Development and characterization of the TOF-Wall detector of the FOOT experiment

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University of Pisa

Department of Natural, Mathematical and Physical Sciences Master’s degree in Physics

Development and characterization of the

TOF-Wall detector of the FOOT experiment

Candidate:

Marco Montefiori

Thesis Advisor:

Matteo Morrocchi

External Supervisor:

Maria Giuseppina Bisogni

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Abstract

Hadrontherapy, also called Particle Therapy, is a consolidated clinical treatment for solid tumors based on the application of charged particles beams. The main advantage of this technique with respect to conventional radiotherapy, based on photons and electrons beams, resides in the different energy loss mechanism that characterizes the interaction of protons and heavier ions with matter. Charge particles release most of their energy at the end of their path inside the medium, while the energy deposition in the entrance channel is low. The effective result is the delivery of a high dose to the anatomic district of interest, sparing the healthy tissues. Another advantage of adopting heavy charged particles in treating tumors consists in their enhanced biological effectiveness with respect to photons and electrons and, as a consequence, their capability to produce a direct damage to the cancerous cells is higher.

Nuclear fragmentation processes induced by the interaction of protons and heavier nuclei with matter are one of the most discussed topics in hadrontherapy. In heavy ion treat-ments, the main effect of nuclear inelastic interactions consists in the fragmentation of the projectile. The reaction products have generally the same velocity and direction of the projectile, but lower mass. Therefore they have a longer range than the primary particle and they will deliver a undesirable dose beyond the tumor volume. Differently, in proton therapy the production of short range target fragments can lead to an enhanced local dose deposition in the entrance region. The lack of experimental data about the reaction cross sections in the energy range of hadrontherapy make the evaluation of the fragments contribution to the dose difficult.

The main goal of the FOOT (FragmentatiOn Of Target) experiment is to measure the target and projectile double differential cross section of nuclear fragmentation reactions relevant for hadrontherapy. To reach this goal, the experimental apparatus is especially designed to adopt inverse and direct kinematic approaches to accurately characterize both the cases. To identify the nuclear fragments produced by different particles beams, FOOT performs measurements of mass, charge and velocity. Charge identification is performed with a combined measure of Time Of Flight (TOF) and energy deposited in a detector named TOF-Wall (TW).

The TW is composed by two orthogonal layers of 20 plastic scintillator bars. The readout of the TW signals is performed by Silicon PhotoMultipliers (SiPMs) optically coupled at the ends of each bar. The requirements of FOOT experiment are to reconstruct the Z of the fragments and their mass with an accuracy respectively of 2-6 % and 3-6%. To reach this goal, an energy resolution of ∼ few % and a TOF resolution of about 100 ps are required.

This thesis work is focused on the optimization of the TW operation conditions to meet the FOOT requirements. SiPMs were firstly characterized to measure their main pa-rameters (gain, dark count rate, crosstalk and afterpulse) as a function of the applied overvoltage. The obtained results were then included in a Monte Carlo simulation to model the SiPMs response when they are irradiated by the scintillation photons produced by the particles impinging on the bars. Simulation outcomes were studied to determine the energy resolution for different particles and by varying the operation parameters of the SiPMs to understand the effective impact of the photodetector in energy measurements. At a fixed SiPMs overvoltage, a resolution of about 6.1% was obtained for protons, while for carbons it varied from a minimum of 2.7% (115 MeV/u Carbon ions) to a maximum of 5.6% (400 MeV/u Carbon ions). Based on these results, the main contribution to the energy resolution is due to the plastic scintillator. In fact, from an additional comparison

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with an ideal case (i.e. SiPMs PDE at 100% and without dead regions), SiPMs noises and finite PDE have no significant impact on the energy resolution. Finally, the simulation performed for a fixed particle (i.e. protons) by varying the SiPMs overvoltage highlights that the impact of the PDE is relevant only for low overvoltage.

In chapter One the basis of the hadrontherapy and of the radiation interaction with matter for the charged particles are introduced. It is followed by a description of the rel-evant radiobiological parameters and an explanation the role of the nuclear interactions in hadrontherapy. Chapter Two is a description of the measurements strategies and the experimental setup of FOOT experiment. Chapter Three is focused on the TW detector. After a description of the structure and the data acquisition system, an overview of some preliminary experimental results and the related issues is given. In chapter Four and chapter Five the features of the main components of the TW (i.e. plastic scintillator and SiPM respectively) are described. Chapter Six presents the SiPMs characterization anal-ysis workflow and the Monte Carlo simulation framework and reports the related results. The conclusive chapter Seven includes the results of preliminary tests on the entire TW, where I contributed significantly both in the detector assembly and test.

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List of Figures

1.1 Brain tumor treated with photon and protons IMRT . . . 2

1.2 Bethe-Bloch . . . 3

1.3 Landau and Vavilov distributions . . . 4

1.4 Beam lateral spread from Multiple Coulomb Scattering . . . 5

1.5 Energy loss by heavy charged particles beams . . . 6

1.6 Abrasion-ablation model . . . 7

1.7 Dose deposition comparison and SOBP . . . 8

1.8 DNA damages . . . 9

1.9 Cell survival fraction . . . 10

1.10 RBE vs LET: experimental data for ions . . . 11

1.11 Target fragmentation in proton therapy . . . 12

2.1 Hydrogen cross section from CH2 and C . . . 17

2.2 Nuclear fragments expected emission with MC: 16_{O at 200 MeV/u on C} 2H4 17 2.3 FOOT: electronic setup . . . 18

2.4 Start Counter and Beam Monitor schematic view . . . 19

2.5 Permanent Magnets . . . 20

2.6 BGO Calorimeter . . . 22

3.1 TOF-Wall picutres . . . 24

3.2 TOF-Wall components . . . 24

3.3 TOF-Wall bar numbering . . . 25

3.4 WaveDAQ scheme . . . 26

3.5 WaveDREAM board . . . 26

3.6 Schematic view of a DRS chip . . . 27

3.7 Scheme of irradiation of the TW in CNAO 2019 . . . 27

3.8 Results of Birks fit at CNAO 2019 . . . 29

3.9 Energy resolution obtained at CNAO 2019 . . . 29

4.1 Energy levels of a plastic scintillator . . . 32

4.2 Scintillation efficiency of plastic scintillator . . . 33

5.1 Scheme of a p-n junction . . . 36

5.2 SiPM internal structure . . . 37

5.3 SPAD and SiPM circuit . . . 37

5.4 Gain and signal amplitude vs overvoltage . . . 38

5.5 Representation of the history of crosstalk excitation . . . 40

5.6 SiPM signals . . . 41

6.1 Experimental setup for SiPM characterization . . . 44 vii

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viii LIST OF FIGURES

6.2 Application of the DLED filter . . . 45

6.3 Undershoot correction . . . 46

6.4 SiPM signals area histogram . . . 47

6.5 Fit gain vs overvoltage . . . 47

6.6 Scatterplot of SiPM signal amplitude vs time distance . . . 48

6.7 SiPM signals amplitude histogram . . . 49

6.8 Fit crosstalk vs overvoltage . . . 50

6.9 SiPM signals delay graphs . . . 51

6.10 Fit of dark count rate and afterpulse vs overvoltage . . . 52

6.11 Experimental setup for SiPM saturation . . . 53

6.12 Responsivity of the calibrated photodiode . . . 54

6.13 Photocurrent cross-calibration . . . 55

6.14 Fit of the SiPM waveform . . . 55

6.15 Voltage drop on the filter . . . 56

6.16 Saturation model . . . 57

6.17 Simulation flowchart . . . 59

6.18 Photons on the SiPM board . . . 60

6.19 Simulated waveform . . . 61

6.20 Charge and photons distributions for C ions of 115 MeV/u . . . 62

6.21 Birks fit for charges and photons . . . 63

6.22 Histograms of reconstructed released energy . . . 63

6.23 Reconstructed energy resolution at 5V overvoltage . . . 64

6.24 Reconstructed energy resolution of protons as a function of SiPM overvoltage 65 6.25 Comparison between energy resolution at 5 V with experimental data . . . 65

