PoGO+ Detector Cell Characterisation and Optimisation of Waveform Selection

PoGO+ Detector Cell Characterisation and Optimisation of Waveform Selection

Parameters

Author:

Rasmus Östlund (891211-0098) rasost@kth.se

Department of Physics

KTH, Royal Institute of Technology Supervisors:

Mózsi Kiss

Mark Pearce

August 11, 2016

Typeset in L ^A TEX

TRITA-FYS 2016:30 ISSN 0280-316X

ISRN KTH/FYS/16:30SE

c Rasmus Östlund, 2016

Abstract

PoGO+ is a balloon-borne experiment scheduled for ight during summer 2016. It aims to measure the polarisation of X-rays originating from the Crab pulsar and nebula by de- tecting Compton scattering in its scintillator based detector cells. PoGO+ is an upgraded version of the PoGOLite Pathnder which ew in 2013 and constituted a conceptual test of the instrument. Since then, extensive simulations and trials have led to a number of changes in the detector in an attempt to enhance the performance.

In the work detailed in this thesis the new detector cells are characterised and ranked according to the detector cell sensitivity, calculated as the number of photo-electrons generated in a photomultiplier tube per keV deposited energy in the detector cell. It is found that the mean of the detector cell sensitivity distribution has increased by a factor of 2.8 relative the PoGOLite Pathnder. As the sensitivity is increased this should signicantly increase the number of detected polarisation events. The detector cell sensitivity is also used to establish a ranking of the constructed detector cells which lead to a suggested, and implemented, polarimeter detector cell conguration. Due to fear of scintillation light leaking from one detector cell to another (an event that would record as either a polarisation event, a false positive, or cause an actual polarisation event to appear false, a false negative) the light-tightness of each detector cell was investigated and found to be negligible or at an acceptable level.

As there are limits to the data storage during ight, as well as a desire to minimise

dead-time that arises when writing to storage, the electronics implement an online event

selection method, the purpose of which is to store relevant events whilst discarding irrele-

vant events. The event selection depends on four parameters, each of which was optimised

in order to achieve at least 95% acceptance (storage) of relevant events and rejecting a

maximum of irrelevant events. The optimal parameters were found and implemented in

the ight electronics.

Sammanfattning

PoGO+ är ett ballongburet experiment schemalagt för ygning under sommaren 2016 vars mål är att mäta polariseringen av röntgenstrålning från Krabbpulsaren och nebulosan genom att detektera Comptonspridning i dess scintillatorbaserade detektorceller. PoGO+

är en uppdaterad version av PoGOLite Pathnder som ög 2013 och var ett konceptuellt test av instrumentet. Sedan dess har omfattande simuleringar och tester lett till ett antal förändringar i detektorn i syfte att förbättra prestandan.

I arbetet som beskrivs i denna avhandling har de nya detektorcellerna karaktärise- rats och rankats enligt deras detektorcellkänslighet, uträknat som antalet fotoelektroner genererade i en fotomultiplikator per keV deponerad energi i cellen. Det uppdagas att genomsnittet av detektorcellkänslighetens fördelning har ökat med en faktor 2,8 jämfört med PoGOLite Pathnder. Eftersom känsligheten har ökat torde detta även signikant öka antalet upptäckta händelser. Detektorcellkänsligheten används även för att etablera en prestandarankning mellan enheterna. Denna ranking leder till den slutgiltiga detek- torcell kongurationen i polarimetern. Vidare har varje detektorcells ljustäthet evaluerats för att undvika att scintillationsljus läcker från en cell till en annan (vilket kan ge falskt- positiva polarisations händelser eller falskt-negativa signaler). Det funna ljusläckaget var försumbart eller inom acceptabla nivåer.

Eftersom det nns gränser för hur mycket data som kan lagras under ygningen, samt

en önskan om att minimera den dödtid som uppstår då data skrivs till minnet, så har

händelseurvalsmetoderna optimerats för den nya hårdvaran. Detta utfördes genom att

replikera elektronikens beteende och analysera data insamlad i laboratorium vilket tillät

optimering av de ingående parametrarna. Den sökta optimeringen var konservativ och

säkerställde att åtminstone 95% av relevanta händelser skrivs till lagring medan maximalt

antal av irrelevanta händelser kasseras. Optimeringen utfördes genom att visuellt granska

ett stort antal energihistogram.

Contents

1 Introduction 3

1.1 Outline of the Thesis . . . . 3

1.2 The PoGO Collaboration . . . . 4

1.2.1 PoGOLite Pathnder . . . . 4

1.2.2 PoGO+ . . . . 5

1.3 Author's Contribution . . . . 5

2 X-Ray Polarimetry 7 2.1 Polarisation of Electromagnetic Radiation . . . . 7

2.2 Measuring Polarisation . . . . 10

2.3 Detector Basics . . . . 12

2.3.1 Scintillators . . . . 12

2.3.2 Photomultiplier Tubes . . . . 13

2.4 PoGO+ Astrophysical Targets . . . . 14

2.4.1 Supernovae and Neutron Stars . . . . 15

2.4.2 Pulsars . . . . 15

2.4.3 The Crab Nebula . . . . 17

3 PoGO+, the Polarised Gamma-ray Observer 18 3.1 PoGO+ Polarimeter . . . . 18

3.1.1 Polarimeter Conguration . . . . 19

3.1.2 Coincidence Detector . . . . 19

3.1.3 Polarimeter Electronics . . . . 20

3.1.4 SAS, the Side Anti-coincidence Shield . . . . 20

3.1.5 SDC, The Smorgas Detector Cell . . . . 21

3.1.6 SDC Performance . . . . 23

3.2 PoGO+ Data Acquisition . . . . 24

3.2.1 Data Acquisition . . . . 24

3.2.2 Online Event Selection . . . . 25

4 Detector Cell Characterisation 30 4.1 Detector Cell Sensitivity . . . . 30

4.1.1 DCS Experimental Setup . . . . 30

4.2 Relative Light Leakage . . . . 33

4.2.1 RLL Experimental Setup . . . . 33

4.3 Results . . . . 34

4.3.1 Reproducibility . . . . 34

4.3.2 Unit Rewrapping . . . . 34

4.3.3 Distributions . . . . 35

4.3.4 Scatter Plots . . . . 35

4.4 Discussion and Conclusion . . . . 41

4.4.1 On the Error of Reproducibility . . . . 41

4.4.2 Rewrap and Remeasure . . . . 41

4.4.3 SDC Performance . . . . 42

4.4.4 SDC Performance Ranking . . . . 42

5 Optimisation of Online Event Selection 44 5.1 Experimental Method . . . . 44

5.1.1 Obtaining Waveforms . . . . 44

5.1.2 Identifying Fast and Slow Outputs . . . . 45

5.1.3 Identifying the Peak Energy . . . . 47

5.1.4 EJ-204 Acceptance and BGO Rejection Eciency . . . . 50

5.1.5 Optimisation method . . . . 53

5.2 Results . . . . 54

5.2.1 Parameter Values . . . . 54

5.3 Discussion and Conclusion . . . . 56

5.3.1 Visual Inspection . . . . 56

5.3.2 Systematic Errors in Peak Energy Identication . . . . 56

5.3.3 Expected number of Pileup events . . . . 57

5.3.4 Disregarding the Forced Slow Output . . . . 57

A SDC Characterisation Data 65

Chapter 1 Introduction

1.1 Outline of the Thesis

Chapter 1 gives a brief introduction to the PoGO Collaboration. Chapter 2 summarises the basic concepts behind polarised radiation and the measurements thereof in the context of the PoGO project. It also provides some physical properties of hardware used in the PoGO+ polarimeter and ends by summarising the properties of the astrophysical targets. Chapter 3 delves into greater detail about the PoGO+ polarimeter, explaining the detector design and the dierent components. It continues with an explanation of the software relevant to this thesis. Chapter 4 details the characterisation of the detector cell performances as well as quantifying the light-tightness of each detector cell, ending in a ranked list. Based on this performance ranking a detector conguration is suggested.

