Charge identification of nuclear fragments with the Time-Of-Flight detectors of the FOOT experiment

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University of Pisa

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

Charge identification of nuclear fragments with the

Time-Of-Flight detectors of the FOOT experiment

Candidate:

Zarrella Roberto

Thesis Advisor:

Bisogni Maria Giuseppina

Research Supervisor:

Kraan Aafke Christine

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Abstract

Charged Particle Therapy (CPT) is an increasingly used technique in the treatment of deep-seated solid tumors. The rationale for this approach is the favorable depth-dose profile of heavy charged particles with respect to conventional X-rays. This is character-ized by low energy deposition in the entrance channel, followed by a high energy release at a certain depth: the Bragg Peak. This behavior makes it possible to spare healthy tissues while delivering high dose to the tumor.

CPT represents a consolidated treatment procedure in clinical practice. Still, research is ongoing to further improve the accuracy of Treatment Planning Systems, by including advanced Monte Carlo models into the dose calculations. One of the many topics discussed in CPT is the contribution of nuclear fragmentation processes to beam dose profiles in both proton and heavy ion therapy. While in proton therapy the short-range recoil nuclei generated in target fragmentation processes could lead to an increased dose in the entrance channel, in ion therapy projectile fragments generate an additional dose tail behind the Bragg Peak. However, it is difficult to exactly evaluate the contribution of fragmentation products to total dose distributions because of the lack of experimental cross section data in the energy range of CPT.

The aim of the FOOT (FragmentatiOn Of Target) experiment is to measure the dou-ble differential cross section of nuclear fragmentation processes relevant for CPT. The apparatus will exploit inverse and direct kinematics to accurately characterize both tar-get and projectile fragmentations. To achieve this goal, the system needs to measure the mass, charge, velocity and energy of the nuclear fragments produced by different beams impinging on tissue-like targets.

This thesis focuses on the development and validation of the charge (Z) identification procedure, based on energy deposition (∆E) and Time-Of-Flight (T OF ) measurements performed with the Start Counter (STC) and TOF-Wall (TW) of FOOT. The former is a thin foil of plastic scintillator, while the latter is made of two orthogonal layers of 20 scintillating bars each. These two detectors provide the ∆E (TW) and T OF (TW and STC) values needed to calculate the Z of nuclear fragments traveling through FOOT.

The data analyzed in this work have been acquired during two test beam data takings performed in early 2019. The first one was carried out at CNAO (Centro Nazionale di Adroterapia Oncologica, Pavia) and was dedicated to energy and T OF calibration mea-surements with protons (60 MeV) and carbon ions (115, 260, 400 MeV/u). The second data taking was performed at GSI Helmoltz Centre for Heavy Ion Research (Darmstadt, Germany). In this case, an oxygen ion beam (400 MeV/u) was used in different acquisi-tions to both calibrate the detectors and observe the nuclear fragmentaacquisi-tions on a 5 mm graphite target.

In this work, data analysis software has been developed to process the raw detector signals. The resulting quantities are then compared to Monte Carlo simulations to cali-brate the detectors in terms of both ∆E and T OF . Furthermore, the β of the particles is retrieved from T OF and calibrated data are used to calculate the Z of nuclear fragments through the Bethe-Bloch formula. A direct comparison with Monte Carlo results is also presented as a validation of the procedure. Using the developed reconstruction and anal-ysis framework, the ∆E and TOF measurements have shown energy and time resolution of a few MeV and 50-80 ps respectively. The resulting Z values have been reconstructed with an uncertainty of 2 to 6%, in agreement with the requirements of FOOT.