7.1 Example of a IV curve of a TW SiPMs board . . . 69

7.2 Set of IV curves for TW edges . . . 70

7.3 Experimental setup used for cosmic rays acquisitions . . . 70

7.4 Example of Landau distribution fit . . . 71

7.5 Results of the attenuation length . . . 72

7.6 Differences of the timestamps between the two ends of a bar . . . 73

7.7 Results for the scintillation light propagation speed . . . 74

7.8 Differences of the timestamps between the layers . . . 75

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List of Tables

2.1 Expected characteristics of target fragments in hadrontherapy with protons 16

3.1 EJ-200 characteristics . . . 25

3.2 TW SiPMs characteristics . . . 25

6.1 Characterization parameters . . . 50

6.2 Time constants of a SiPM waveform . . . 56

6.3 Fit results for the saturation model . . . 57

6.4 Characteristics of the ions included into the SiPMs MC simulation. . . 58

6.5 Reconstructed energy resolutions at 5 OV . . . 64

6.6 Reconstructed energy resolutions for protons . . . 64

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Chapter 1 Introduction to Hadrontherapy

1.1 Hadrontherapy

According to estimates of the World Health Organization (WHO), the number of deaths caused by cancer in 2018 amounts to 9.6 millions [1]. One of the main oncological treatments is radiotherapy [2], adoptable in combination with surgery or chemotherapy-immunotherapy. It makes use of ionizing radiation to kill the cancerous cells and stop their uncontrolled proliferation. At the same time, healthy tissues or Organ at Risk (OAR) surrounding the tumor have to be spared. The most common used radiations in radiotherapy are X-rays and electrons, both produced by LINAC accelerators. The main disadvantage in adopting this kind of radiation is the high dose released in the healthy tissues surrounding the tumor. In case of deep-seated tumors, it is necessary to cross-fire the clinical region from many angle to increase the lethal damage. The most optimized version is the IMRT (Intensity Modulated RadioTherapy). The radiation beams are con-formed and modulated in intensity to achieve a resulting irradiation that cover the entire tumor volume while minimizing the dose to healthy tissues.

Hadrontherapy [3] is a form of radiotherapy for the treatment and cure of solid tumours that are surgically inoperable or resistant to conventional radiotherapy. Unlike radiother-apy, it involves the use of proton and heavier ions (mainly C ions). The peculiar feature is their depth-dose profile, in which the released energy increases up to a specific region known as the Bragg Peak (BP). The results in adopting proton and heavy charge particles is to deliver a high dose to deep-seated tumors and sparing the healthy tissues and the OAR. The typical energy range for therapeutic applications is 50–250 MeV for protons and 50–400 MeV/u for carbon ions. Figure 1.1 reports an example of a brain tumor treated with IMRT and hadrontherapy. The dose maps superimposed to the clinical images show clearly that using charged particles instead of X-rays or electrons leads to a dose sparing to the surrounding healthy tissues.

1.2 Physics

In their passage through matter, protons and heavy ions undergo three main interac-tions that lead to kinetic energy losses and deflection of the particles from their incident direction:

• inelastic collision with atomic electrons • elastic scattering with nuclei

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2 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY

Figure 1.1: Comparison between brain tumor treated with photon (top) and protons (bottom) IMRT along axial, coronal and sagittal planes (from [4])

• nuclear interactions with the nuclei, both elastic or inelastic

In addition, there are also two energy loss mechanisms by radiative emissions. These are emission of Cherenkov light and emission of radiation (Bremsstrahlung).

The total energy dE lost by the particle per length unit dx is defined stopping power S:

S = dE

dx (1.1)

Nevertheless, due to particles mass and energy in the range of hadrontherapy, radiative energy losses are negligibles.

1.2.1 Inelastic collisions with the atomic electrons

The energy loss per unit length of heavy charged particles was firstly explained by Bohr in a classical approach. Quantum mechanical corrections were introduced by Bethe and Bloch in the following formula ([5]):

dE dx el = 2πNar2emec2 ρtZt At Z2 β2 1 2ln 2mec2β2γ2Wmax I2 t − β2₋ δ 2 − C Z (1.2)

with 2πNare2mec2 = 0.1535 MeV cm2/g and where

• Na is the Avogadro number.

• me and re are the mass and the classical radius of the electron.

• Zt, At and It are the atomic number, the mass number and the mean excitation

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1.2. PHYSICS 3 • Z, β = v/c and γ = 1/p1 − β2 are the atomic number, the velocity relative to light

speed c and the Lorentz factor of the incident particle. • It is the mean excitation potential of the absorber.

• Wmax is the maximum energy transfer in a single knock-on collision given by

Wmax =

2mec2β2γ2

1 + 2γme/M + (me/M )2

(1.3) with M mass of incident particle.

• δ is the density correction, which considers the polarization of the target medium given by the electric field of the particle. This term becomes relevant only for high energies.

• C is the shell correction, only significant when the particle velocity is comparable with the one of orbital electrons.

Figure 1.2: Example of mass stopping power (1 ρt

dE

dx) as a function of the energy of the

projectile for different heavy charged particles (from [5]).

The Bethe-Bloch formula, given by Equation 1.2, provides an average value of energy loss per unit of lenght. For any particle, the number of interaction suffered follows a certain statistical distribution depending on the thickness of the absorber, so the effective energy loss value undergo on straggling. The κ parameter is used to define the different regions of validity:

κ = ∆

Wmax

(1.4) where ∆ is the actual energy loss in a single interaction and ∆ is its mean value. Wmax

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4 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY κ >> 1: if the thickness of the medium x is large (or β << 1), there will be a great number of interaction per unit of length, thus the energy loss follows a Gaussian distribution according with Central Limit Theorem

f (∆) = √1 2πσe −∆−∆ 2σ2 (1.5) with σ2 = 1 − 1 2β 2 1 − β2 σ 2 0, σ02 = 156.9 · ρt· Zt At · x MeV2

κ ≤ 0.01: if the absorber is thin or β ∼ 1 the energy distribution is well described by the Landau theory ([6])

0.01 < κ < 1: Vavilov, along the line of Landau’s formulation, derived a more accurate straggling distribution by introducing the kinematic limit on the maximum trans-ferable energy in a single collision ([7]). An example of these latter distributions is shown in Figure 1.3.

Figure 1.3: Example of Landau (L) and Vavilov distributions for different values of κ (from [5]). In the picture, φ and λ are two parameters respectively proportional to the probability density function and the energy loss.

1.2.2 Multiple Coulomb Scattering

Charged particles elastic scattering with the target nuclei are well described by the Rutherford differential cross-section

dσ dΩ = Z 2_Z2 tr 2 e mec/βp 4 sin4(θ/2) (1.6)

where p is the momentum of the incident particle and θ the scattering angle. The sin−4(θ/2) dependence highlights the fact that the particle is scattered at small angles. Nevertheless, the cumulative effect of these small deflections is a change in the particle starting direction. This is usually referred to as Multiple Coulomb Scattering (MCS). In 1948 Mòliere calculated the angular distribution P (θ, x) as a function of the penetra-tion depth x by solving the transport equapenetra-tion [8]. For small angles (θ ' 0), this function can be expressed in a Gaussian form [9]:

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1.2. PHYSICS 5

P (θ) = √ 1 2πσθ

e−2σθ2θ2 (1.7)

The standard deviation of this distribution was calculated by Highland ([10]) and it is given by: σθ = 13.6 M eV pv Z r x X0 1 + 0.038 ln x X0 (1.8) where p, v and Z are respectively the momentum, velocity and atomic number of the particle, x is the penetration depth and X0 is the radiation length of the medium.