Chapter 5 gives the technicalities of the online event selection and the optimisation

thereof.

1.2 The PoGO Collaboration

Figure 1.1: Photograph of PoGOLite Pathinder (5 m in height) taken pre-ight in 2013. The polarimeter is visible as the large circle centred inside the gondola.

Courtesy of the PoGO Collaboration.

The PoGO Collaboration is a ongoing international project headed by the Particle and Astroparticle group at the Royal Institute of Technology in Sweden. Nowadays the collaboration includes participants in both private and public institutions in Sweden and Japan. PoGO is an acronym derived from Polarized Gamma-Ray Observer where observer denotes an instrument for measuring polarisation, the PoGO Polarimeter. The polarimeter has come in two iterations, the PoGOLite Pathnder which ew in 2013 and PoGO+ which is scheduled to y during 2016 and is the focus of this thesis.

The overreaching aim of the project is to measure the polarisation of X-rays originat- ing in bright astrophysical sources in order to gain better understanding of the processes which are responsible for the observed high-energy emission.

1.2.1 PoGOLite Pathnder

The PoGOLite Pathnder ew in June 2013. The instrument remained aloft for 13 days

before being brought down near Norilsk, Russia. The instrument is visible in Figure 1.1

and the ight path in gure 1.2. During ight the instrument was carried to a height of

40 km by a helium balloon, which lled a volume of roughly 10 ⁶ m ³ .

Originally, PoGOLite was an instrument meant to house 217 detector cells and the PoGOLite Pathnder was constructed as a test, housing 61 detector cells [1]. Follow- ing the Pathnder ight it was decided to focus on better detector cell performance rather than more detector cells. For more information on the PoGOLite design and the subsequent results from the ight, see [2, 3].

Figure 1.2: The circumpolar path of the 2013 ight. The instrument started in Esrange, Sweden and followed the polar winds around the polar circle, but due to drifting northwards it was landed in Norilsk, Russia rather than completing the circumnavigation. Courtesy of the PoGO Collaboration.

1.2.2 PoGO+

The current incarnation of the PoGO polarimeter, PoGO+, is the focus of this thesis. It is an upgraded version of the PoGOLite Pathnder where development based on extensive testing and simulation has led to better performance. The name switch from PoGOLite to PoGO+ was to discern internally between the previously proposed 217 detector cell instrument, the Pathnder and the new, upgraded 61 detector cell version.

Operative dierences include aiming the instrument using a novel sun tracker rather than the star tracker used in PoGOLite as well as landing in Canada rather than com- pleting a full circumpolar lap. This brings the total air time to about a week, which is roughly half the ight-time of PoGOLite Pathnder.

1.3 Author's Contribution

This work was conducted as part of the PoGOLite/PoGO+ Collaboration and as such makes use of hardware and software which has been developed by Collaboration members.

In preparation for the 2016 ight of the PoGO+ polarimeter the performance of all

parts of the detector has been tested and calibrated in a number of ways. This author

aided in the detector cell construction and handled the testing of each individual detector

cell by way of laboratory measurements and subsequent analysis. A total of 79 detector cells were characterised and a relative performance ranking was formed which led to a proposed, and accepted, detector cell conguration for the 2016 ight. Each detector cell unit was also tested for light-leakage. Following the detector cell characterisation the author also optimised the parameters involved in the online selection by analysing waveforms recorded from the dierent scintillator types constituting the detector cells.

The parameters were chosen largely based on visually inspecting a great number of pulse

height distributions. These hundreds of distributions are stored and databased for refer-

ence.

Chapter 2

X-Ray Polarimetry

Polarimetry is the study of the polarisation in electromagnetic waves. Commonly, the waves have interacted with some material, where a polarimetric study can give some insight on the materials characteristics such as geometric or electromagnetic properties.

For example photons reected on the accretion disk surrounding a black hole are expected to be polarised, where the polarisation depends on the inclination of the disk relative the line of sight. For PoGO+, the measured polarisation will provide insight into the regions producing the photons as well as the processes responsible for the high-energy emission.

2.1 Polarisation of Electromagnetic Radiation

Polarisation is one of the fundamental properties of electromagnetic radiation and can, intuitively, be visualised as oscillations of the wave in the plane perpendicular to the direction of propagation. For a more accurate understanding, one can examine the be- haviour of the electromagnetic eld vector, E(z, t) travelling along the z-axis. Commonly, this is taken as E(z, t) = E(0, 0) cos(ωt − kz − φ) where φ is some arbitrary phase in the wave, ω is the angular frequency and k = ω/c is the absolute value of the wave vector.

(a) Linear polarisation: E

and E

have the

same phase. (b) Circular polarisation: E

has been shifted

±90

with regards to E

.

Figure 2.1: Visualisation of polarised waves propagating along the z-axis. The

green curve symbolises E y , the purple curve symbolises E x and the dotted red

curve represents the total polarisation.

Since the electric eld is perpendicular to the z-axis it is found that (where z = 0) E _x (t) = E _x (0) cos(ωt − φ ₁ )

E _y (t) = E _y (0) cos(ωt − φ ₂ ) (2.1) where φ 1 , φ ₂ are some phase shifts. This gives three types of polarisation:

If the phases are equal (φ 1 = φ ₂ ) E will sweep out a line in the x, y-plane (see Figure 2.1:a) and the radiation is said to be linearly polarised with an angle of polarisation ψ ∈ [0, π] . Since the plane of polarisation has no set direction, the location of the linear polarisation in the xy-plane is not a vector. In astronomy, the x and y components are commonly known as horizontal and vertical polarisations respectively.

If the phases are shifted 90 ^◦ (φ 2 = φ ₁ ± π/2 ), E will sweep out a circle (see Figure 2.1:b), and the radiation is said to be circularly polarised. The circular case give rise to two special cases, here taken for φ 1 = 0

E _x (t) = E(0) cos(ωt) E _y (t) = ±E(0) sin(ωt)

where a positive sign denotes a counter-clockwise motion called right-hand circular po- larisation and a negative sign left-hand circular polarisation.

The third case is the general case where E sweeps out an ellipse with some eccentricity, and the radiation is consequently said to be elliptically polarised. Here the polarisation angle corresponds to the angle between the x-axis and the semi-major axis of the ellipse, dened in the counter-clockwise fashion [4].

Macroscopic and Microscopic Polarisation

Any individual wave is polarised as shown above, called microscopic polarisation, yet the total received radiation from an astrophysical object is generally a collection of dierently polarised waves yielding a macroscopic polarisation. When the source or the interstellar medium prefers one direction over other, the radiation is said to be partially polarised with a fraction of polarisation dened as

p = I _p

I ∈ [0, 1]

where I is the total intensity and I p is the intensity of some polarisation angle. Since any polarisation can be expressed as a superposition between circularly and linearly polarised radiation, the degree of polarisation can be subdivided into;

p _L = I _L

I ∈ [0, 1] and p C = I _C

I ∈ [−1, 1]

where the sign of p C depends on the orientation of the circular polarisation [4].