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List of Figures

1.1 Bethe-Bloch . . . 3

1.2 Bragg peak . . . 3

1.3 Landau and Vavilov distributions . . . 4

1.4 Range of Hadrons . . . 5

1.5 Beam lateral spread from Multiple Coulomb Scattering . . . 6

1.6 Abrasion-ablation model . . . 7

1.7 Dose deposition comparison and SOBP . . . 9

1.8 TPS comparison: photons vs C-ions . . . 10

1.9 Contribution of projectile fragmentation: 12C ions . . . 10

1.10 DNA damage . . . 12

1.11 Cell survival curves . . . 13

1.12 RBE vs LET: experimental data for ions . . . 14

1.13 MC simulation of target fragmentation contribution for a proton beam . . 15

2.1 Hydrogen cross section from CH2 and C . . . 18

2.2 Nuclear fragments expected emission with MC: 16O at 200 MeV/u on C2H4 21 2.3 FOOT: electronic setup . . . 21

2.4 Start Counter and Beam Monitor schematic view . . . 22

2.5 Permanent Magnets . . . 23

2.6 TOF-Wall bar . . . 25

2.7 BGO Calorimeter . . . 26

2.8 FOOT electronic setup geometry in FLUKA . . . 26

3.1 Analysis workflow . . . 29

3.2 STC: schematic view . . . 30

3.3 TW scheme and mounted system . . . 32

3.4 WaveDAQ scheme . . . 33

3.5 WaveDREAM board . . . 33

3.6 Schematic view of a DRS chip . . . 34

3.7 CNAO experimental setup . . . 35

3.8 Acquisition pattern at CNAO . . . 35

3.9 GSI Experimental setup . . . 36

3.10 STC: Channel WF . . . 38

3.11 STC: CFD method application . . . 39

3.12 STC channel WF: protons . . . 40

3.13 STC: sum of proton WFs . . . 40

3.14 STC: Dynamic range overflow . . . 41

3.15 STC: Pole-Zero Cancellation . . . 41

3.16 TW: channel WF and CFD . . . 43 vii

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viii LIST OF FIGURES 3.17 TW: application of the median filter correction to spiked signals from WDB

78 and 79 . . . 44

3.18 CLK: phase difference between WFs . . . 45

3.19 CLK: phase linear fit . . . 45

3.20 CLK:∆CLK example . . . 46

3.21 CLK: Dynamic range overflow . . . 47

3.22 TW: Charge variation along central bars . . . 48

3.23 Labels of TW positions . . . 49

4.1 Energy calibration curve example . . . 53

4.2 Map of TW positions with reliable energy calibration . . . 54

4.3 Example of energy calibration curve for board 79 . . . 55

4.4 Example of energy calibration curve for board 82 . . . 55

4.5 Data-MC comparison for ∆E: example for 12_{C and} 16_{O . . . .} ₅₆

4.6 Data-MC comparison for ∆E: protons . . . 57

4.7 Raw T OF CNAO . . . 58

4.8 Raw T OF GSI . . . 59

4.9 Cabling offset ∆i map: CNAO data set . . . 60

4.10 TOF0 correction . . . 60

4.11 ∆i map for cabling offset: GSI data set . . . 61

4.12 Data-MC comparison for T OFcal: CNAO . . . 62

4.13 Data-MC comparison for T OFcal: GSI . . . 63

4.14 TW time stamps . . . 63

4.15 TW: Front-Rear time difference and CLK jitter . . . 64

4.16 Data-MC comparison for reconstructed Z: CNAO . . . 65

4.17 Z reconstructed: CNAO board 79 and 82 . . . 67

4.18 Data-MC comparison for reconstructed Z: GSI . . . 68

4.19 Reconstructed fragments for GSI runs . . . 69

4.20 Visualization of ghost events . . . 70

4.21 Energy deposition filter for ghost discrimination: GSI . . . 71

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List of Tables

2.1 Expected characteristics of target fragments in protontherapy . . . 19

3.1 EJ-204 characteristics . . . 30

3.2 EJ-200 characteristics . . . 31

3.3 TW SiPMs characteristics . . . 31

3.4 MC values for T OF and ∆E . . . 37

4.1 Calibrated energy resolutions . . . 57

4.2 T OFraw resolution . . . 59

4.3 T OF0 fit results for CNAO data . . . 60

4.4 TW and STC time resolutions . . . 64

4.5 Z reconstructed: CNAO . . . 66

4.6 Reconstructed Z with one TW layer: CNAO board 79 and 82 . . . 66

4.7 Reconstructed Z for GSI: fit results . . . 68

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Chapter 1 Charged Particle Therapy

According to World Health Organization (WHO), cancer is currently one of the lead-ing causes of death worldwide, with 9.6 million deaths in 2018. [1]. Radiation therapy, or radiotherapy, is currently one of the main treatment options in oncology, usually in com-bination with surgery and chemotherapy. This technique uses ionizing radiation beams to damage cancerous cells in order to stop (or at least inhibit) their uncontrolled prolif-eration, either through direct or indirect interactions with their DNA.