Equation 1.8 shows that angular distribution is narrower for high momentum. On the other hand, for a fixed value of velocity, lateral dispersion increases for lighter particles. Figure 1.4 reports some example of lateral spread of several ion beams due to MCS.

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Figure 1.4: Lateral spread of hadron beams caused by MCS obtained from Monte Carlo simulations:(a) Lateral spread for different beams with a fixed range of 15 cm in water as a function of penetration depth; (b) Beam width after 15 cm of water for different ions as a function of energy (from [11]).

1.2.3 Range

The Bethe-Bloch formula shows that for non-relativistic energy, the leading term is given by the 1/β2 factor. The sharp decrease of the stopping power reaches a minimum

around β ' 0.96, called minimum of the ionization curve. As the particle velocity in-crease, the 1/β2 _{factor becomes almost constant and the logarithmic realitivistic rise is}

mitigated by the density correction.

The typical behavior of the stopping power as a function of the penetration depth is shown in Figure 1.5a. A larger energy per unit of length is released close to the end of particle trajectory rather than its beginning. This region is known as Bragg peak. The expected value of the pathlength of the particle when all the kinetic energy is lost is called range. In Figure 1.5b a beam attenuation profile is plotted as a function of absorber thickness. In the first part of the graph, almost all the particles survive, while towards the end of the path the curve slopes down over a certain spread of thickness. This result is due to the statistic mechanisms explained in the previous sections (energy straggling and MCS) and it is known as range straggling.

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6 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY Assuming that the energy loss is continuous, i.e. in the Continuous Slowing Down Ap-prossimation (CSDA) [5], the range is related to the particle initial kinetic energy E0 by

the formula: RCSDA= Z E0 0 dE dx −1 dE (1.9) (a) (b)

Figure 1.5: (a) Typical curves of the energy released by one (solid line) or multiple (dashed line) heavy charge particle inside a material as a function of the distance traveled (from [12]). (b) Transmission curve for hadron beam (from [5]).

1.2.4 Nuclear Interactions

In addition to the electromagnetic mechanisms explained in the previous sections, charged particles can suffer nuclear interactions with the medium nuclei. This type of reactions can subdivided in:

• Elastic collisions: the total kinetic energy is conserved and the involved nuclei are preserved.

• Inelastic collisions: their outcome is a production of secondary fragments.

The most frequent inelastic nuclear reactions are peripheral collisions, that in energy range of hadrontherapy are well described by abrasion-ablation model [13] that is schema-tized in Figure 1.6: firstly, in the overlapping zone of the primary particle and target nucleus (called fireball), involved nuclei get abraded and nucleons are released; after-wards, the ablation process takes place, i.e. nuclei fragments and fireball de-excite into their ground state, with possible emission of γ-rays or light particles.

Nuclear fragments produced by the primary particles and have the same velocity of the projectile thus are mainly forward peaked. The ones generated from target nuclei at rest are isotropically emitted.

From a theoretical point of view, the result of nuclear interactions is an attenuation of the starting number N0 of a beam particles as a function of the deph penetration x:

N (x) = N0 e− x

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1.3. RADIOBIOLOGY 7

Figure 1.6: Visualization of the abrasion-ablation model for a proton-nucleus (top) and nucleus-nucleus (bottom) interaction (from [14]).

where λ is the mean free path related to the reaction cross-section σR with the formula:

λ = 1 n · σR

(1.11) where n is the number of target nuclei per unit of volume.

A good representation of σR is given by the Bradt-Peters equation [15]:

σR = πr20f1(E)

h

A1/3_p + A1/3_t − f2(E)

i

(1.12) where r0 ' 1.2 fm is the nucleon radius, Ap and AT are the mass numbers of projectile

and target nuclei and f1,2(E) are functions of parametrization.

In particular for the light fragments (A < 20), experimental data about σR still do not

completely cover the entire energy range of hadrontherapy. Some data about fragmenta-tion of carbon ions are available ([16]), but data about proton cross sections are missing. This lack of experimental values has implications concerning the modeling of the biological effectiveness of the nuclear fragments deriving from protons and heavier ions.

1.3 Radiobiology

The fundamental parameter used to quantify the biological effects of a radiation is the absorbed dose D, defined as the ratio of the energy dE deposited in a certain volume and the mass dm of that volume:

D = dE

dm (1.13)

It is measured in Gray (Gy): 1Gy = 1 J kg−1_{. [}₁₇_]

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8 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY characteristic depth-dose profile. The photon dose decreases exponentially with penetra-tion depth, while the heavy charged particles depth-dose profile shows a at plateau region with low dose and a distinct peak close to the end of range of the particles. The effective result in using charged particles instead photons is to achieve the same biological effect with lower integral dose to healthy tissue. The dose delivery is usually calculated with a Treatment Planning System (TPS), a software that calculates the number, orientation, type, and characteristics of the radiation beams in order to optimize the clinical treat-ment. Firstly medical images obtained from Computed Tomography (CT) allow to model the anatomic district of clinical interest. Then the target volume, beam directions and shapes are defined and dose profile is evaluated. A representation of typical dose-depth profiles for different type of radiations is shown in Figure 1.7a. To cover the whole tumor area, a series of pencil beams with different initial kinetic energies are used, forming the so-called Spread-Out Bragg Peak (SOBP). This technique is schematized in Figure 1.7b. By looking at the dose profiles of charged particles in Figure 1.7a, some differences can be noted in case of protons and carbon ions. First of all, carbon ions have a narrower BP region and have a higher peak/entrance channel dose ratio. This aspect suggests that using carbon ion could lead to spare more the healthy tissues. On the other hand, carbon ions dose-depth curves show a tail beyond the BP. This effect is caused by the projectile fragments, which have the same velocity but lower charge, have longer range that goes beyond the BP region. The result is a non-negligible dose deposition in healthy tissues located behind the tumor volume.

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Figure 1.7: (a) Comparison between the dose deposited in water by different types of impinging beams and (b) example of Spread-Out Bragg Peak formed by a series of proton beams (from [11]).

1.3.1 DNA damages and cell survival model

When a radiation passes through a biological tissue, it releases energy through the physical mechanisms explained in the previous section. The ionization phenomena pro-duces chemical and biochemical changes with consequent functional and morphological alterations leading to biological damage. These effects occur at the level of the cell nu-cleus. The deoxiribonucleic acid (DNA) is the most sensitive target as it has a complex structure with less ability to repair damage.

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1.3. RADIOBIOLOGY 9 DNA damages are typically classified into:

• direct damage: the energy of the radiation is released directly on the biomolecules; • indirect damage: the energy is released to the water molecules resulting in the production of free radicals, highly reactive chemical species that interact with the biomolecules, altering their chemical structure.

Regardless of the type of damage, the effective result is the alteration of DNA helix structure. There are three kind of lesions schematized in Figure 1.8.

• Single Strand Break (SSB): damage involves only one of two strands. This lesion is readily repairable using the opposite strand as a template, thus the biological effect is limited.

• Double Strand Break (DSB): both sides of the helix are broken. Usually, this kind of lesion is irreversible, thus can lead to cell death. In hadrontherapy, the aim of charged particles is deliver this type of damage to cancerous cells.

