shock and the particles in it are
accelerated, emitting radiation that can be modelled as synchrotron radiation. Initially
the PWN expands freely inside the cold matter ejected in the supernova explosion. In this phase, where the Crab nebula currently is, high energy X-rays are expected to be emitted [12]. The polarisation in the nebula can be studied by observing the off-pulse 1 behaviour in a system.
Emission Models
Figure 2.5: Schematics of the regions where emission arises according to polar cap (yellow), slot gap (magenta) and outer cap (blue) models. α is the angle between the rotational axis Ω and the magnetic axis B. The light cylinder, centred at the pulsar and aligned with its rotational axis, has its radius where the co-rotating speed equals speed of light. Adapted from [13].
The strong magnetic field and the rapid rotation in a pulsar make the emission process complicated and it is not yet fully understood. For example if the radiation is produced at a distance from the pulsar surface, relativistic effects have to be taken into account since the particle velocities are very high [13]. Three models of the emission are the polar cap, outer gap and slot gap models. The regions in which the emission arises are seen in figure 2.5. The models mentioned treat the neutron star as a dipole but other models, where multipolar components are included, do exist, see for example [14]. In the polar cap model, the charged particles accelerate close to the surface at the po- lar caps of the pulsar, the yellow region in figure 2.5. Data from the Fermi LAT has ruled out the possibility that radiation originates from particles near the surface of the ms-pulsars 2 that so far have been detected and that the emission seems to take place higher up in the magnetosphere where the relativistic effects are larger. In the outer gap model, the particles accelerate high up in the magnetosphere, where the magnetic field is distorted due to relativistic retardation. Slot gap model, also called the two pole caustic model, is a combination of the two models above. The particles start to
1 off-pulse = the phase where the electromagnetic beam from the pulsar isn’t in the line-of-sight of an observer.
2 ms-pulsar is a pulsar with a period in the millisecond range
accelerate close to the surface of the pulsar, along the last open magnetic field line far up in the magnetosphere [15]. The polarisation pattern in these models can distinguish them from each other, something that is not possible when only studying the intensity of a X-rays from a pulsar [10].
The three models above all relates to emission taking place close to the pulsar. In the striped pulsar wind model synchrotron radiation is created in the wind zone between the light cylinder and the cold Supernova remnant, where the electromagnetic radiation will slow down as it interacts with the matter [16].
The Crab System
The Crab system consists of a ms-pulsar and a PWN, both parts of a supernova recog- nised by Chinese astronomers in the year 1054 [17]. The pulsar has a rotation of 33 ms but is slowing down due to particle emission and from not yet fully understood glitches [18].
Being a bright source from the radio to the gamma wavelengths in the electromagnetic spectrum it is a well studied system. Polarisation measurements have been made in the optical range [19] and an attempt has been made to measure the polarisation in the gamma range, however with an instrument that was not intent as a polarimeter and therefore not calibrated [20].
The first attempt to measure polarisation in the X-ray region was made in the 1970’s when polarimeters on board the OSO 8 satellite made it possible to perform measure- ments at 2.6 and 5.2 keV [21]. Until recently this was the only polarisation measurements made in the X-ray regime but in 2013 PoGOLite Pathfinder made measurements in the 20-120 keV energy range. This flight was however mainly to gain experience for future campaigns and learn how to improve the polarimeter to be able to reduce the background and to distinguish between signals from the nebula and the pulsar [22].
2.3.2 X-ray Binaries
X-ray binaries emit a high intensity of X-rays as the mass of the companion star, the donor, falls onto the massive accretor - a black hole. When the mass of an object exceeds 3 times the solar mass, it is too massive to be a neutron star. The gravitational force inward is so strong that not even the degeneracy pressure can hold against it, as it can when a neutron star is produced. Instead the star keeps collapsing until it gets so dense so that not even light can escape from it - a black hole is created. Just as a neutron star the angular momentum and magnetic flux of the original star is conserved but the enormous radius reduction increases the rotation and the magnetic field strength [23].