Stokes Parameters

In order to determine the polarisation of an arbitrary electromagnetic beam the Stokes parameters are commonly used. They are dened as:







 I Q U









=









hE _x ² i + hE _y ² i hE _x ² i − hE _y ² i 2hE _x E _y cos(δ)i









E _x (t) and E y (t) , and δ = φ 2 − φ ₁ is the phase dierence. They constitute the observables of the electromagnetic beam [5], describing:

i) I = hE x ² i + hE _y ² i : The total intensity of the beam.

ii) Q = hE x ² i − hE _y ² i : The degree of planar polarisation with regard to two ortogonal axes in the beam. Visualised in Figure 2.2:a,d.

iii) U = 2hE x E _y cos(δ)i : The degree of polarisation with regard to two axes rotated 45 ^◦ with regard to the axes in Q. Visualised in Figure 2.2:b,e.

iv) V = 2hE x E _y sin(δ)i : The degree of circular polarisation in the beam. Visualised in Figure 2.2:c,f.

For macroscopic radiation, the Stokes parameters relate as I p ² = Q ² + U ² + V ² where I _p ≤ I is the polarised intensity. The dierent degrees of polarisation are given as:

m p = I _p

I ∈ [0, 1], m L = pQ ² + U ²

I ∈ [0, 1] and m C = V

I ∈ [−1, 1]

The polarisation angle ψ is dened as the angle between E(z, t) and the positive x- axis. In elliptical polarisation, ψ denes the angle between the positive x-axis and the semi major axis of the ellipse [4]. With regard to the Stoke parameters

ψ = 1

2 arctan U

Q ∈ [0, π] (2.2)

(a) Horisontal polarisation for

Q > 0 and U = V = 0. (b) 45

linear polarisation for

U > 0 and Q = V = 0. (c) Right-hand circular polari- sation for V > 0 and Q = U = 0 .

(d) Vertical polarisation for

Q < 0 and U = V = 0. (e) −45

linear polarisation for

U < 0 and Q = V = 0. (f) Left-hand circular polarisa- tion for V < 0 and Q = U = 0.

Figure 2.2: Example of polarisation for a wave propagating along the z-axis given specic ideal Stokes parameters.

2.2 Measuring Polarisation

Electromagnetic radiation interacts with matter through several processes depending on the energy of the incident photons where three dierent processes dominate three dierent energy regions. At the lowest energies the photoelectric eect dominates, in intermediate energies the Comptom eect rules the interactions and at higher energies pair production takes over (see Figure 2.3).

Compton Scattering

With respect to the PoGO+ polarimeter, Compton scattering is the process measured to determine the polarisation of radiation. When a photon undergoes Compton scattering, it interacts with an electron assumed to be at rest relative to the photon. As the electron gains momentum, the direction and frequency of the photon changes accordingly. If the photon energy is given as E γ = hν then the post scatter energy is

E _γ ⁰ = hν ⁰ = E _γ



1 + E _γ

m _e c ² (1 − cos θ)

 −1

Figure 2.3: The dierent interactions in their respective region of dominance.

Generated with data from [6]. The mass attenuation coecient can most easily be understood as a variant of the interaction cross-section (in units cm ² , or area per unit particle rather than unit mass).

where ν is the frequency, m e the electron rest mass and θ the polar scattering angle as seen in Figure 2.4:a. The scattering angles are determined by the Klein-Nishina formula [7].

dσ dΩ = 1

2 r ² _e k ² k ₀ ²

 k k ₀ + k ₀

k − 2 sin ² (θ) cos ² (φ)



(2.3) where k 0 and k are the momenta of the incident photon and scattered photon respec- tively, r e is the electron radius and φ is the azimuthal scattering angle, dened from the polarisation vector as seen in Figure 2.4:a. As the trigonometric term disappear when φ → ±90 ^◦ the probability of scattering is highest perpendicular to the polarisation vector of the incoming photons. This results in a modulation curve as seen in Figure 2.4:b with a modulation factor given by

M = C max − C min

C _max + C _min

where C max and C min are the maximum and minimum of the modulation curve. The degree of polarisation is given by

p = M M 100

where M 100 is the modulation factor for a 100% polarised beam, either measured from a beam with a known polarisation or obtained through simulations. The modulation factor and the polarisation angle were, for PoGOLite, found by tting

f (x) = T (1 + M cos(2x + 2α) (2.4)

to the observed curve. Here T is the average of the modulation curve as per Figure 2.4:b,

M is the modulation factor and α is the polarisation angle [7]. Compton scattering has

a 180 ^◦ symmetry which is seen by the factor 2 in Equation 2.4.

(a) Compton scattering. (b) Modulation curve.

Figure 2.4: Diagram of Compton scattering and example modulation curve.

E _γ and E γ ⁰ are the energies of the photon before and after scattering with corre- sponding k-vectors ~k 0 and ~k. The angle θ is the polar scattering angle (between

~ k ₀ and ~k along z-axis) and φ the azimuthal angle between polarisation vector

~ e 0 (here along the x-axis) and the projection of ~k on the xy-plane. Plotting the probability of scattering as a function of azimuthal angle yields the modulation curve.

2.3 Detector Basics

While there are dierent methods available to detect and measure electromagnetic radi- ation, the PoGO polarimeters make use of scintillators coupled to photomultiplier tubes to determine the azimuthal scattering angle of incident photons.

2.3.1 Scintillators

A scintillator denotes a uorescent material which emits optical photons when excited by some process, normally ionizing radiation. Ideally, the output should be linearly proportional to deposited energy and the material should be optically transparent to the wavelength distribution it emits so as not to re-absorb the photons, allowing detec- tion by some photo-sensitive detector. In the PoGO+ polarimeter two dierent types of scintillators make up the main detector cells, an organic scintillator and an inorganic scintillator.

In the context of this thesis, the most important property of a scintillator is its decay time. This is the mean time after excitation where the intensity of the uorescent emission has decreased by a factor e ⁻¹ [8]. This property is important as it governs the rise time of the measured signal as a larger number of de-excitations during some time interval gives a faster rise of the resulting pulse during the same interval.

Organic (Plastic) Scintillators

In organic materials orescent light originates from transitions in energy levels, where an

electron is excited when energy from an incident particle is absorbed. This is a molecular

property, thus independent of the physical state of the matter [8]. In PoGO+ the plastic scintillator used is the EJ-204 scintillator by Eljen Technology which has a relatively fast decay time of 1.8 ns [9].

Inorganic Scintillators

For an inorganic scintillator the energy states are determined by the crystal lattice rather than the electron conguration of molecules. When an electron in an inorganic scintil- lator absorbs energy it can be excited from the valence band into the conducting band, leaving a hole where subsequent de-excitation releases a photon [8]. In PoGO+ a bismuth germanium oxide (BGO) scintillator is used. This scintillator is has a high density due to the high atomic number, which increases the probability for interactions with pho- tons and it has a decay time of 300 ns [10], which is slow as compared to the EJ-204 scintillator.

2.3.2 Photomultiplier Tubes

Some photosensitive device is needed to convert the emitted scintillation photons to a readable signal. The most common such device is the photomultiplier tube, the PMT, which converts incident photon energy to a readable current. An incoming photon hits the photo-cathode (conducting metal) window on the PMT which absorbs energy and emits one or more electrons via the photoelectric eect. The interior of the PMT is kept in a vacuum to eliminate collisions between the electrons and other gaseous particles (diusing the kinetic energy of the electrons), eliminate parasitic currents (ionized particles in the gas) and to help the photoelectric eect since the energy supplied to the electron must overcome the work function (a potential barrier the electron must overcome to escape).