• Clustered damages: they occur when two or more lesions are formed within a few tens of DNA base pairs. The outcome of these interactions mainly depends on the position of the damaged DNA sites. [18]

Figure 1.8: Representation of DNA damages (from [18])

A quantity related to radiation damage and thus frequently used in dosimetry and radiobiology is the Linear Energy Transfer (LET), defined as follows:

LET = dE dx

∆

(1.14) where dE is the average value of energy loss due to interactions with the target electrons along a distance dx without considering all the secondary electrons produced by the interaction whose kinetic energy is greater than a value ∆. For neutral radiations (photons and neutrons), LET is referred to the stopping power of secondary particles produced by the interactions of the primary particles. [19]

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10 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY • sparsely ionizing radiations: they are characterized by a low LET value (∼ 0.25

keV/µm) and include photons and electrons.

• densely ionizing radiations: they are characterized by a high LET value (∼ 250 keV/µm) and include protons, α particles, heavier ions and neutrons.

The impact of ionizing radiations on biological tissues is evaluated by studying their clonogenical capability. Cell coltures in vitro are irradiated and their proliferation is analyzed with the cell survive curves, where the surviving fraction is plotted in semi-logarithmic scale as a function of the delivered dose. A mathematical model that well describes cell survival curves is the linear-quadratic model:

S(D) = e−αD−βD2 (1.15)

where S is the surviving fraction, D is the absorbed dose and α and β are parameters that describe respectively the radiosensitivity of the exposed cells. The curvature is measured in terms of the α/β ratio, corresponding to the dose at which the linear α and quadratic β contributions are equal. Tumors and early, acute reactions in normal tissues have gen-erally high α/β ratio (around 10 Gy), while late normal tissue complications normally have low α/β ratio (around 2 Gy) [11].

As can be seen from Figure 1.9, the curve has a different shape depending on the ra-diation LET: for low-LET rara-diation (blue curve), low dose region indicates a repairable damage, while for higher doses follows an exponential behaviour highlighting irreversible lesions (red curve); on the other hand, for high-LET doses only lethal damage can occur. Therefore, the purely exponential term is always dominant and the surviving model is described by:

S(D) = e−αD (1.16)

Figure 1.9: Representation of cell survival fraction as a function of absorbed dose for high and low LET radiation (from [20])

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1.3. RADIOBIOLOGY 11

1.3.2 Relative Biological Effectiveness

At equal absorbed doses, radiations of different kind produce different biological effects. In radiobiology, these differences are evaluated by means of a quantity called Relative Biological Effectiveness (RBE) defined as the ratio of the dose DX of a reference radiation,

(typically X-rays or γ-rays produces by60Co decay) to the dose D of a radiation of interest

resulting in the same biological effect (endpoint). RBE = DX D endpoint (1.17) The RBE is a quite complex quantity, depending on physical parameters, like radiation type, dose and LET, as well as biological ones (tissue type, cell cycle phase, oxygen con-centration etc.).

In ion therapy, RBE is used to define the RBE-weighted dose or biological dose, obtained by multiplying the absorbed dose by the RBE value. This quantity provides the conven-tional photons dose that produces the same biological effects of the radiation of interest. Figure 1.10 shows the behaviour of the RBE as a function of the LET of several ion beams, obtained from experimental data. The general trend consists of an increase of RBE from low-LET up to 100-200 keV/µm, followed by a decrease for higher LET due to the "overkilling effect", i.e. the damage induced in cells overcomes the amount needed to cause death and tissues receives unnecessary dose.

Figure 1.10: RBE10 values obtained for different ion beams in in-vitro experiments. The

subscript refers to the fixed percentage (10% in this case) of surviving cells. The displayed data are taken from the Particle Irradiation Data Ensemble (PIDE) of GSI (from [21]).

For protons, instead, a significant increase in RBE with radiation LET has not been observed. Protons used in therapy generally have an entrance energy between 150 and 250 MeV, corresponding to a low-LET in water of about 1 keV/µm that reaches ∼ 6 keV/µm only in the last mm of the SOBP [11]. For that reason, a fixed value of RBE equal to 1.1 is currently adopted for protons, thus they are considered 10% more efficient than therapeutic photons along they entire track. This choice can lead to an underestimation

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12 CHAPTER 1. INTRODUCTION TO HADRONTHERAPY of biological effects. In fact, different radiobiological studies have shown a non-negligible RBE enhancement with values up to 1.6 both in entrance channel and in the SOBP region [21].

One of the physical factors determining the enhancement of the RBE for protons is the role of the nuclear interactions. A recent work published by Tommasino & Durante [22] provides a plausible explanation of the proton RBE increase. Differently from heavy ions, nuclear interactions for protons result only in fragments deriving from the target nuclei, having very short range and high LET (and RBE). These particles release their energy in ∼ 10 - 100 µm, thus they can increase the local dose. Experimental results suggest that only about 60% of primal particles reach the Bragg Peak. Figure 1.11 shows that the contribution of the nuclear interaction with respect to the ionization events is relatively low at the BP, while is substantial in the entrance channel. The overall effect is that about 10% of the biological effect induced in the entrance channel is due to nuclear fragment, while it is equal to 2% at the BP. However, the lack of experimental values about

Figure 1.11: Representation of the impact of the target fragmentation in proton therapy at different positions along the Bragg curve (from [22])

their cross section values makes the contribution of target fragmentation very difficult to quantify. The available models are not accurate enough and a direct comparison with data is still not possible in most of cases.

1.4 Thesis objectives

To summarize, the main issues in hadrontheapy related to nuclear fragmentation are essentially two. On one hand, the enhanced RBE due to the production of low-range fragments may determine an increased dose in the entrance channel. This effect is mainly important in proton therapy. On the other hand, for heavy ions, forward-generated frag-ments lead to dose tails beyond the SOBP.

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1.4. THESIS OBJECTIVES 13 The FOOT (FragmentatiOn On Target) experiment is aimed to provide new data about fragmentation cross sections. FOOT will perform a series of double differential cross sec-tion measurements at hadrontherapy energies in order to provide available experimental data for TPS and Monte Carlo simulations that are still missing in physical databases (e.g. [23]). As will be explained in the next chapter, FOOT experimental setup is com-posed by several detectors. One of the main components is the Time Of Flight (TOF) detection system, composed of the Start Counter (STC) and the TOF-Wall (TW). The latter is composed by two layers, both of 20 scintillator bars 3 mm thick, 20 mm wide and 440 mm long, for a total active area of 40 × 40 cm2_{. The readout of the bars is performed}

by Silicon Photomultipliers (SiPMs) that are optically coupled at both ends of each bar. TW is dedicated to the charge identification that is performed by measuring the energy deposition in the detector and the measurement of TOF of the fragments. In order to maximize the resolution in Z reconstruction a fine tuning is necessary to achieve the best performances in terms of energy and time resolution.

During my thesis, I worked on the characterization and optimization of TW detector and, in particular, I focused on the SiPMs study. My main contribution has been the char-acterization of the SiPMs and the development of a MC simulation of their response. In the next chapters a description of the FOOT experimental setup is given with particular attention to the TW. Subsequently my experimental work and the obtained results are illustrated.

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Chapter 2 The FOOT experiment

The FragmentatiOn Of Target (FOOT) experiment aims to measure the double differ-ential cross section of nuclear fragmentation in the typical energy range of hadrontherapy. These data are fundamental to improve the quality of the TPS for proton and ion ther-apy. This project have been approved and funded by Istituto Nazionale di Fisica Nucleare (INFN, Italy) and nowadays it counts over 100 members. The FOOT collaboration in-volves eleven INFN sections and laboratories, ten Italian, three foreign universities and three research insitutions [24].