Cygnus X-1
Cygnus X-1, or Cyg X-1, got its prefix X-1 because it was the first X-ray source to be detected. The system consists of a black hole accretor, surrounded by an optically thick, geometrically thin accretion disk and a supergiant donor. Closer to the centre the disk is replaced by a hot inner flow. Cyg X-1 is most of the time in a state where it emits hard X-rays that are believed to reflect off the accretion disk, creating a polarised flux.
In this so called hard state the net polarisation fraction is high enough to be detectable
by both PoGOLite and PoGO+ and was therefore a secondary target for the PoGOLite mission in 2013 [23] [24]. Cyg X-1 was not in the hard state during the observation and no polarisation could therefore be detected [25].
2.3.3 Gamma Ray Bursts - GRB
The name originates from shortlived, about 10 ms-10 s, bright flashes of gamma rays that occur randomly across the sky. The origins of the bursts are still not entirely known but according to accepted models they are believed to come from massive stars or merging binaries collapsing into black holes. Polarisation measurements can reveal more about their origins, magnetic field structure and emission mechanisms. Despite the name, GRBs also emit radiation in a broader energy range, including the hard X-ray range. However, it is unlikely that a GRB would appear within the narrow field-of-view of PoGOLite and PoGO+ [17] [26].
2.3.4 Active Galactic Nuclei - AGN
An AGN is a supermassive, about 10 6 – 10 9 solar masses, black hole surrounded by a spinning accretion disk. The disk contains dust, gas and stars that feed the black hole and makes it grow and, in the energy release, radiate mostly in the infrared part of the spectrum. This process makes the AGN a highly luminous source.
In an AGN the disk material falls onto the black hole as an ionized plasma that also generates magnetic fields. Particles in the plasma can be accelerated to ultra high en- ergies and punch through the accretion disk, creating two opposite jets. The jets are enormous lobes of plasma where the aligned magnetic field leads to synchrotron radia- tion being emitted in the radio range [17]. Even if most of the emission seen in the jets is radio emission, they are also emitting X-rays which can be created in synchrotron or synchrotron self Compton emission but also from Compton scattering photons on the ac- cretion disk or from cosmic microwave background (CMB). All these processes suggested have a different polarisation signature, meaning that by X-ray polarisation measurement, the emission processes in AGN can be better understood [27]. AGNs are not targeted by the PoGO+ mission.
2.4 Detection Techniques
Below follows a description of interaction processes that can occur in Compton polarime- ters such as PoGO+ and how the polarisation is measured.
2.4.1 Interaction Processes in Compton Polarimeters
Compton Scattering
When the photon energy E γ is in the range 10 keV-1 MeV, Compton scattering domi-
nates. This process has previously been described, since it together with inverse Compton
scattering and synchrotron self Compton is an important process in astrophysical emis-
sion. The Klein-Nishina formula described in equation 2.8 gives the differential cross
section for a polarised photon to scatter at a polar angle θ relative to the incoming photon and an azimuthal angle φ relative to the polarisation vector. As earlier noted, photons have higher probability to scatter at a polar angle perpendicular to the incident photon.
Using another form of the Klein Nishina-formula dσ
dΩ = Zr 2 o
(1 + α(1 – cosθ)) 2
1 + cos 2 θ 2
1 + α 2 (1 – cosθ) 2
(1 + cos 2 θ)(1 + α(1 – cosθ))
(2.12) with α = E γ /m 0 c 2 , the dependence on the atomic number Z of the scatter material can be seen. A material with high Z increases the probability to scatter but as will be seen below, photoabsorption has a stronger Z dependence. It is therefore more common to use a material with a low Z when scattering is preferred [28].
Photoelectric Absorption
In photoelectric absorption a photon is absorbed by an atom that transforms the energy to an electron that is released. This photoelectron has the energy
T e = E γ – E B,e (2.13)
where E γ is the energy of the absorbed photon and E B,e is the binding energy of the released electron. The angular distribution of the photoelectron is given by the differential cross section [29]
dσ
dΩ ∝ Z 5 m e c 2 E γ
7/2
sin 2 θcos 2 φ
(1 – β · cosθ) 4 (2.14)
where θ is the polar angle between the incoming photon and the photoelectron, φ is the azimuth angle of the photoelectron with respect to the polarisation direction, Z is the atomic number of the absorbing material and β = v/c is the velocity of the electron. As can be seen in equation 2.14, the probability for photoabsorption:
i) increases with the atomic number as Z 5
ii) decreases with increasing photon energy, roughly as E –3 γ .