If subjected to oxygen an oxide layer will form on the photo-cathode, increasing the work function and hindering electron emission.

The emitted electrons are accelerated towards the rst of a series of dynodes where they multiply by way of secondary emission. The multiplied electrons are in turn acceler- ated toward the second dynode where the process repeats itself. After passing all dynodes in the series the cascade of electrons hits the anode where the signal (current) has been magnied substantially, allowing detection of individual photons even when the energy of the incident photon is low [8]. If the average ratio of emitted secondary electrons per incident primary electron (secondary emission ratio) for each dynode is denoted δ, then the magnication (gain) would ideally be µ = δ ⁿ

for n 0 dynodes. In reality, each dynode does not necessarily have the same secondary emission ratio and there is some collection eciency as not all electrons reach the dynodes. The gain of the PMT thus becomes µ = αδ ₁ δ ₂ . . . δ _n

−1 δ _n

where α is the collection eciency [11]. This process is exemplied in Figure 2.5.

In PoGO+ the PMTs are provided by Hamamatsu [12]. Following are some charac- teristics which dier between individual PMTs.

PMT Dark Current

Even when a PMT is operated in complete darkness some current will pass through it

due to a number of reasons. Since the work functions of the photo-cathode and dynodes

are small (so as to allow a weak signal to multiply and become detectable) the surfaces

Figure 2.5: A simplied view of a PMT. An electron ejected from the photo- cathode is multiplied at each dynode. The multiplicative factor at each dynode is dependent on the kinetic energy of the incoming electron, and thus dependent on the accelerative voltage applied between dynodes [8].

will spontaneously emit electrons at room temperature. Furthermore PMTs operate at very high voltages while being sensitive to very small currents (10 ⁻⁹ A), thus detectable leakage current (I = V/R) may be generated with suciently weak insulation. Dark current may also be generated by radioisotopes trapped in the glass window or from residual gasses inside the interior vacuum (10 ⁻⁶ Pa) [11]. The dark current is generally considered as a source of noise.

PMT Single Photo-Electron Peak

In the single photo-electron region the ux (or energy) of incident photons is suciently low that only a single photo-electron is emitted from the photo-cathode. The single photo-electron peak is a characteristic of the PMT and is a measure of the PMT gain.

In the context of this thesis, the single photo-electron peak is used to determine the performance of the separate detector cells.

PMT Gain

The gain is a measure of how much the signal is amplied over the course of the dynodes.

This varies substantially with PMTs and the applied voltage. In the context of PoGO+

this quantity was taken as a measure of each PMTs performance (where the best PMT has the highest gain and vice versa).

PMT Blue Sensitivity

The blue sensitivity is understood as a measure of the quantum eciency of the PMT, the ratio between ejected photo-electrons to incident scintillation photons. The blue sensitivity is measured by placing a blue lter in front of the PMT and the values for blue-sensitivity are supplied by the manufacturer.

2.4 PoGO+ Astrophysical Targets

Polarimetry has a long history in astronomy and astrophysics beginning in the mid-19th

century with studies treating the linear polarisation of light reected from the moon [4].

PoGO+ is part of an ongoing eort to measure polarisation in high energy radiation (X- ray and above) as it has not been measured with a dedicated polarimeter since the 70's (instead relying on re-purposed detectors). Specically, the PoGO+ instrument aims to investigate the Crab nebula and pulsar by measuring the polarisation of emitted X-ray radiation.

2.4.1 Supernovae and Neutron Stars

At the end of the life of a massive star (a main sequence mass of 10-20 solar masses, M  , with a core mass of about 2M  ) it expels the outer layers which form the super- nova remnant [13]. At this point the star has exhausted all the available fuel and as nuclear fusion stops, the core collapses as the pressure from fusion no longer balances gravity. Depending on the mass of the progenitor star the collapse may stop when the electron degeneracy sets in and stops the collapse (Pauli principle disallows two identical fermions from occupying the same quantum state resulting in a pressure resisting fur- ther compression of matter). This would result in a white dwarf, but if the progenitor mass is large enough, electron degeneracy cannot maintain equilibrium with gravity and electrons capture start producing neutrons via inverse beta decay [13]: p + e ⁻ → n + ν _e (where n and p denote neutrons and protons and ν e is the electron neutrino) and the collapse continues.

When all available electrons have been captured, the core is essentially one massive nucleus and would have a mass of about 1.2-1.6M  . The collapse is stopped by the neutron degeneracy pressure, forming a neutron star. If the core mass exceeds 2M  the degeneracy pressure is not enough to balance gravity and the core collapse to a black hole [14].

It has not been determined exactly what processes trigger the supernova explosion, but it is clear that as the core collapses enormous amounts of energy is released, expelling the outer shells of the pre-supernova star at kinetic energies in the range of 10 ⁴⁴ J [13].

2.4.2 Pulsars

As a neutron star has an immense density (1 − 2M  with a radius of ∼15 km) it retains almost the entire angular momentum of its progenitor, coupled with a strong magnetic

eld (∼ 10 ¹² G) the neutron star may beam electromagnetic radiation from the poles.

If the magnetic and rotational axes are disaligned by some angle α, an observer would experience this beam as a pulse whenever the beam is in line-of-sight (see Figure 2.6:a).

These types of neutron stars are called pulsars, a contraction of pulsating star.

At formation, a pulsar typically has a rotational period of about 0.1 seconds [15]

(the fastest observed pulsar has a period of 1.397 ms [16]). The pulsar spin periods are

extremely stable, however they lose rotational kinetic energy in some combination of

dipole radiation and relativistic particle outow [17].

(a) The pulsar beam electromagnetic radiation from the poles along B. If B and Ω are disaligned by an angle α the pulsar appears to pulsate to a distant observer.

(b) The pulsar magnetosphere and the dier- ent regions of emittance. The magnetosphere is limited by the radius of the light cylinder R

where co-rotation would reach the speed of light in vacuum.

Figure 2.6: Simplied geometry of a pulsar and its magnetosphere. Here, B is the magnetic axis, Ω is the rotational axis and α is the angular separation of B and Ω.

Pulsar Magnetosphere

A simple way of looking at a pulsar is as a fast-spinning dipole (in reality multiple poles may form). On the surface of a neutron star with a magnetic eld of strength ∼10 ¹² G there will also be a strong electric eld which causes charged particles to be ripped from the surface and accelerated along the magnetic eld lines releasing high energy photons which in turn produce positron-electron pairs. This process lls the magnetosphere of the neutron star with charged particles (plasma), from the surface to the edge of the magnetosphere. The plasma eectively screens the longitudinal component of the electric

eld, trapping the plasma along the magnetic eld lines, rotating with the star. This is called co-rotation, and this holds true out to the light cylinder at radius R L = c/Ω where Ω = ^2π _P R is the angular velocity of the star, P is the period and R the radius of the star.

At this distance, a particle co-rotating with the star would reach the speed of light in vacuum.

As co-rotation is no longer possible outside the light cylinder two vastly dierent kind of eld lines arise: closed eld lines, limited by the light cylinder and open eld lines that reach beyond, cannot close and spirals to innity. Close to the surface of the star the open eld lines only occupy small regions close to the magnetic poles, called the polar caps [14]. A simplied view of this can be seen in Figure 2.6:b.