The experimental setup have to be designed as a portable system in order to be suitable for those facilities that can provide the beams with energy and resolution typical of an hadrontherapy treatment. In Europe they are:

• CNAO (Centro Nazionale di Adroterapia Oncologica) in Pavia, Italy, where proton and carbon beams are available.

• HIT (Heidelberg Ion Therapy) center in Heidelberg, Germany, providing helium, carbon and oxygen beams.

• GSI in Darmstadt, Germany, that provides helium, carbon, oxygen and other ion species.

The final goal of the experiment would be to measure the heavy fragment cross section with maximum uncertainty of 5% and the fragment energy spectrum with an energy resolution of the order of 1-2 MeV/u, in order to contribute to a better radiobiological characterization of the protons. Moreover, FOOT aims to perform the charge identifica-tion (ID) at the level of 2-3% and the mass identificaidentifica-tion with an accuracy of about 5%. In addition, FOOT will be able to provide other data in terms of direct kinematics about the fragmentation cross sections of C and O beams. The latters are increasingly considered in particle therapy as promising alternatives to carbon ions for radioresistent tumor.

2.1 Measurement strategies

The most challenging goal of the FOOT experiment is the characterization of the target fragmentation induced by proton beams inside the human body. In order to study the yield and energy of the fragments, FOOT has been designed to be a fixed target experiment: the beams of interest, in the hadrontherapy energy range, are sent on a target composed by those elements typical of the human tissues, such carbon, hydrogen

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16 CHAPTER 2. THE FOOT EXPERIMENT and oxygen. The choice of adopting a pure gaseous hydrogen target have been discarded because of many technical difficulties: for example, due to the low density of this kind of target, the interaction rate will be very low.

The expected characteristics of the target nuclear fragments produced by the interactions with protons (p → X) are reported in Table 2.1.

Nucleus E [MeV] LET [keV/µm] Range [µm]

15_O _1.0 ₉₈₃ _2.3 15_N _1.0 ₉₂₅ _2.3 14_N _2.0 ₁₁₃₇ _3.6 13_C _3.0 ₉₅₁ _5.4 12_C _3.8 ₉₁₂ _6.2 11_C _4.6 ₈₇₈ _7.0 10_B _5.4 ₆₄₃ _9.9 6_Li _6.8 ₂₁₅ _26.7 4_He _6.0 ₇₇ _48.5 3_He _4.7 ₈₉ _38.8 2_H _2.5 ₁₄ _68.9

Table 2.1: Expected physical characteristics of target fragments for a 180 MeV proton beam (from [22]).

As can be seen from this table, nuclear fragments have high LET and very short range, for this reason they have low probability to leave the target and being detected. On the other hand, the choice of adopting a relatively thin target (∼ µm) implies other issues, such mechanical problems arising from the potential fragility of the target and extremely long data acquisition needed due to a decreasing of the interaction rate.

In order to overcome all these difficulties, the FOOT experiment uses an inverse kine-matic approach: rather than accelerating therapeutic proton beams onto biological tar-gets, FOOT studies the fragmentation of accelerated beams of ions composing the human body (e.g., carbon and oxygen) onto an hydrogen-enriched target. If the energy per nu-cleon is kept the same, this inversion results in a reference system change by applying a Lorentz transformation. In the new frame system, the produced fragments have a boost in energy, thus they can be easily escape the target and be detected. This kind of strategy also allows greater target thickness to be used, with a consequent increase of the interac-tion rate. In order to correctly apply the Lorentz boost, the inverse kinematic strategy needs an emission angle resolution accuracy with respect to the original beam of the order of mrad, thus both the projectile and target fragments directions have to be measure with the same order of accuracy. To achieve this experimental request, the MCS inside the target and secondary fragmentation events have to be kept in consideration. The target thickness is limited to be ∼ 2-5 mm and its density thickness should be of the order of g/cm2_.

To obtain the double differential cross sections of hydrogen, a composite target C2H4

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2.1. MEASUREMENT STRATEGIES 17 cross sections of C2H4 and C targets with the formula:

σ(H) = 1 4 σ(C2H4) − 2σ(C) (2.1) The same procedure is also valid for differential cross sections and it let to obtain the cross section for other elements. For example, for oxygen measurements, an additional PMMA (PolyMethyl MethAcrylate) target will be used. A disadvantage of such a method is that the the uncertainties are the quadratic sum of the uncertainties of the both individual targets. Hydrogen cross sections, which are small compared to carbon cross sections, are obtained with larger error bars (see Figure 2.1).

Figure 2.1: Example of hydrogen cross section calculation from CH2 and C experimental

data. Note the large resulting error bars for H (from [16]).

Preliminary studies with MC simulations with FLUKA codes have been performed in order to drive the experimental design. In particular, fragments production has been evaluated in terms of angular distribution.

Figure 2.2: Preliminary MC study on the emission angle of nuclear fragments from an

16_{O beam at 200 MeV/u on a 2 mm polyethylene (C}

2H4) target (from [25]).

The lower mass fragments can be emitted with a wide angular deflection from the incident beam direction with respect to the heavier ones. With the aim to get a good

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trade-18 CHAPTER 2. THE FOOT EXPERIMENT off between the system portability and a large geometrical acceptance, the experiment project will consider the implementation of two different setups:

• a setup based on electronic detectors and a magnetic spectrometer in order to iden-tify the heavier than 4_{He fragments (Z ≥ 3) and that cover an angular acceptance}

up to 10-20 degrees with respect to the beam direction.

• an emulsion spectrometer coupled with the interaction region to measure the pro-duction of the light fragments (Z ≤ 2) having an angular acceptance of about 70 degrees.

2.2 Electronic setup

The aim of the FOOT electronic setup is to detect the heavier fragments to measure their production cross section and to perform their charge and isotopic identification. The experimental request to the detector performances to achieve these results are:

• momentum resolution σ(p)/p at the level of 5%; • Time Of Flight (TOF) resolution lower than 100 ps; • energy resolution σ(Ek)/Ek ∼2%;

• deposited energy resolution σ(∆E)/∆E ∼ 2%.

Once the released energy ∆E and the TOF or the kinetic energy are measured, the charge of the fragments is estimated by inverting the Equation 1.2. On the other hand, the mass identification is performed by extracting momentum and kinetic energy from the following relationships:

p = mβγ Ek= mc2(γ − 1) Ek =

p

p2_c2_{+ m}2_c4_{− mc}2 _(2.2)

where β = v/c and γ = 1/p1 − β2 derive from TOF measurements.

A representation of the FOOT electronic setup is shown in Figure 2.3. There are three

Figure 2.3: Schematic view of the electronic setup of FOOT for the detection of ion fragments heavier than He (from [26]).

main regions that can be identified: the upstream region (or pre-target region), the mag-netic spectrometer and the downstream region.

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2.2. ELECTRONIC SETUP 19

2.2.1 Upstream region

The two detectors placed in the pre-target region are dedicated to the monitoring of the incident particles beam. They are the Start Counter (STC) and the Beam Monitor (BM).

Start Counter

The first component of the detector chain is a plastic scintillator (EJ-204) layer, char-acterized by a light yield of 104 _{ph/MeV. The STC is placed about 20-30 cm before the}

target and its main purpose is to monitor the rate of primary particles and to provide the first timestamp of the detected fragment in order to estimate the TOF. The scintillator layer thickness has been chosen to minimize the impact of primary beam and to obtain a good time resolution that matches the one of the TW. This thickness is set to 250 µm. A representation of the STC is reported if Figure 2.4a.

The output scintillation light flows through four read-out channels and it’s collected by 48 3×3 mm2 _{Hamamatsu MultiPixel Photon Counter Silicon PhotoMultipliers (MPPC}

SiPMs).