In addition the absorption probability has discontinuity jumps connected to the binding energies of the different electron shells. A small increase in energy, so that the photon energy exceeds the binding energy of an additional shell, increases the probability to absorb abruptly [30]. Figure 2.6 shows this behaviour.
The φ–dependence in equation 2.14 implies that the photoelectric effect can be used to determine the polarisation direction of incoming radiation. Gas pixel detectors can make use of this dependence but for a Compton based polarimeter such as PoGO+ this signature is not measurable due to the short electron interaction length.
2.4.2 Scintillators
The basic principle of a scintillator is as follows: Incoming radiation interacts with the
atoms in the material, leaving them in an excited state. The excited states will emit light
Figure 2.6: The Photoabsorption probability in lead (barns/atom) vs the energy of the in- cident photon (MeV). The absorption probability increases abruptly when the photon energy exceeds the binding energy of an additional shell, giving the so called shell peaks in the figure.
Adapted from [31].
when they relax to the ground state - they scintillate. The light in the scintillator is then collected and converted into an electric signal in a process described in a later section.
There are some criteria for an ideal scintillator. The light output (fraction of incident energy that appears as light) should be high, as well as the efficiency (probability for the radiation to be absorbed). The scintillator should have a good energy resolution and the decay time should be low enough to generate a fast output pulse 3 . Other criteria are that the scintillators need to be easy to work with and be able to be produced at a reasonable cost. Last but not least, the material needs to be transparent in the emitting wavelength region in order for the light to be transferred to the PMT. In a balloon-borne or space based detector a low mass is also important.
An extra requirement on Compton polarimeters that use the same material for both scattering and photoabsorption is sufficiently high cross sections for both photoabsorp- tion and Compton scattering in the measured energy range.
Scintillators can be organic or inorganic. Organic scintillators, for example plastic, ab-
3 As can be seen later, a system of scintillators with fast and slow decay times can be used to distinguish
signals from different detectors, meaning that also a longer decay time can be suitable for a scintillator.
sorb the incident radiation in two ways, either by exciting the atom to a higher electron level or by exciting to one of the vibrational levels that are associated with every elec- tronic level. The energy difference between the electronic levels are usually around a few eV, while the spacing between vibrational levels is in the order of 0.1 eV. The deex- citation from a vibrational level is quick and doesn’t lead to an emitted photon, whereas the deexcitation from an electronic level leads to fluorescence. The transparency demand is fulfilled as the emitted photon generally has a lower energy than required for absorption.
Inorganic scintillators are grown crystals with a single crystal structure: a polycrys- talline structure is opaque due to reflections and absorptions in the crystal. The discrete energy levels have an electronic band structure, where the valence band is full and the conducting band empty. In the scintillating process, incident radiation excites valence electrons across the energy band to the conducting bands, where the electron eventually loses its energy by emitting a photon and falls back to the valence band again. Impurities called activators are added to the crystals to increase the photon emission probability and reduce the self absorption of the emitted light. The activators provide states in the energy gap so that emission can occur between these states. In this way scintilla- tors can be designed so that the wavelength of the emitted photons has the wavelength corresponding to the best sensitivity to the connected PMT [30].
2.4.3 Photomultiplier Tubes - PMTs
Figure 2.7: PMT schematics. The scintillator light (dashed yellow) hits the photocathode (red), resulting in an escaping electron (dashed). The electron is focused by an electrode (blue) and travels through an array of dynodes (black) multiplying the electrons, that are subsequently collected in the anode (green).
To convert the light signals from a scintillator, a PMT is needed. A PMT can convert light from only a hundred photons into a reasonable signal and it is generally sensitive to light from ultraviolet up to near infrared. The construction can be seen in figure 2.7 and is as follows: The incident light is converted to electrons in the photocathode, a semitransparent material that absorbs the photons, deposits the energy to electrons that migrate through the material to subsequently escape the surface of the photocathode.