While there is no complete model that fully explains the origin of the observed elec-

tromagnetic spectra from pulsars there are three main contenders [1]; the polar cap

model, the caustic model and the outer gap model. These three models have similar

intensity proles as a function of time (light curves) but predict dierent polarisation

characteristics. Measuring the polarisation could potentially discriminate between them,

lend credibility to one model over the other or set limits on future models, each of which is a desirable outcome.

The Polar Cap model

The polar cap model posits that the emission originates in the polar cap region. There, electrons are accelerated from the surface along the open eld lines and produce curvature radiation. With the strong magnetic eld, 1-γ pair production (normally two photons are required to conserve momentum, here the magnetic eld absorbs the leftover energy) creates electron-positron pairs which in turn are accelerated along the magnetic eld lines, producing high energy synchrotron radiation which constitutes the observed gamma-ray radiation [18]. Observations with the Fermi Large Area Telescope strongly disfavoured this model [19].

The Outer Gap Model

Dierent current ows throughout the outer magnetosphere may result in large regions of magnetospheric charge depletion. These regions extend from the null-charge surface to the light cylinder. E · B = 0 along the borders of this region, caused by a charge layer on the boundary of the closed and open eld lines, the null-charge surface keeping plasma from owing into/out from the region. However, toward the light cylinder there is no border and charged particles may escape, depleting the region of charge (giving rise to a vacuum). This region is called the outer gap and is visible in gure 2.6. While E · B vanishes along the edges of the outer gap there is still a signicant E·B component within, which accelerates particles along the gap where they emit high-energy synchrotron and curvature radiation which in turn pair-produce particles which emit high-energy radiation causing the observed high-energy emission [1, 20].

The Caustic Model

In the (two pole) caustic model two assumptions make up the name. One, that each of the peaks in the light curve originates in dierent magnetic poles (two pole) and two, the radiation is caustic (special relativity eects cause photons emitted at dierent altitudes to pile up at the same phase of a pulse). The emission takes place in a narrow gap trailing the last open eld lines stretching from the polar cap to the light cylinder [21] (seen in Figure 2.6)

2.4.3 The Crab Nebula

The Crab Nebula is possibly the most well studied extrasolar object and is the remnant

from the rst recorded supernovae in history, witnessed by Chinese astrologers in 1054

AD. Three main parts make up the nebula, the outermost part being a very faint and

freely expanding supernovae remnant. Further in lies the bright Crab synchrotron nebula,

which consists of an expanding shell of thermal gas and at the centre one nds the Crab

pulsar [22].

Chapter 3

PoGO+, the Polarised Gamma-ray Observer

3.1 PoGO+ Polarimeter

Figure 3.1: Cross-section of the PoGO+ polarimeter. The instrument is housed inside the pressure vessel, which in turn is housed inside the the rotation frame assembly, allowing the instrument to rotate. Image courtesy of the PoGO collab- oration.

As briey mentioned in Section 1.2 the PoGO+ polarimeter consists of 61 detector cells. In the PoGOLite Pathnder the detector cells were called PDCs, short for phoswich detector cells, alluding to the sandwiching of an EJ-204 scintillator between a BGO crystal and another 'slow' scintillator. Following the omission of the 'slow' scintillator for PoGO+

the detector cells now resemble a smorgas, Swedish for an open sandwich. The PoGO+

detector cells are henceforth abbreviated as SDCs, short for Smorgas Detector Cells.

Figure 3.2: Top view of the detector conguration. The 61 centred, light grey units are SDCs while the darker outer rim is the SAS units. Number order denotes performance ranking, 0 being the best performing SDC and 60 being the worst.

3.1.1 Polarimeter Conguration

The PoGO+ polarimeter consists of 61 hexagonal SDCs arranged in a hexagonal hon- eycomb structure. This structure is in turn surrounded by 30 pentagonal SAS units, the Side Anti-Coincidence shield (SAS). The incident ux is collimated by 67.5 cm long, hexagonal copper tubes placed directly above the SDCs, see Figure 3.1 for a labelled cross section of the polarimeter and Figure 3.2 for a top view of the detector cell conguration.

The position of each SDC in the honeycomb pattern is determined by their perfor- mance ranking, with the best performing SDC placed in the centre and the rest spiralling out with decreasing performance (see Figure 3.2). The best performing SDC is then con- nected to the worst performing PMT and vice versa to attain as uniform performance as possible.

3.1.2 Coincidence Detector

If a photon scatters in any detector cell, it may be absorbed by a neighbour. This would constitute a good event as the photon would be traceable through the two separate detector hits and the scattering azimuthal angle could be estimated (see Figure 3.3).

In order to make sure that the detected two-hit event is actually a Compton scattering followed by photo-absorption and not two separate events (separate photons arriving in separate detector cells) the electronics check for coincidence hits. This means that if one detector observes a hit (Compton scatter) another detector must observe a hit (photo- absorption) within some narrow time limit to constitute a valid coincident hit and by extension a good event.

Historically (during PoGOLite) the coincidence requirement gave rise to some prob-

lems due to unintentional optical cross talk, where scintillation photons escape one de-

tector cell and is detected by a neighbouring PMT, giving a false positive (or a false

Figure 3.3: Example of a scattering event in a detector cell. An incident photon scatters in the central unit and subsequent absorption is detected in a neighbour.

Since each detector cell act as a pixel (no spatial resolution) and centre-to-centre scattering is assumed only a discrete number of angles are measurable (the gure is a simplication, in reality scattering to adjacent cells are allowed but the num- ber of angles are still discrete). To give a continuous distribution of scattering angles the instrument is rotated. The 0-angle is chosen as an arbitrary reference (for astrophysical measurements it is related to some universal direction such as the celestial north).

negative, where photons leak from a good Compton event, registering as a three or more detector hit which is discarded). Thus great care was taken in attempting to make each unit as light-tight as possible.

Since each detector cell lacks spatial resolution and the scattering is assumed to be centre-to-centre a low number of discrete possible scattering angles can be inferred (see Figure 3.3). By rotating the instrument a continuous distribution is produced

3.1.3 Polarimeter Electronics

The signal output from the PMT is read by one of six FADC boards (ash analog to digital converter) custom-built for the PoGO+ polarimeter. Each FADC board has 16 PMT input channels. The FADC boards are used to digitise and sample the waveforms collected from the 93 PMTs in ight (61 SDC units, 30 SAS units and 2 neutron scintillators).

The trigger logic (determining what data to store and what to discard) is handled by the DIO board (digital input/output). The specics of the trigger logic is covered in-depth in Section 3.2. The SDC-PMT pairing to a specic FADC board is chosen in a pattern which would minimise the loss in eciency in the event that one board fails. This pattern is visible as the petal conguration in Figure 3.4.

3.1.4 SAS, the Side Anti-coincidence Shield

The anti-coincidence shield consists of 30 pentagonal, 20 cm long BGO scintillators con-

nected to PMTs. They work together with the BGO scintillators at the bottom of each

SDC as a veto to reduce background events originating from high energy photons and

charged particles incident from the side or from below the polarimeter.

Figure 3.4: Top view of the detector conguration. The 61 centred units are SDCs while the outer rim is the SAS units. The dierent colors correspond to the 6 FADC groups.

3.1.5 SDC, The Smorgas Detector Cell

Figure 3.5: The PoGO+ SDCs. The left gure shows the unclad bottom t- ted into the pixel seat. Middle upper gure shows a wrapped SDC where the numbering denotes production number and production date. Middle lower gure shows an unclad SDC, a 12 cm EJ-204 scintillator glued to a 4 cm long BGO scintillator crystal. The gure to the right shows the front of the SDC, covered by the top-cap.