Beam Monitor

The BM is a Ar/CO2 (80/20%) drift chamber placed between STC and the target. It

consists of 12 layers of alternated horizontal and vertical wires. Each layer is composed of 3 rectangular cells (16×11 mm2_{) with the long side perpendicular to the beam direction.}

The overall dimensions are 11×11×21 cm3_{. A picture of the BM is shown in Figure 2.4b.}

The main goal of the BM is to provide an accurate measure of the direction and the impinging point the primary beam on the target. This information is crucial to tracking the particles and to reject eventually pre-target fragmentation events. In particular, the position resolution is of about 140 µm and angular resolution of ∼ 1 mrad.

(a) (b)

Figure 2.4: Technical drawings of the (a) Start Counter in its aluminum frame (from [27]) and (b) Beam Monitor (from [25]).

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20 CHAPTER 2. THE FOOT EXPERIMENT

2.2.2 Tracking system

The magnetic spectrometer is placed right after the target and it aims to provide a measure of the fragments momentum. The structure includes a magnet system, two pixel detectors and a microstrip detector.

Permanent Magnets

The magnetic system is used to estimate the fragments momentum by bending their trajectory inside a magnetic field. This is provided by a couple of Permanent Magnets (PMs), both composed by a ring of 12 blocks. The structure is preserved by an exter-nal aluminium case. The magnet layout, called Hallbach configuration (see Figure 2.5a), ensures a nearly uniform field along the transverse (xy) plane, while the longitudinal com-ponent (z) follows a two Gaussian distribution due to the effect of the separation between the two PMs. The shape of the magnetic field inside the PMs is reported in Figure 2.5b. The material of the magnets, Samarium-Cobalt (Sm2Co17), resists to radiation damage.

To improve the accuracy of p measure, the transverse component ∆pT has to be

maxi-mized. The momentum deflection is given by the formula:

∆pT = q

Z L

0

Bdl (2.3)

where q is the fragment charge, B is the intensity of the magnetic field and L is its length in z.

(a) (b)

Figure 2.5: (a) Schematic view of the permanent magnets in Hallbach configuration and (b) simulated transverse magnetic field along z at x = 0, y = 0. Both graphs are taken from [25].

Vertex

The first detector of the magnetic spectrometer is the Vertex detector (VTX) and it is placed at ∼ 0.5 cm after the target. The structure is composed by a stack of four layers of MIMOSA28 (M28) chips implemented by the Strasbourg CRNS PICSEL group [28]. These chips, belonging to the family of CMOS Monolithic Active Pixel Sensors (MAPS), are widely used in optical imaging, X-ray imaging and in experiments of particle and heavy-ion physics. Each sensor is a pixel matrix having 928 rows and 960 columns and a thickness of 50 µm with 20.7 µm pitch. The total sensitive area amounts to 20.22 × 22.71 mm2. The entire stack includes two sub-stations, each composed by two sensors at

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2.2. ELECTRONIC SETUP 21 2 mm distance, placed at 10 mm from each other.

The VTX contributes to the momentum measurement by evaluating the vertices of the fragment trajectories i.e. the interaction point of the primary particles inside the target. The passage of a fragment through the system produces a signal inside the pixel, thus the position can be reconstructed with a resolution of few µms.

Inner Tracker

The second detector of the magnetic spectrometer is the Inner Tracker (IT). Its purpose is to provide a measure of the direction and the transverse component of the incident fragment. It is placed between the two PMs, at a distance of ∼ 20 cm from the target. The arrangement of the sensors follows the one implemented in the PLUME project [29]. The structure foresee two planes of 8 M28 each. Every single chip has a thickness of 50 µm, an active area is of 2 × 2 cm2 _{and is divided into 4 ladders. The sensors are glued}

on a module of kapton Flexible Printed Cable (FPC). To minimize the horizontal dead area, the maximum distance between each chip is of 30 µm.

Microstrip Silicon Detector

The final component of the magnetic spectrometer is the Microstrip Silicon Detec-tor (MSD). The structure is composed by three layers of orthogonally oriented silicon microstrips. Each layer covers an active area of 9 × 9 cm2 _{and has a thickenss of 150}

µm, while the microstrip pitch is of 125 µm. The role of MSD is not only to provide the last information about fragment trajectory to complete the momentum measurement, but also to make an estimation of the released energy ∆E. In this way, together with the measurements provided by TW detector, an independent estimation of ∆E is available.

2.2.3 Downstream region

The last part of the FOOT electronic setup is dedicated to the measurement of the TOF and the released energy of the detected fragments. In this region there are a plastic scintillator (the TOF-Wall detector) and a calorimeter, both placed at a variable distance 1-2 m, from the target, depending on the energy of the primary beam.

TOF-Wall detector

The first component of the downstream region is the TW. It is composed by two layers, both of 20 bars of a plastic scintillator (EJ200, Eljen Technology) of 44 × 2 × 0.3 cm3_{, wrapped with aluminum and black tape. The bar thickness is a compromise}

between the energy resolution (2-3 %) and time resolution (70 ps) and it allows to reduce the production of secondary fragments. Each end is polished and optically coupled to 4 SiPMs. The photodetectors are Hamamatsu MPPCs with 25 µm cells size and 3 mm pitch, matching the scintillator thickness. The detector structure allows the identification of the hit position of fragments, thus the final point of their trajectory

The TW has been developed by the University and INFN section of Pisa and its charac-terization is the main objetive of this thesis work.

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22 CHAPTER 2. THE FOOT EXPERIMENT Calorimeter

The Bismuth Germanate (BGO) crystal Calorimeter is the last detector of the elec-tronic setup. As reported in Figure 2.6b, the structure includes 32 modules, each com-posed by 9 BGO crystals arranged in a truncated pyramidal shape (Figure 2.6a), having 2 × 2 cm2 and 2.9 × 2.9 cm2 surfaces and a length of 24 cm. The aim of this detector is

to measure the kinetic energy of the incident fragments. The choice of BGO as detection material is due to its high density. Previous tests have shown that the achieved energy resolution is around 1-3 %.

A relevant issue for this kind of detector is the production of neutrons as a result of the nuclear interactions of the fragments with the BGO crystal. They leave the detector, leading to an underestimation of the fragments kinetic energy.

(a) (b)

Figure 2.6: Technical drawing of the BGO Calorimeter: (a) 9-crystals module prototype showing the housing box and the front-end boards and (b) geometry of the full detector (from [25]).

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Chapter 3 The TOF-Wall detector

The TOF-Wall (TW) is the detector of the FOOT experiment whose purpose is to give information about the Time-Of-Flight (TOF) and the released energy ∆E to reconstruct the charge of the impinging particles. To meet the FOOT requirements, the detector should achieve a 2-3% accuracy for ∆E measurements and at least 70 ps time resolution for heavier ions (C, O). TW data also contribute to the global reconstruction of the particle tracks. In this chapter a detailed description of the structure of the detector and of the data acquisition is given. Subsequently, preliminary experimental results of a TW prototype with the related issues are reported.