The cathode material needs to be thick enough so that the photons interact instead of
going through, but not so thick that the migrating electrons lose too much of their energy
before reaching the surface. If the electrons have too low energy, they will not escape
the cathode-vacuum barrier potential that exists between the material and the vacuum.
The efficiency of the photocathode can be given by the quantum efficiency QE:
QE = number of emitted photoelectrons
number of incident photons (2.15)
In practice, photocathodes often has a maximum quantum efficiency of 20 – 30%.
The electrons subsequently move in a multiplier structure where the relatively few orig- inal electrons are multiplied up to around 10 7 – 10 10 electrons by moving in an array of dynodes that reemit more than one electron for every electron hitting the material.
The charged electrons are collected in the anode where they are formed to a readout sig- nal. The tube is in vacuum in order for the low energy electrons to efficiently accelerate through the tube. To be able to correlate the readout signal to the incoming photon energy, linearity between the number of photoelectrons from the photocathode and the pulse amplitude at the anode is an important property in a PMT [28].
2.4.4 Polarisation Measurements
Figure 2.8: Example of a modulation curve with the maximum C max , minimum C min and average T number of counts. The expected polarisation angle Ψ 0 is found where the number of counts are at a minimum.
As described in earlier sections, the azimuthal scattering angle in Compton scattering depends on the polarisation angle. This dependency creates an observed anisotropy in the scattering angle that can be visualised in a so called modulation curve that in turn can be fitted to a harmonic function [32]:
f(Ψ) = T[1 + M(cos(2(Ψ – Ψ 0 ))] (2.16)
Ψ = φ – 90 ◦ (2.17)
Ψ being the polarisation angle, φ the azimuthal scattering angle, Ψ 0 = a phase that gives the expected angle where Ψ peaks, T = the average number of events
T = C max + C min
2 (2.18)
and M = the modulation factor
M = C max – C min
C max + C min (2.19)
An example of a modulation curve can be seen in figure 2.8.
In terms of the modulation factor M, the polarisation fraction is given by
p = M
M 100 (2.20)
Where M 100 is the modulation factor for a 100% polarised beam, that is, when all pho- tons have their electric fields aligned in a certain direction [10]. The modulation factor depends not only on the polarisation of the incident photon beam but is also detector specific.
Another important figure of merit is the minimum detectable polarisation (MDP). MDP is a measure of what the polarisation fraction would be if it would have a certain prob- ability to be due to statistical fluctuation. This means that MDP 99 is a measure of the polarisation fraction that would correspond to 1% chance of being due to chance. MDP 99 is given by
MDP 99 = 4.29 M 100 R S
s
R S + R B
T tot (2.21)
Where R S , R B and T tot are the signal rate, the background rate and the total exposure
time [33]. A high M 100 is therefore preferred to be able to detect a low polarisation
fraction.
Chapter 3 PoGO+
PoGOLite was originally conceived as a lightweight polarimeter with 217 plastic scin- tillators, designed to detect at least 10% polarisation from a 200 mCrab point source in the energy range 25-80 keV in one 6h flight [34]. As a Compton polarimeter it was based on the principle that polarised photons favour to scatter perpendicular to their electric field vectors. As a part of the investigations, a smaller project started - PoGO- Lite Pathfinder: a 61 scintillators polarimeter that could detect 1 Crab point source. The pathfinder was launched from SSC Esrange Space Center on July 12th 2013 and made a near circumpolar flight before it landed in Norilsk in Russia. During the flight, data from the Crab system was gathered as well as valuable experience to be used for a future flight with the upgraded PoGO+ mission. This chapter describes the new polarimeter and upgrades that were made towards the planned mission in the summer of 2016. The upgraded polarimeter is described in more detail in [3], whereas components like cooling system, pressure vessels and communication system can be studied more closely in [25].
3.1 The Design of PoGO+
The detector array consists of 61 hexagonal scintillator assemblies in a honeycomb struc- ture, surrounded by anticoincidence systems to reduce background signals. One hexago- nal scintillator assembly is called an SDC and consists of three major parts: a collimator, a plastic scintillator and a BGO crystal.