In the last years, the number of patients treated with Charged Particle Therapy (CPT) has increased substantially, especially in the treatment of deep-seated tumors located near vital organs. The main advantage of using proton or heavy ion beams (instead of “con-ventional” X-rays) is their finite range depth-dose profile, characterized by an increasing energy deposition up to the Bragg Peak (BP) region. This behavior makes it easier to deliver a high dose to the tumor while sparing healthy organs surrounding the cancerous tissue and provides a better shaping of the treated volume. Moreover, hadron beams show an increased biological effectiveness with respect to photons, meaning that they need a lower dose deposition to produce the same amount of cell damage.

The dose delivery in CPT sessions is usually calculated with Treatment Planning Systems (TPS). These systems are required to be fast and are therefore largely based on analytical calculations, which are generally validated by comparing with measurements and Monte Carlo (MC) calculations. Patient bodies are modeled with medical images obtained from Computed Tomography (CT) scans, allowing for an accurate identification of the cancer region. Then, the energy, direction, fluence and number of beams to employ are calculated by the TPS optimizing the dose deposition profile and the coverage of the disease.

CPT is currently a consolidated technique in clinical practice and its effectiveness has been well-established. At the end of 2018, there were 82 CPT facilities worldwide in clinical operation with a total number of 220000 patients treated. Most of them were treated with protons (∼ 86%), while the other ones received carbon ions (∼ 12%) or other particles (∼ 2%). [2]

1.1 Physics of Charged Particle Therapy

Any charged particle entering an absorbing medium is subject to various types of interactions. In the energy range of CPT (up to 250 MeV for protons and up to 400 MeV/u for12C ions), the behavior of heavy charged particles (i.e. with mass much greater than electrons) traveling through matter can be accurately described considering 3 main

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2 CHAPTER 1. CHARGED PARTICLE THERAPY processes:

• Inelastic collisions with atomic electrons, which lead to energy loss and determine particles longitudinal energy deposition profile and range.

• Elastic scattering with nuclei of the medium, or Multiple Coulomb Scattering (MCS), which is the main responsible for the lateral spread of the beam.

• Collisions with the material nuclei, both elastic or inelastic.

The first two processes are the result of electromagnetic forces, while the last one is the consequence of nuclear interactions between projectile and target nuclei.

1.1.1 Electromagnetic energy loss and range of heavy charged

particles

The main sources of heavy charged particles energy loss are inelastic collisions with the atomic electrons of the medium. During these interactions, electrons receive enough en-ergy to escape the atoms, which are thus ionized. Since these interactions are intrinsically stochastic and occur with a certain probability, only an average value for the stopping power dE/dx can be defined. The mean energy lost through collisions by a particle with charge Z inside an homogeneous material of density ρtis given by the Bethe-Bloch formula

dE dx coll = KρtZt At Z2 β2 1 2log 2mec2β2γ2Wmax I2 t − β2₋ δ 2− C Z (1.1) where

• me and c are the electron mass and the speed of light.

• β and γ are the Lorentz factors of the incident particle. • K is a constant defined as K = 4πr2

eNAmec2, where NA and re are respectively

Avogadro’s number and the electron classical radius. Its value is 0.307075 MeV cm2_{/g. [}₃_]

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

potential of the absorber (target).

• Wmax is the maximum energy transferable to an electron of the material with a

single collision, given by

Wmax =

2mec2β2γ2

1 + 2γme/M + (me/M)2

(1.2) where M is the mass of the incident particle. If the energy of the particle is low, i.e. if 2γme M , the expression becomes simply Wmax = 2mec2β2γ2. In the energy

range of CPT this condition is always verified.

• δ represents the density correction, only significant for very high energies.

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

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1.1. PHYSICS OF CHARGED PARTICLE THERAPY 3

Figure 1.1: Example of mass stopping power (_ρ1

t

dE

dx) as a function of the energy of the

projectile for different heavy charged particles (from [4]).

The behavior of < dE/dx >coll for different particles is displayed in Figure 1.1. The curves

are only drawn in the energy range (_{0.1 . βγ . 1000) where Equation 1.1 is accurate} up to a few %. As it can be seen, the energy deposition has a minimum (at βγ ' 3) and grows at the sides. For high energies, the logarithmic term becomes dominant and determines the relativistic rise (up to the density correction plateau). At low energies, the collisional term prevails and dE/dx is approximately proportional to 1/β2_.

The latter is the behavior expected for CPT energies and it represents the main ad-vantage of using hadronic beams. The typical resulting energy deposition as a function of the penetration depth inside a material has the shape shown in Figure 1.2. This is charac-terized by low energy deposition in the entrance channel, followed by a region where the particle looses more and more energy while slowing down. The maximum energy release is found in a region called Bragg Peak (BP).