3.1 Detector structure

The TW detector is composed of two layers of palastic scintillator bars (EJ-200, Eljen Technology), arranged orthogonally. A layer is composed of 20 bars, 3 mm thick, 20 mm wide and 440 mm long each, for a total sensitive area of 40 × 40cm2_{. The bars}

are wrapped with an enhanced specular reflector. A layer covers a sensitive area of 40 × 40 cm2, enough to cover the angular aperture of the nuclear fragments at a distance

of 1 m from the target. The pictures in Figure 3.1 show the TW in frontal and lateral view. Each bar end is optically coupled with a readout system composed by four 3 × 3 mm2 _{Hamamatsu MPPC SiPMs, model S13360-3025PE [}₃₀_{]. They are connected as the}

parallel of two branches, each one composed by a series of two devices (see Figure 3.2). A single SiPM has 14400 microcells with a pitch of 25 µm, therefore a single readout channel has a dynamic range of 57600 microcells. The advantage of this configuration is to decrease the total capacitance, thus the rise time of the signal will be reduced. SiPMs belonging to the same readout channel has similar breakdown voltage and dark count rate. The SiPMs characteristics are reported in Table 3.2

The adopted bar numbering convention is illustrated in Figure 3.3. The horizontal bars are located in the front layer and they are numerated from 20 to 39 (top to bottom), while the verticals ones in the rear layer are labeled from 0 to 19 (left to right).

3.2 The WaveDAQ system

The WaveDAQ is the trigger and data acquisition system and it is adopted of the STC and TW data. It is based on the DRS4 ASIC chips developed at PSI (Paul Scherrer Institut, Villigen, Switzerland) in collaboration with INFN (section of Pisa). The sketch of

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24 CHAPTER 3. THE TOF-WALL DETECTOR

(a) (b)

Figure 3.1: Picture of the frontal (a) and lateral side (b) of the TOF-Wall.

(a) (b)

(c)

Figure 3.2: (a) Circuital representation of the two-branches parallel of SiPMs, (b) picture of a SiPM board and (c) scheme of the coupling between SiPMs and scintillator bars.

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3.2. THE WAVEDAQ SYSTEM 25 Light yield = 104 _photons/MeV

Light emission peak = 425 nm Mean att. length = 380 cm Rise time = 0.9 ns

Decay time = 2.1 ns

Pulse Width, FWHM = 2.5 ns Table 3.1: Characteristics of the EJ-200 scintillator (from [31]).

Cell size = 25 µm

Total number of cells = 14400 Fill factor = 47%

Dark count rate (20◦ _{C, 5V OV) = 400 kcps}

Photon detection efficiency (450 nm) = 25% Break-down voltage = 53 ± 5 V

Table 3.2: Main characteristics of the SiPMs used for the TW readout (from [30]).

Figure 3.3: Scheme of TOF-Wall bar numbering.

a WaveDAQ crate is shown in Figure 3.4. The signals arriving from the two detectors are received by 16 digitising boards, called WaveDREAM (Waveform Drs4 REadout Module) boards (WDBs). Each of them is based on two Domino Ring Sampler chips (DRS4) that allow a data sampling speed of 0.5-5 GSample/s in a dynamic range of 1 V, together with 900MHz bandwidth variable gain amplifiers to allow direct connection to the detector signals. Six WBDs are dedicated to the read-out of the TW signals. Each board is also provided of two additional channels (numerated 16 and 17) always dedicated to the clock signals sampled by the DRS chips. The first chip is connected to the channels 0-7 and 16, while the second one sample channels 8-15 and 17. The data are digitised by DRS4 at 80 MHz with a 16-bits depth and sent to a readout FPGA (Field Programmable Gate Array), having a TDC (Time to Digital Conversion) logic that allows high precision time bin measurement. A picture of a WDB is shown in Figure 3.5.

The two central slots in a crate are reserved for custom designed boards. They are: • Data Concentrator Board (DCB): its aim is to provide the two reference clocks for

the WDBs. The clock signals have a high time and phase stability, the measured jitter is ∼ 5 ps. Processed data are merged into a single Gigabit Ethernet interface. • Trigger Concentrator Board (TCB): it receives all trigger informations from the

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26 CHAPTER 3. THE TOF-WALL DETECTOR

Figure 3.4: Scheme of the WaveDAQ crate. Arrows show connections in the backplane: red for data transmission to backend machines, blue for trigger serial links, orange for trigger signal distribution and green for hardware compensated clock distribution. Brown arrows show low level access for slow control and configuration (from [32]).

.

Figure 3.5: The WDB with the two DRS4 chips, the ADCs and the central FPGA high-lighted (from [32]).

WDBs and collects data to be processed on the FPGA. Once a single event is acquired, a trigger signal is generated.

The sampling of the SiPM signals acquired from STC and TW is performed by the DRS4 chips belonging to the family of the switched capacitor arrays. Their peculiarity is to exploit a series of capacitors to sampling data at several GHz of frequency. Figure 3.6 shows a schematization of a DSR.

A circular signal called domino wave is created and it propagates continuously along the chain. The task of the domino wave is to close the switches of the cells (1024 per channel in DRS4) of the buffer, thus the input signal is stored in the corresponding capacitor. The storing procedure repeats until an external trigger is received by the chip that stops the domino wave. The stored voltages are then sent to a read out shift register

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3.3. PRELIMINARY TESTS 27

Figure 3.6: Schematic view of the circuit of a Domino Ring Sampler (from [33]). and finally digitalized by an ADC. The rotating signal inside the DRS chip is controlled by a Phase Locked Loop (PLL). It is an electrical circuit that fixes the frequency of the domino wave at a specific fraction of a reference clock and use the reference signal to keep stable the clock phase.

3.3 Preliminary tests

A preliminary version of the TW detector was tested during two beam tests performed in 2019 at CNAO and GSI.

The goal of the CNAO beam test was the detector energy and time calibration. The detector was irradiated with carbon beams of three different energies (i.e. 115 MeV/u, 260 MeV/u and 400 MeV/u) and with proton beams of 60 MeV. The beam was scanned across the detector as reported in Figure 3.7 so to irradiate all the bars (with the exception of the most peripheral ones) at their center and to perform at the same time the scan of two bars at different irradiation positions.

Figure 3.7: Scheme of irradiation during the test of the detector (from [34]). The timestamp of the event TL/R at two edges of the bar (labelled with L and R) by

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28 CHAPTER 3. THE TOF-WALL DETECTOR crosses a threshold value given by a fixed fraction of the effective amplitude of the signal acquired by the SiPMs. Each timestamps related at each bar i of both the layer was determined as the average value of the timestamps Ti,L and Ti,R of the signals generated

at respectively the left and the right edge: Ti =

Ti,L + Ti,R

2 (3.1)

The time resolution σi,j between two bars of the two layers is defined by starting from

the distribution of the difference between the timestamps defined by Equation 3.1:

∆T = Ti− Tj (3.2)

where Tj is the timestamp of the j − th bar of the rear layer (j = 0, 1, ... , 19) and Ti is

the timestamp of the i − th bar of the front layer (i = 20, 21, ... , 39). By averaging the two timestamps of a couple of bars i, j, the TOF-Wall timestamp is defined:

∆TT W =

Ti+ Tj

2 (3.3)

By propagating the error in Equation 3.3 the time resolution is simply given by σT W =

σi,j/2. Experimental values for σi,j between 35 ps and 50 ps are obtained with carbon

ions, which correspond to a σT W between 20 and 25 ps. For protons, an averaged σi,j of

160 ps is achieved, corresponding to a σT W of 80-100 ps.

The total collected charge Q of each bar was evaluated by the square root of the product of the charge at two edges of the bar (labelled with L and R) so that:

Qi =pQi,L· Qi,R (3.4)

The collected signal is then converted into energy released by the particle in the scintillator bar through a model based on Birks law (see Chapter 4):

Qi =

si· Ei

1 + ki · Ei (3.5)

where siis proportional to the light yield of the scintillator and kirepresents the saturation

factor of the plastic scintillator. Figure 3.8a shows an example of the fit of Equation 3.5 to the experimental data, while Figure 3.8b shows a distribution of the resulting ki

parame-ters. By inverting the previous formula, the released energy distribution was reconstructed and the energy resolution was evaluated as σE/µE. The obtained results are plotted in

Figure 3.9 for both the detector layers.