A schematic overview of PoGOLite can be seen in figure 3.1 but the figure equally pictures the principle of PoGO+ since the only geometrical difference is one extra block of polyethylene (yellow) at the bottom. A source photon that enters the detector from the top is scattered and subsequently absorbed in the plastic scintillators (blue). A cos- mic photon entering the detector at an angle is absorbed in the collimators (light blue).
Atmospheric photons are absorbed by the BGO scintillators in the SDC or side antico-
incidence shield (red), while the atmospheric neutrons are absorbed or slowed down in
the polyethylene shield or neutron shield. The different parts in the system are described
below.
Figure 3.1: Overview of PoGOLite where the only geometrical differences between the figure and PoGO+ are one additional block of polyethylene in yellow at the bottom and the lengths of the collimators in light blue and plastic scintillators in blue. The total length of the instrument is however the same. The red BGO scintillators at the bottom of the SDCs and the SAS confine the collimators and plastic scintillators. Below the bottom BGOs are the PMTs seen in grey while the green part contains the electronics for the data acquisition. Adapted from [3].
3.1.1 SDC
Collimator
PoGOLite used 2 mm thick plastic scintillators to actively collimate the incoming radi- ation. However it turned out to be too hard to distinguish if the scintillation occurred in the plastic scintillator or collimator when the energies were low. The active collima- tors where therefore replaced by 0.5 mm thick passive copper rods, giving a collimator thickness of 1 mm, resulting in an increased detector area.
Plastic Scintillator
The use of the same scintillator for both absorption and Compton scattering in a balloon
project means that trade-offs and different considerations are needed: The scintillator
material needs to have a reasonably high cross section for both photoabsorption and
Compton scattering in the hard X-ray region, a low weight, a short decay time and
be possible to produce at a reasonable cost. After these considerations, the chosen
scintillators for both PoGOLite and PoGO+ was EJ-204 plastic scintillators from Eljen
Technology with a decay time of 1.8 ns. For the PoGO+ flight, the plastic scintillators
were shortened from 20 cm to 12 cm. Since the background is impinging the detector in
every direction while the signal only comes from the top, a decrease in detector length reduces the background more than the signal, resulting in a higher signal-to-background.
BGO
On the bottom the plastic scintillators are glued to inorganic scintillators made of Bis- muth Germanium Oxide (BGO) with a decay time of about 300 ns [25]. BGOs are, with their high atomic number, good absorbers that can stop radiation coming from the bot- tom. In addition BGOs form a part of an anticoincidence system: the much longer decay time is reflected in the waveform of the signal, which means that signals from a BGO scintillator and a plastic scintillator can be distinguished by looking at their respective waveform.
Miscellaneous
The plastic scintillators and the BGOs are wrapped with reflective film to maximise the light collection. The wrapping material has been updated on both the BGOs and the plastic scintillators since the previous flight.
Another update that has been done on PoGO+ is to coat the scintillators with opaque heat shrink and Tedlar to prevent light leakage between the SDCs. If light escapes into a neighbouring scintillator and is collected by its PMT, it will look like an additional sig- nal (so called crosstalk ) and hence mimic a polarised event. Details about the updated coating and reflecting material can be found in [35] and [36].
Between the BGO crystal surface and the PMT window, a 1 mm thick silicon wafer and optical grease has been applied to assure optical contact during flight.
3.1.2 Photomultiplier Tube
The photomultiplier tubes (PMTs) are modified version of the Hamamatsu Photonics R7899 and are chosen because they have a sufficiently low dark current level, for exam- ple to be able to detect 90 ◦ Compton scattering events from 15 keV photons impinging the detector [25]. According to equation 2.9, the deposited energy at Compton scattering is approximately 0.5 keV for these energies.
The PMT response can be visualised in an energy spectrum as the single photoelec- tron peak, or SPE peak. This peak occurs from events when the incoming photon only have enough energy to release one electron from the photocathode. This single electron give rise to a peak in the low energy regions and set a limit on the minimum deposited energy that can be detected.
The PMT efficiency is measured by a unitless figure of merit called blue sensitivity index
(BI) which is related to the quantum efficiency of the PMT, meaning that it gives a mea-
sure of the number of electrons that are created per incoming photon. BI is a measure
of the cathode current when a blue filter has been placed in front of the PMT [37]. A
high index represents a good efficiency and vice versa and each PMT’s index is provided
by the manufacturer.