Figure 1.2: Typical curves of the energy released by one (solid line) or multiple (dashed line) heavy charged particles inside a material as a function of the distance traveled. The region of maximum deposition is the BP (from [5]).

Equation 1.1 represents an expression for the average energy lost per unit length by a heavy charged particle. The interactions are stochastic in nature, so the total energy

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4 CHAPTER 1. CHARGED PARTICLE THERAPY deposited by the same particle in an absorber is not constant. The actual distribution of deposited energy depends on the thickness of the medium:

• If the absorber is thick, the total energy deposited is the result of many independent small releases and can be modeled with a Gaussian distribution.

• If the absorber is thin, the distribution depends on fewer interactions and develops a long tail at high energies caused by hard collisions. The form of this distribution has been calculated by Landau [6], Symon and Vavilov [7] in different energy ranges, defined by the parameter

k= ∆

Wmax

(1.3) where ∆ represents the mean energy lost in the absorber and Wmax comes from

Equation 1.2. If k 1 (thick absorber or β 1), the Gaussian model is still quite accurate. If k ≤0.01 (thin material or β ' 1), the distribution is well described by the Landau theory. For intermediate values of k, the Vavilov distribution represents a more precise model. An example of these curves is displayed in Figure 1.3.

Figure 1.3: Example of Landau (L) and Vavilov distributions for different values of k (from [4]). In the picture, φ and λ are two parameters respectively proportional to the probability density function and the energy loss.

The trend shown in Figure 1.2 also highlights an important difference between charged particles and photons. While photons show an exponential attenuation in tissue, charged particles can only travel a finite distance inside the medium and this makes it possible to define an actual value for the range R of the beam. The most common definition of this quantity is obtained in the Continuous-Slowing-Down Approximation (CSDA). The value of RCSDA is defined as the range of a particle whose energy loss is equal to the stopping

power dE/dx, i.e.

RCSDA= Z L 0 dx= Z 0 E dE dx −1 dE (1.4)

where L is the maximum range of the particles and E their initial kinetic energy. The integration of Equation 1.4 leads to

RCSDA(v) =

M

Z2F(v) (1.5)

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1.1. PHYSICS OF CHARGED PARTICLE THERAPY 5

Figure 1.4: Transmission curve for an hadronic beam showing two other possible defini-tions of beam range(mean and extrapolated range). The curve shows the relative intensity of the transmitted beam as a function of the thickness of the absorber (from [4]).

most important parameters in CPT. A precise knowledge of the position of the BP is the main key to deliver the right amount of dose to the disease while avoiding healthy tissues. This concept is further explored in Section 1.2

1.1.2 Multiple Coulomb Scattering

Heavy charged particle beams are also subject to Coulomb elastic scattering with the nuclei of the absorber. These processes are still electromagnetic and their main effect is to increase the lateral spread of the beam, widening the transverse region where parti-cles deposit their energy. Cumulative deflections at small angles can lead to a significant change in the particle direction. This is usually referred to as Multiple Coulomb Scatter-ing (MCS). The first description of MCS is contained in Molière’s theory (1948) and it describes the statistical distribution F(θ, x) of the scattering angle θ at penetration depth x. For small angles (θ ' 0) the function can be written as a Gaussian [8]

F(θ, x) = 1 πσθ e− θ2 2σ2 θ (1.6)

where the standard deviation, first obtained by Highland [9], is given by

σθ = 13.6MeV pv Z r x X0 1 + 0.0038ln x X0 (1.7)

where p, v and Z are respectively the momentum, velocity and atomic number of the particle while X0 is the radiation length of the material. Some examples of how MCS

determines the lateral spread of hadron beams is shown in Figure 1.5. It is important to note that the impact of MCS becomes lower for beams with higher initial momentum. This implies that, considering particles with the same velocity, lateral dispersion decreases as the mass of the projectile increases. Having a narrower beam is one of the main advantages of using heavier ions in CPT and it is the reason why He and C treatments where first proposed.

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6 CHAPTER 1. CHARGED PARTICLE THERAPY

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Figure 1.5: Lateral spread of hadron pencil 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 [10]).