Each SDC was assembled in the PoGO laboratory at AlbaNova University Center in Stockholm. They consist of the following components given in order of assembly and can be seen in Figure 3.5, or as a simplied schematics in Figure 3.6.

a) EJ-204 scintillator [23]

At the heart of the SDC lies the EJ-204 scintillator. It is a plastic scintillator

produced by Eljen Technology under the name EJ-204. It was chosen for PoGO+

since plastic scintillators have a favourable interaction cross section for Compton scattering and a satisfying sensitivity to photo absorption, the two properties used to measure polarisation. EJ-204 specically was chosen due to the short decay time. In PoGO+ the EJ-204 scintillators are 12 cm long regular hexagons with a at-to-at distance of 27.75 mm.

The emission distribution peaks at a wavelength of 408 nm and the decay time is 1.8 ns.

b) BGO scintillator [24]

An inorganic BGO crystal scintillator is glued to the EJ-204 scintillator using an optically transparent glue. It has a hexagonal top which rounds down to a cylindrical bottom and acts both as a light-guide between EJ-204 and PMT as well as an anti-coincidence veto together with the SAS units. Signals originating from the BGO are used in the online veto. BGO is short for Bismuth Germanium Oxide, Bi 4 Ge 3 O 12 , and the scintillators are supplied by the Nikolaev Institute of Inorganic Chemistry.

The emission distribution peaks at a wavelength of 480 nm and the decay time is 300 ns.

c) ESR sheet [25]

The hexagonal parts are wrapped in one layer of ESR (Vikuiti enhanced specular reector lm) produced by 3M. ESR is optically reective (> 98% reectance across the visible spectrum) but transparent for higher energies. The ESR sheet increases the light collection at the PMT.

d) PTFE tape

Two layers of PTFE tape cover the circular and curved part of the BGO scin- tillator where the ESR lm cannot easily be applied. The tape is 0.2 mm thick and 12 mm wide.

e) Grey Tedlar sheet [26]

A 37 µm thick sheet of grey Tedlar is wrapped outside the ESR sheet. Tedlar is produced by DuPont and is non-transparent. The Tedlar layer thus aids in the light-tightness of the units.

f) ESR top sheet

A small hexagonal sheet of ESR is folded over the top.

g) Black Tedlar top sheet

A small hexagonal sheet of black Tedlar is folded over the top outside the ESR top sheet. Together they make up the top cap.

h) Heat-shrink

The SDC is then covered in heat-shrink from top to bottom. Heat-shrink is a plastic material which shrinks when exposed to heat. Along with Kapton tape (DuPont) the heat-shrink keeps the dierent layers xed in position as well as increases light-tightness and provides some mechanical protection.

i) Pixel seat

The bottom part is covered by the pixel seat, manufactured by the AlbaNova Workshop and made of plastic. The pixel seat xes the SDC to the baseplate in the polarimeter (xes the position inside the polarimeter) and helps guide the SDC to PMT connection.

During PoGOLite there were some problems with optical cross talk, where scintillation photons escape from one scintillator and get detected in a neighbouring PMT, so the Tedlar and black heat-shrink were added in an attempt to eliminate the light leakage.

The ESR sheets and PTFE tape help increase light collection, as much of the light that travels to the sides is reected back, increasing the chances it will reach the PMT. The materials and assembly techniques used were determined through extensive testing and comparisons in the PoGO laboratory [27, 28].

Figure 3.6: The dierent parts of the SDC, labeled in order which they are layered: a): The EJ-204 scintillator, b): The BGO scintillator, c): ESR sheet, d): PTFE tape, e): Tedlar sheet, f): ESR top, g): Black Tedlar top, h) Black heat shrink and i): Pixel seat. e) and f) together make up the top-cap. Figure is not to scale.

3.1.6 SDC Performance

Detector Cell Sensitivity

In the connes of the PoGO project each SDC is ranked according to its detector cell

sensitivity, abbreviated DCS E , with index denoting the energy at which the DCS was

measured. DCS has the unit photo-electrons per keV and is determined by irradiating the

SDC with photons from a radioactive source of some well determined energy. Measuring the output with a PMT yields a histogram of counts per channel number (where the channel number is proportional to energy). This histogram will have two Gaussian peaks, the single photo-electron peak (SPEP) and the photo-absorption peak (PHAP). The detector cell sensitivity is then calculated as:

DCS E = k · X _PHAP

E · X _SPEP (3.1)

where E is the incident radiation energy in keV, k is a gain conversion factor used when the PHAP and SPEP are measured at dierent gains and X PHAP and X SPEP is the photo-absorption peak position and single photo-electron peak position respectively.

Radioactive sources

The radioactive sources used are the isotopes americium-241 (Am241) and barium-133 (Ba133). The energy of the main emission (gamma radiation) of the Am241 source is E _Am241 = 59.5 keV. The Ba133 source energy was taken as a weighted sum of the relevant decay energies as per Table 3.1.

Table 3.1: Energy for the barium-133 source. Note that the following com- ponents of the source energy spectra only covers 52% of the radiation. The remaining radiation will have a negligible eect due to the dynamic range of the electronics as well as a small absorption cross-section for higher energies. Data collected from [29].

Decay Mode Energy (keV) Intensity Normalized Intensity Weighted Energy (keV)

XR kα2 31.82 15.10% 29.01% 9.23

XR kα1 32.19 27.60% 53.03% 17.07

XR kβ3 36.3 2.64% 5.07% 1.84

XR kβ1 36.38 5.10% 9.80% 3.56

XR kβ2 37.26 1.61% 3.09% 1.15

sum 173.948 52.05% 100.00% 32.86

This yields a weighted radiation energy of E Ba133 = 32.9 keV.

3.2 PoGO+ Data Acquisition

3.2.1 Data Acquisition

As the incoming photon deposits energy in a scintillator it gives rise to scintillation light,

a signal which is recorded by the connected PMT and read from the anode by one of

several FADC boards included in the PoGO+ electronics. The sampling rate is 100 MHz,

which means one sample point is taken every 10 ns. 50 sampling points make up a

waveform, as seen in Figure 3.7. Dierent scintillators give rise to dierent waveforms

due to the decay time, where a short decay time (EJ-204) gives a fast rise time in the

signal and a comparatively long decay time (BGO) causes a slower rise.

(a) Waveform recorded from the EJ-204 scintil-

lator. These are referred to as fast waveforms. (b) Waveform recorded from the BGO scintilla- tor. These are referred to as slow waveforms.

Figure 3.7: Example waveforms as recorded with a PMT from two dierent scintillator types. Each point is referred to as a sample point. 50 such sample points are stored for each waveform, giving a window of 500 ns. The rst few sample points make up the baseline, a constant readout in the FADC and ADC values are proportional to the deposited energy.

The energy deposited in the scintillator is calculated as the dierence in ADC value of the peak sample point value and that of the baseline of the waveform as seen in Figure 3.8. The dierence in decay times allows discrimination between events recorded in the EJ-204 scintillator and the BGO scintillator by introducing the fast output and slow output, meant to approximately determine the peak of the fast or slow waveforms respectively.

3.2.2 Online Event Selection

During ight the FADC boards continuously read signals from the PMTs at 100 MHz.

However, it is desirable to minimise dead time (writing to storage) and the required storage space by selecting only the correct events: Compton scattered photons in the EJ- 204 scintillator. In practice this is done by checking a few criteria in the data acquisition procedure, as detailed below and in Figure 3.9.