3.1.3 Shielding
The polarimeter has two shields to remove unwanted signals. The outer passive shield consists of polyethylene and is chosen because it is hydrogen rich and therefore an ef- fective neutron absorber. This neutron shield is necessary, since the flux of atmospheric neutrons is quite high and can mimic polarised events when neutrons interact with pro- tons in the plastic scintillator. Even if the shield can’t remove the neutrons entirely, it can reduce the number and their kinetic energies enough to result in a too weak signal to be detected in the plastic scintillators [10]. Using data from the 2013 flight, the ge- ometry of the shield has been changed to optimise the reduction without increasing the weight [25].
The inner shield is the side anticoincidence shield (SAS), an active shield that consists of 30 BGOs with corresponding PMTs. Particles interacting in the SAS are vetoed by the flight electronics unlike the BGOs in the SDCs that are actively removed by waveform selection in the analysis described further in this section.
3.1.4 Neutron Detectors
Figure 3.2: The two neutron detectors assembled to their corresponding PMT. The bottom detector shows how short the scintillator is in comparison to the PMT. The detectors are coated in opaque heat shrink and Tedlar to prevent light leaking out to neighbouring detectors.
Courtesy of the PoGO Collaboration. Credit: M. Kiss.
The polyethylene shield doesn’t fully shield the detector from the atmospheric neutrons.
To be able to estimate the neutron flux inside the detector, two neutron detectors are placed inside the neutron shield. One neutron detector consists of a 1.5 cm long LiCAF (LiCaAlF 6 ) scintillator sandwiched between two 4 cm long BGOs. Figure 3.2 shows the detectors when assembled to their respective PMTs. The BGO crystals are used to detect and absorb incoming photons.
The 6 Li inside the detector has a high cross section, 940 barn, for capturing thermal neutrons. The neutron capture occur via the following process:
6 Li + n → 4 He(2.73MeV) + 3 T(2.05 MeV) (3.1)
The decay products deposit their energies within µs, leading to a mono-energetic signal
for each neutron capture [10].
The LiCAF detector has a slow rise time, about 1600 ns, which can be compared to the plastic scintillator’s 1.8 ns and BGO’s 300 ns. Signals from the LiCAFs are therefore easy to distinguish from signals coming from the BGOs in the neutron detectors.
3.1.5 The Assembled Polarimeter
Figure 3.3: Schematic view of the polarimeter electronics in PoGO+. The signals from the PMTs are digitised and sampled by the six FADC boards - two of which are to the SAS PMTs.
The FADCs are connected to the minion logic board with several connectors, one for each logic operation. The DIO contains the logic that determine whether a signal should be recorded or not. If it is recorded, the signal is sent to the converter and stored.
The heart of the detector is the 61 detector cells, each consisting of an SDC and a PMT.
When adding the 30 SAS units described above and the two neutron detectors, there are 93 PMTs to be read out in total.
A simplified overview of the polarimeter electronics in PoGO+ can be seen figure 3.3:
The PMTs are connected to six waveform digitiser boards with amplifiers and Flash Analog to Digital Converters (FADCs) that sample the signals at 100 MHz 1 , an upgrade from the previous flight with PoGOLite, where the sampling rate was 37.5 MHz [38].
Two of the FADCs are assigned to the PMTs connected to the SAS. All FADCs are connected to a logic board through several connectors - one for each logic operation. The logic board is in turn linked to the DIO (Digital Input/Output) that contains the trigger logic that determines whether a signal should be recorded as a valid hit or not. The logic operations are described briefly in section 3.2 below and in more detail in [39]. A signal from a valid hit is converted to a readable signal and transferred to the data acquisition (DAQ) storage.
1 The neutron detectors are sampling at a lower rate, ≈ 16.7 MHz
Figure 3.4: The final detector configuration in PoGO+. The numbers correspond to one unit of SDC and PMT in the polarimeter. The colours represent the different FADC boards that are connected to the units. Figure adapted from [40].