1.1.3 Nuclear Interactions

Heavy charged particles can also undergo nuclear interactions with the material nuclei. The contribution of these collisions to energy loss is less significant than electromagnetic ionizations, but it still needs to be considered when modeling beam transport. The interactions can be both elastic or inelastic. The first ones do not deposit energy in the medium and only account for an additional broadening of the beam, somewhat raising the tails of the angular distribution. The second ones are more violent collisions between projectile and medium nuclei and can lead to:

• Nuclear fragmentation, which can involve the break-up of either or both projectile and target nuclei with the emission of lighter particles.

• Nuclear excitation, with the consequent relaxation of the nuclei through the emission of prompt γ radiation (0-10 MeV). These processes occur along the path of the projectile, up to 2-3 mm before the BP. [11]

Among these ones, the main process relevant for energy deposition calculations in CPT is nuclear fragmentation. In proton therapy only target fragmentation is possible, gener-ating secondary protons and neutrons; in heavy ion therapy, both target and projectile fragmentation can occur, strongly reducing the fluence of primaries as well as creating secondary fragments. As an example, in a typical carbon treatment only 50% of the primaries reach the BP and the resulting projectile fragments can deposit energy in the body up to a few cm behind the BP. [10] This means that an in-depth knowledge of the cross sections σinelof nuclear inelastic collisions is crucial to provide an accurate modeling

of hadron beams. In particular, total nuclear cross section are used to calculate the varia-tions in the fluence of primaries along the track, while double differential cross secvaria-tions are needed to evaluate the characteristics of the nuclear fragments produced (charge, mass, direction and velocity).

Most of the nucleus-nucleus collision models describe the interaction as a two step process, called cascade-evaporation or, more frequently, abrasion-ablation model. [12]

• Abrasion: the projectile and target nuclei overlap, forming a hot reaction zone (fireball) that gets abraded. The fragment of the projectile nucleus continues with

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1.1. PHYSICS OF CHARGED PARTICLE THERAPY 7 almost the same direction and velocity, while the remaining target fragment is just slightly affected by the interaction.

• Ablation: the two nuclei fragments and the fireball are generated in a highly excited state. The ablation step consists of the decay of the residual particles into their ground state, with possible emission of γ-rays or light particles.

Figure 1.6 contains a visualization of the abrasion-ablation model. Note that target fragments have a much lower velocity than the projectile, meaning that they will be emitted almost isotropically. Instead, projectile fragments are mainly emitted forward and can penetrate deeper inside the material with respect to the initial particle.

Figure 1.6: Visualization of the abrasion-ablation model for a proton-nucleus (top) and nucleus-nucleus (bottom) interaction (from [11]).

The abrasion-ablation model is sufficiently accurate in describing peripheral collisions between projectile and target, which also constitute the majority of nuclear interactions in the energy range of CPT. In this framework, an approximated expression for the cross section of inelastic nucleus-nucleus interactions can be obtained through the Bradt-Peters formula [13]

σinel = σtot− σel = πr20

A1/3_p + A1/3_T − b2 (1.8)

where r0 ' 1.2 fm is the nucleon radius, b is an overlapping factor and Ap and AT are the

mass numbers of projectile and target nuclei. This formula is accurate only for energies ≥ 1.5 GeV/u and σinel starts showing energy dependence outside that range. At lower

energies, a typical parametrization adopted for proton-nucleus interactions in [10]

σinel = σ0 · f (Ep, ZT) (1.9) where σ0 = πr02 h 1 + A1/3_T − b0(1 + A −1/3 T ) i2 b0 = 2.247 − 0.915(1 + A −1/3 T ) (1.10)

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8 CHAPTER 1. CHARGED PARTICLE THERAPY is a Bradt-Peters like geometrical factor and f is a function that depends on projectile energy Ep and target atomic number ZT. The function f can have very different and

complex shapes depending on the projectile energy and type of target chosen.

In the energy range relevant for CPT, experimental values for σinel are unfortunately

poorly known, especially for light nuclei (A < 20). This makes it difficult to provide a sufficiently accurate model for particle transport and energy deposition. This is particu-larly true for double differential cross section (d2_{σ/dEdΩ) data, which should provide the}

probability of emitting a fragment in the energy range dE within the solid angle dΩ. The consequences of the uncertainty on σinel in CPT is discussed in Section 1.2.

1.2 Radiobiology in Charged Particle Therapy

Heavy charged particle treatments are mainly indicated for deep-seated, radioresistant, hypoxic tumors, which can be located near Organs At Risk (OAR) such as the spinal cord or optical nerves. The typical depth-dose profile of CPT makes it possible to better spare healthy tissues, which makes heavy charged particles advantageous also in the treatment of pediatric cancer. Moreover, hadrons show an enhanced biological effectiveness in cell killing with respect to photons, allowing for an even lower dose exposure.