Criterion 1: Trigger

∆w(n) > T _T

For each waveform sample point w(n) read, the FADC compares the current point to an earlier point separated by the fast separation constant, δ f . If the dierence ∆w(n) = w(n) − w(n − δ _f ) exceeds the trigger threshold, T T , then a trigger candidate is found. In

ight, photo-absorption causes a trigger and the DIO then checks for coincident Compton scatter. For the purposes of this thesis, the trigger threshold parameter was set to 10.

T _T = 10

During PoGOLite, the trigger was set to 300 ADC across all units, (corresponding to

around 20 keV). In PoGO+, the trigger will be set individually for each PMT-SDC pair

(a) Waveform originating from the EJ-204 scin- tillator. Here, the fast output is close to the slow output, and the waveform originates in the EJ204 scintillator or the PMT.

(b) Waveform originating from the BGO scintil- lator. Here, the fast output is much smaller than the slow output and the waveform originates in the BGO scintillator.

Figure 3.8: Example waveforms describing the energy and output characteris- tics. δ f and δ s denote the horizontal separation between baseline and fast or slow output respectively. The vertical separation between baseline and peak gives the energy. ADC values are proportional to the energy deposited. The fast and slow outputs are calculated for each waveform and represents two guesses for the peak position.

to account for dierences in ADC value to keV conversion. Once a trigger candidate is

identied the waveform is scanned for the fast and slow output values.

Figure 3.9: Flowchart detailing the data acquisition steps. 50 sample points, w(n) are stored for each waveform, corresponding to 0.5 µs at 100 MHz. Each sample point is continuously checked for a trigger by checking if w(n)−w(n−δ f ) >

T _T where δ f is the fast separation constant and T T is a trigger threshold value. If a waveform sample point fulls this criterion the waveform is scanned for the fast and slow outputs which in turn are compared according to the fast branch cut, [ Fast Output] > [Slow Output] · 2 ^−N − [ Oset] where N is the slope parameter.

If this criterion is fullled a level zero trigger is issued and the board waits 37 clocks. If no waveform discrimination (WD) or upper discrimination (UD) signal is received, every board that has recorded a hit stores their waveforms.

Fast and Slow output

(a) Fast waveform (waveform originating from an

EJ-204 scintillator) (b) Slow waveform (waveform originating from a BGO scintillator)

Figure 3.10: Example waveforms with identied Fast and Slow output in red

and blue respectively. The sample point causing the trigger is drawn in green. In

this example the separation constants are δ f = 6 and δ s = 37 . Only 50 sample

points are stored for oine analysis, which is why the slow line appears to be cut

o in Figure (a). Online the entire buer is available for scanning.

The outputs are dened as

[ Fast Output] = max (w(n) − w(n − δ f )) for n ≥ δ f ∈ buer [ Slow Output] = max (w(n) − w(n − δ s )) for n ≥ δ s ∈ buer

and are calculated for every waveform. Each waveform sample point w(n) is kept in a ring buer of sucient size for scanning the waveform. The slow and fast outputs are scanned for separately, meaning they do not necessarily occur at the same position in the waveform, as exemplied in Figure 3.10. Plotting the fast output against the slow output yields a two dimensional histogram where two dierent branches are implied, one corresponding to events originating from EJ-204 and one corresponding to events from BGO (see Figure 3.11). For high energies these branches are substantially separated which makes it easy to distinguish between EJ-204 and BGO events. At lower energies the separation between the branches diminishes and distinguishing between events becomes increasingly dicult.

(a) Output branch histogram. (b) Magnied around the single photo electron peak region (high density).

Figure 3.11: Example of a 2D histogram examplifying the fast and slow branches. Data is collected with an SDC irradiated with the Am241 source.

Concentrations of events, branches, correspond to photoelectric absorption in the EJ-204 scintillator (fast) and BGO scintillator (slow). The single photo-electron peak is PMT-specic and thus occurs at the same position for both EJ-204 and BGO.

Criterion 2: Waveform Discrimination

Once both the fast and slow outputs are determined the fast branch cut (FBC) is applied which checks if the fast output is greater than some linear function of the slow output:

[ Fast Output] > [ Slow Output]

2 ^N − [ Oset] where

( N = 0, 1, 2, . . .

[ Oset] = 0, ±1, ±2, . . . (3.2)

The slope is limited to by the 2 ^N parameter in the FADC board, corresponding to a

binary bit-shift operation. If this returns false, the board issues a WD-signal to the DIO

(a) If the pulse is recovering (falling) from a pre- vious event when a trigger occurs it may reach the absolute UD level. In this case, the actual pulse height is low (below the relative UD level) but the event is still discarded as it saturates.

(b) If the pulse is recovering from below the baseline (rising) when a trigger happen it may not reach the absolute UD level. However the calculated pulse height may be larger than the relative UD level and the event is discarded.

Figure 3.12: Sketch of two cases where the event fails the upper discrimination check. Both the absolute UD and relative UD is needed to pass all cases.

a L0 trigger to the DIO which then waits 37 clocks, allowing other boards to issue WD or UD (upper discrimination) signals. If no such signals arrive within this time window, a level one, L1, trigger is issued to each FADC board. Any board with an event above the hit threshold (set to 10 ADC during POGOlite [30]) then stores their waveform.

Upper Discrimination

Some waveforms are saturated, causing the ADC value of each consecutive waveform sample point to remain constant at some value. The possible cause of this could be high energy particles (cosmic rays) or a falling baseline where the waveform is recovering from a previous event when the trigger occurs. The latter case would push the pulse to saturation while the actual deposited energy is within normal bounds. To avoid these events, as the saturation makes it impossible to calculate the peak height, an absolute upper discrimination is used which discards waveforms reaching saturation levels (set to 3700 ADC value). The absolute UD is checked for each waveform sample point continuously.

There is also a relative upper discrimination check, which compares the fast output

to a set value. This is to deal with cases arising when the trigger res during a rising

slope, when the pulse is recovering from below the baseline. Even though the absolute

UD saturation level is not reached the fast output is outside the expected range (above

the relative UD level) and the event is discarded. The absolute and relative UD can be

seen in Figure 3.12.

Chapter 4

Detector Cell Characterisation

In order to select the 61 units for ight (out of 79 units produced) a set of tests were constructed to measure the energy dependent detector cell sensitivity (DCS, as per Sec- tion 3.1.6) and the relative light leakage (abbreviated RLL, quantifying the light leaking from each SDC) of each detector unit. The rst of the tests allowed an absolute ranking of DCS performance and the second to detect and correct units which leaked excessive amounts of light.

4.1 Detector Cell Sensitivity

For the DCS ranking, the photo-absorption peaks of the BGO and EJ-204 scintillators were found for each SDC. The measurement was carried out inside a light-tight box, henceforth referred to as the darkbox, whose purpose was to keep the PMT from be- ing exposed to ambient light and minimise background. A radioactive source was also placed inside the darkbox, irradiating the SDC. The sources used are the radioisotopes americium-241 and barium-133, abbreviated Am241 and Ba133.

4.1.1 DCS Experimental Setup

Each SDC is connected to a PMT by way of optical grease (which bridges the refractive index gap between the scintillator and PMT) and placed inside the darkbox. Then four consecutive measurements are carried out:

1. A background is taken over 120 s real time.

2. A collimated Am241 source is placed in front of the SDC and measured for 120 s real time.

3. A Ba133 source (not collimated) is placed directly in front of the SDC and measured for 120 s real time ¹ .

4. A background is taken over 120 s real time.

1

Some units were re-wrapped. At that point only the Am241 source was available and this step was

thus excluded.