The PMTs connected to each board are spread out in the polarimeter to reduce sys- tematic errors and fatal problems if a board stops working during flight. In figure 3.4 every FADC board is represented by a colour and every number represents one SDC and PMT unit. The configuration has been determined after performance tests on each of the SDCs where the units that performed best were placed in the inner rings. In order to get an evenly distributed performance the best SDC has been paired with the flight PMT with the lowest blue sensitivity index [39].
For every incoming sample point, the amplitude is calculated as the value of the cur- rent point and the value of a point three samples earlier. When this value exceeds a threshold level, 50 sample points are recorded during approximately 0.5 µs. These 50 points create a waveform, which is recorded as a signal.
3.2 Data Selection and Polarisation Measurement
Not all signals are saved for later analysis. The first selection is done online during flight, the so called online selection or online veto, by the FADC boards and the DIO. In this way signals that are considered noise or background can be rejected right away, which is an advantage since data storage is limited. The remaining data is analysed offline to further fine tune the selection.
The online selection scheme consists of four discriminations. For an event to be recorded,
the energy deposition must be at least as large as the smallest photoabsorption. This
level is called the trigger level. A 90 ◦ Compton scattering signal from this lowest photon
energy is used as a hit threshold. When the trigger level has been reached, all events
exceeding the hit threshold are read out. The threshold is set to make sure that photons
that deposit a small energy when Compton scattering are encountered, but to be able to
eject electronic noise. The waveform discrimination threshold rejects BGO events while
(a) Fast waveform (b) Slow waveform
Figure 3.5: Example of waveforms from the plastic and BGO scintillators. Each waveform consists of 50 sample points (x-axis) sampled at 100 MHz and the height (y-axis) is proportional to the deposited energy that gave rise to the waveform. The differences in waveforms originate from the rise time in the plastic and BGO scintillators, making it possible to distinguish them from each other.
(a) Fast waveform (b) Slow waveform
Figure 3.6: Example of waveforms from the plastic and BGO scintillators with some of the
concepts explained.
the upper threshold rejects large amplitude signals that might come from cosmic ray in- teractions.
Figure 3.5 shows waveforms originating from signals in plastic and BGO scintillators.
The fast waveform in figure 3.5a can clearly be distinguished from the slower waveform originating from the BGO, making waveform discrimination possible.
Since the online selection decides what data to be recorded, it is done with a gener- ous approach to make sure that the rejected data doesn’t contain signal events. In the offline analysis additional parameters can be looked upon to narrow down chosen events further. Figure 3.6 shows a fast and a slow waveform with lines to explain different concepts used in the offline analysis. As earlier described a waveform contains 50 points sampled with 100 MHz, meaning that the time between two points are 10 ns and it takes 500 ns to record one waveform. The y value in the figure is the output, which depend on electronic noise, voltage setting and the energy of the incoming photon. Below follows explanations of different concepts:
Fast output (ADC channels)
0 500 1000 1500 2000 2500 3000 3500 4000
Slow output (ADC channels)
0 500 1000 1500 2000 2500 3000 3500 4000
1 10 10 2
10 3
Fast Branch
Figure 3.7: Fast branch histogram. The area between the two red lines contains the fast events.
The starting point (SP) is the point where the waveform starts to rise. The baseline, or the pedestal, is the level prior to the waveform. Everything under the baseline is elec- tronic noise from the FADC: when there is no recorded hit in the PMT, a signal with an output up to the baseline is still current in the FADC. So when a signal is measured, the only value of interest is the value above the baseline.
Three different outputs that are measured are the fast output (fast), the slow output (slow) and the peak output (peak). The fast and slow separations indicate which data points, counted from the starting point, that are used to distinguish fast waveforms from interactions coming from the BGO:
Fast = Output[SP+Fast Separation] – Output[SP] (3.2)
hist_peak
Entries 399189 Mean 262.4 Std Dev 403.6Energy (ADC channels)
0 500 1000 1500 2000 2500 3000 3500 4000
1 10 102 103
hist_peak
Entries 399189 Mean 262.4 Std Dev 403.6Waveform Peak
(a) Peak
hist_peak
Entries 366291 Mean 161 Std Dev 120.5Energy (ADC channels)
0 100 200 300 400 500
10 102 103