The energy resolution depends on the released energy in the scintillator bar. Never-theless, Figure 3.8a shows that the collected charge as a function of the released energy saturates. This non linear response might influence the performances of the detection sys-tem, leading to a slight worsening of the energy resolution. The saturation effects have to be investigated in order to understand if they are due to the plastic scintillator only or if the photodetectors contribution is not negligible. The identification of each contribution to the resolution of the detector is, in fact, fundamental in the optimization of the design of the detector. My thesis work aims to investigate the impact of the TW readout SiPMs on the detector performances in terms of energy resolution.

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3.3. PRELIMINARY TESTS 29

(a) (b)

Figure 3.8: (a) Picture of the Birks like model fit for the measured charges as a function of the released energy and (b) k parameter measured in all the investigated position of the two layers (from [34]).

Figure 3.9: Plot of energy resolution obtained independently for each layer and averaging the reconstructed energy on the two layers (from [34]).

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Chapter 4 Organic scintillators

The term scintillator refers to a material that converts the energy released in its volume by ionizing radiation into visible or ultra-violet light. This process is know as scintillation or fluorescence and it can be used to convert the energy released by the radiation in a processable signal.

The main characteristics of a scintillator material are:

• Scintillation efficiency: it represents the fraction of released energy in the material that is converted to scintillation light.

• Linearity in response: the light produced by fluorescence should be directly propor-tional to the energy deposited by the detected radiation.

• Light yield: it is the quantity of light produced for energy unit released in the material. Generally it is measured in number of photons per MeV and it can be expressed as a percentage with respect to reference materials, such as NaI(Tl) or Anthracene.

• Transparency to the wavelength of its own emission.

• Response time: it is defined by two time constants, a rise time and a decay time describing the time distribution of the emitted photons. They have to be short to have a prompt response when the energy is released in the scintillator.

• Index of refraction: usually required to be close to 1.5, as for glass, in order to achieve a good optical coupling with the photodetector.

There is not a material that meets all the above properties. In fact, there are different types of scintillators, each with features that make it suitable for certain applications. For example, inorganic scintillators (mainly alkali halides, e.g NaI) usually have slower response but higher light yield, a wider range of linearity and high atomic number. These characteristics make them the optimized choice in γ-ray spectroscopy. On the other hand, organic scintillators (aromatic hydrocarbons containing linked or condensed benzene-ring structures) generally have a lower light output, but their faster response makes them suitable for TOF and time resolution measurements.

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32 CHAPTER 4. ORGANIC SCINTILLATORS

4.1 Scintillation in organic scintillators

While in inorganic scintillators the fluorescence is based on a crystalline structure, in organic scintillators the production of scintillation light arises form transitions in energy level structure of a single molecule. A wide category of organic scintillators is based on a particular electronic arrangement known as π-molecular orbitals [12]. Figure 4.1 shows a representation of this electronic configuration typical of an organic scintillator. Each energy level belongs to a specific value of spin components of the molecule and contains a set of sub-levels that are associated with the vibrational excitations. Typically, the energy gap between the singlet ground state S0 and the corresponding excited states S1

is around few eV, while the spacing between vibrational states is ∼ 0.15 eV. When a radiation interacts with the scintillator, its kinetic energy is absorbed and the electrons excite and occupy the higher energy levels. Possible vibrational excited states decay immediately (∼ ps), without any radiative emission. From an energy excited state there is a high probability to decay to one of the vibrational states of the ground state S0 within

a characteristic time of the order of nanosecond. This kind of energetic transition is also called prompt fluorescence and happens with a light emission which energy is equal to the energetic gap between the two states involved in transition.

Figure 4.1: Energy levels of the π-molecular orbitals structure of an organic scintillator. The image is inspired by [12].

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4.2. LIGHT AND TIME RESPONSE OF ORGANIC SCINTILLATORS 33 It is also possible that an excited singlet state decays passing first through triplet states. This phenomenon is known as intersystem crossing. Therefore, these kind of de-excitation is usually less probable since they violate the selection rules of the quantum mechanic. Once the ground vibrational triplet state T0 is reached, the system decays to

the ground energy state S0with the same light emission process of the prompt fluorescence

but with longer characteristic time (∼ ms). This emission is called phosphorescence. Regardless the type of emission (fluorescence or phosphorescence), the de-excitation stars from the lowest vibrational level of the lowest excited singlet state.

4.2 Light and time response of organic scintillators

The scintillation efficiency differs for each type of scintillator and also depends on the type of charged particle producing the ionization. A significant side effect of organic scintillator is that their light response to heavy charged particles is typically non-linear, while for electrons the light output is linear for energies above about 125 keV ([12]). Figure 4.2 displays the light yield curves of a plastic scintillator to electrons and protons.

Figure 4.2: Scintillation efficiency of a common type of plastic scintillator (NE-102) for electrons and protons. The fit curves are referred to Birks-like models with one or two free parameters (from [12]).

In order to describe the light yield of organic scintillator, in 1964 J.B. Birks hypoth-esized that the fluorescence light produced per unit of length dL/dx is directly propor-tional to the energy released dE/dx [35]. Therefore, he firstly proposed the following semi-empirical formula:

dL dx = S

dE

dx (4.1)

where S is the scintillation efficiency.

Nevertheless, Birks suggested that the non-linear behaviour is due to high ionization den-sity along the particle track. This effect could damage the molecules inside the material,

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34 CHAPTER 4. ORGANIC SCINTILLATORS causing a drop in scintillaiton efficiency. The first assumption is that the density of dam-aged molecules is proportional to the energy released and can be expressed as B(dE/dx), where B is a proportionality constant. The second hypothesis is that a fraction k of these damaged molecules can lead to quenching effect observed for heavy charged particles. To account for these observations, Birks rewrote his formula as follows:

dL dx =

S dE_dx

1 + kB dE_dx (4.2)

The latter expression for organic scintillators light output is known as Birks’ formula. In the limit of small dE/dx, as in the case of fast electrons (either directly or produced by γ-ray interactions), Birks’ formula reduces to:

dL dx e = S dE dx (4.3)

Therefore, in this regime the light output per unit of energy loss is a constant dL dE e = S (4.4)

and L has a linear trend as a funcion of the initial particle energy E. There are several other versions of Equation 4.2. For example, an alternative formula was carried out by Craun and Smith ([36]) that takes into account of an empirical fitted parameter C:

dL dx =

S dE_dx

1 + kB dE_dx + C (dE_dx)2 (4.5)

The “halo” model proposed in [37], is the combination of a Birks-like term and a linear one dL dx = A(1 − fh)dE_dx 1 + B(1 − fh)dE_dx + Afh dE dx (4.6)

where the parameter fh represents the fraction of energy deposited in the halo.

However every type of expression for the light output reduces to the limit 4.4 for low values of dE/dx.

On the other hand, the energy losses are higher for heavy charged particles. In these sit-uation quenching effects become prominent and the Birks’ formula reaches the saturation limit [12]. dL dx sat = S kB (4.7)

The pulse shape of an organic scintillator depends on the emission time constants. Since the absorption time is almost instantaneous, the pulse profile shows a leading edge most depending on the rising time of the scintillator. Once the maximum in light intensity is reached, the shape follows an exponential decay determined by the two different charac-teristic times of fluorescence and phosphorescence. One approach takes into account the time constant τ1 for the population of the excited levels. The overall shape of the time

pulse is given by [12]:

I = I0 e−t/τ − e−t/τ1

(4.8) where τ describes the decay of the excited levels.

Another mathematical description includes the convolution of a Gaussian function f(σ; t) with a decreasing exponential [38], so that

Development and characterization of the TOF-Wall detector of the FOOT experiment