The PMT is operated at 12 V and controlled through a control voltage. The control voltage is slowly ramped, meaning it is steadily increased from 0.0-4.7 V over 5 seconds before each measurement, and steadily decreased from 4.7-0.0 V over 5 seconds after each measurement. The PMT has an internal DC-DC converter with conversion factor 250 meaning a supplied control voltage of 4.7 results in an actual voltage of 1175, providing the potential dierence accelerating electrons. The PMT is connected to a pre-amplier (Ortec model 113 [31]) with input capacitance set to 200 pF (inversely proportional to output voltage) and an amplier (Canberra model 2026 [32]) set to a gain factor of 100.

The background measurements are carried out in order to make sure that the background does not substantially change over time (the PMT readout is dependent on temperature and has some settling time from power-up). One further background measurement is taken daily at gain factor 500, to determine the single photo-electron peak of the PMT.

The data is collected by a multichannel analyser (MCA8000A) and software (ADMCA) produced by Amptek [33].

Figure 4.1: Experimental setup of the DCS tests. On top is a side view of the SDC-Source geometry where the source is either Am241, Ba133 or removed for background. Below is a schematic view of the dierent electronics involved in a measurement.

Analysis method

The data is collected as a series of pulse height distributions via ADMCA. The analysis software is written for the C++ based toolkit ROOT, developed by CERN [34]. The analysis is done by tting a function [27, 28] to the observed histogram, obtaining the position (channel number) corresponding to the photo-absorption peak for both the EJ- 204 and BGO scintillator (visible in Figure 4.3). The function is

S(x) = s _peak (x) + s _bg (x)



 

 

s _peak (x) = p ₀ exp



− ¹ ₂ 

p

−x p

 2  s _bg (x) = p ₃ + p ₄ x + p ₅ exp h

− _x−p ^p

7

i (4.1)

where s peak (x) represents the peak, s _bg (x) represents the background and p i are free parameters. The peak is assumed to be Gaussian while the background consists of a linear part and a semi-exponential part.

The same function is also tted to the daily single photo-electron peak measurement,

and the two positions, SPEP and PHAP (see Section 3.1.6), give the DCS (with con-

(a) Peak position as a function of increasing gain. As the electronics reached saturation around 3000 no further peak shift was visible.

(b) Below the saturation level the peak position is linearly proportional to the gain.

Figure 4.2: A pulse generator was connected in place of the PMT and measured with the setup in Figure 4.1. A Gaussian was tted to the peak and the peak position is plotted here for dierent gain and control voltage. As can be seen in (b), the peak position is linearly proportional to the gain below saturation levels.

version factor k = 5, as the PHAP was measured at gain 100 and SPEP at gain 500) DSC = 5

E

X _PHAP

X _SPEP (4.2)

where the peak position scales linearly with the gain as can be seen in Figure 4.2

(a) Fit for the EJ-204 PHAP. Data recorded

with the Am241 source. (b) Fit for the BGO PHAP. Data recorded with the Am241 source.

Figure 4.3: Example of two dierent photo-absorption peaks (PHAP) tted for in the same data. Here, the number of entries corresponds to number of bins, not counts. The red curve is the total t, S(x), the green curve the tted Gaussian signal s peak (x) and the magenta curve the background, s bg (x) . In the

t statistics, parameter p 1 (p1) gives the photo-absorption peak position with

errors, used to calculate the detector cell sensitivity (Section 3.1.6).

4.2 Relative Light Leakage

Light tightness is an important factor of the PoGO+ polarimeter. If one SDC is allowed to leak scintillation photons to other SDCs, the detector will record the event as hits in two separate detector cells, much like a Compton event (Section 3.1.2). Due to diculties in appraising a absolute light-tightness, the SDC units were tested for leakage relative to each other. Relative Light Leakage is henceforth abbreviated RLL.

4.2.1 RLL Experimental Setup

Figure 4.4: The setup inside the darkbox during the RLL tests.

A blue LED is placed in the previously mentioned darkbox, irradiating the SDC at an angle as per gure 4.4. Each SDC is in turn connected to the PMT with optical grease.

Great care was taken in ensuring that leaks not part of the SDC were sealed. This involved wrapping all PMT cabling in multiple layers of opaque, black plastic sheets and covering the small gap between PMT-SDC in multiple layers of black electrical tape.

Two measurements are taken for each SDC: A 120 s live time background measure- ment (LED turned o) and subsequently a 120 s live time signal measurement (LED turned on). The amplier gain was set to 1000 during these measurements. The PMT control voltage was ramped up to 4.7 V before each set of measurements as the LED could be turned on and o remotely (so the dark box did not need to be opened) and ramped down between change of SDC.

Analysis method

For each measurement a simple Gaussian curve is tted to the single photo-electron

peak giving the single photo-electron peak position. Then the full spectrum is integrated

from the single photo-electron peak (parameter p 1 ) minus one standard deviation of the

Gaussian curve (parameter p 2 ) up to the maximum bin, 4096 (number of entries in Figure

4.3). This gives the total number of counts while discarding the noise occurring below

the single photo-electron peak. Comparing the integrated spectra for the background

(LED o) with that of the signal (LED on) gives the relative increase in signal due to

LED light leaking into the scintillator.

The gure of merit is chosen as (relative light leakage)

RLL = R 4096

p

−p

F _LED (x) dx R 4096

p

−p

F _BG (x) dx (4.3) where F LED (x) is the spectrum recorded from the LED on case, F BG (x) is the spectrum recorded with the LED o and p 1 , p 2 , p ⁰ 1 and p ⁰ 2 are the peak position and standard deviation for LED on and LED o respectively.

4.3 Results

4.3.1 Reproducibility

A reproducibility test was performed to estimate the error of reproducibility, as in the error arising from dierences in handling the detector cells, setting up each measurement and other hard-to-control sources of systematic errors. This was done by testing ve units with the method described in Section 4.1.1. Each unit was tested ve times and cleaned with isopropanol between measurements. The maximum relative deviation (deviation from the mean) of the calculated DCS was taken as the best-estimate of the error in reproducibility. The resulting data is summarised in Table 4.1 and the largest dierence over ve measurements with one unit is below 3%. This means that the method in applying optical grease is either consistent or the precise amount of grease has a negligible eect on measurements. Furthermore the placement (connection) of PMT-SDC does not change or aect the measurement in any signicant fashion. Other experimental dierences, such as source placement or light tightness of the dark box (background) should not aect the peak position of the spectra.

Table 4.1: Summarised results from the reproducibility tests. The largest rel- ative deviation from the mean (across all ve units) is 2.87%. The unit names correspond to production order.

Unit P01 P02 P03 P04 P05

Am241 EJ204 mean DCS 59.5 1.254 1.233 1.320 1.200 1.259 maximum Rel.Dev. 0.49% 1.45% 0.78% 0.44% 0.74%

BGO mean DCS 59.5 0.593 0.592 0.626 0.584 0.606 maximum Rel.Dev. 0.38% 2.87% 1.69% 1.04% 1.12%

Ba133 EJ204 mean DCS 32.9 0.612 0.601 0.642 0.585 0.612 maximum Rel.Dev. 0.70% 1.61% 1.32% 0.21% 1.21%

4.3.2 Unit Rewrapping

On analysing the data collected in the RLL tests eight units were found to leak excessively

(a RLL of ∼5 to ∼35 where the rest had an RLL less than 5, see Figure 4.11). It was

assumed that the leakage was due to gaps in the wrapping (around the top cap) and