CPT currently represents a viable treatment solution and a consolidated technique in clinical practice. Still, there is ongoing research on factors such as Relative Biological Effectiveness (RBE) variability and nuclear fragmentation. These effects are currently not or only partly included in Treatment Planning Systems (TPS). Treatment planning could be substantially improved if the calculations accurately take into account the biological effect of nuclear fragmentation and its influence on RBE. This should eventually lead to a new generation of TPS: biologically-driven Treatment Planning Systems (BioTPS)

1.2.1 Dose deposition

A fundamental parameter used to quantify the effects of radiation i.e. absorbed (or physical ) dose D, defined as the quantity of energy dE released by ionizing radiation in a volume of mass dm

D= dE

dm (1.11)

Dose is usually expressed in Gray (1Gy = 1J/kg). [14]

A comparison of the depth-dose profiles obtained from different types of ionizing ra-diation is shown in Figure 1.7a. X-rays deliver higher doses in the entrance channel than the rest of the target. This means that, for deep-seated tumors, radiotherapy beams need to be delivered from many different angles in order to spare surrounding tissues while de-livering a high dose onto the disease. In this way, even though at low doses, a significant amount of healthy cells is exposed to ionizing radiation and potential damage. On the contrary, hadronic beams show a favorable dose ratio between deep and shallow regions. Thus, directing the BP on the tumor, healthy tissues receive a much lower amount of dose. This also makes it possible to use fewer beam directions (see Figure 1.8).

The technique employed in CPT to cover a region broader than the BP is shown in Figure 1.7b. A series of beams (protons in the case displayed) with the same direction but different energies and intensities is delivered onto the patient, delivering a total dose profile usually called Spread-Out Bragg Peak (SOBP). Obviously, this approach relies on a precise knowledge of the range of the particle. Small modifications could either lead

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1.2. RADIOBIOLOGY IN CHARGED PARTICLE THERAPY 9 to an incomplete irradiation of the tumor or move one of the BPs over a healthy region. The topic of range uncertainty is a major issue in CPT. This uncertainty arises from

(a) (b)

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 (from [10]).

different factors, such as morphological changes in the patient (tumor shrinkage, cavity filling/emptying, inflamation, etc.), the conversion of Computed Tomography images in stopping power values inside TPS or patient mispositioning. In general, the range of therapeutic beams inside the patient is known with an uncertainty that goes up to 3% of the expected value. [15, 16] This uncertainty is usually taken into account in treatment plans by introducing additional safety margins (3% of the range + 3 mm) to the cancerous region and by avoiding the delivery of beams in the direction of an OAR.

Figure 1.7a also shows some important differences in dose deposition profiles of heavy ions with respect to protons

• A narrower BP region and a higher peak/entrance channel dose ratio. This feature can be used to both deliver even less dose to healthy tissues and create a more precise profile of the disease. Ions with higher atomic number Z produce a narrower and steeper BP.

• A dose tail after the BP, caused by nuclear fragmentations. In particular, this effect is caused by projectile fragments, which mostly have the same velocity of the primary but lower charge and thus a longer range (∝ Z−2) that goes over the BP region. This effect is one of the main disadvantages of heavy ion beams and needs to be considered in TPS since it delivers additional dose to healthy tissues. Moreover, the contribution of nuclear fragmentation increases for heavier projectiles.

The difference between treatments with photons and carbon ions is clearly visible in Figure 1.8. The total dose deposited in healthy tissues is lower and more localized in carbon treatment, but the tails created by nuclear fragments can not be neglected. This issue represents the main reason why 4He beams are currently under study as a viable solution. On one hand, the binding energy between nucleons in α particles lowers the number of projectile fragmentations with the respect to carbon ions; on the other hand, the higher mass decreases the contribution of MCS with respect to protons.

The exact impact of nuclear processes is difficult to estimate because of missing cross section data. A good evaluation of the contribution of projectile fragments can only be

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10 CHAPTER 1. CHARGED PARTICLE THERAPY

Figure 1.8: Comparison of TPS for lung cancer with Intensity Modulated Radiation Therapy (IMRT) and carbon ions CPT. The figure shows the difference in “dose bath” of healthy tissues for the same dose delivered to the tumor. Note also the dose tails in carbon treatment caused by projectile fragmentations (from [10]).

obtained through double differential cross section values of the respective processes. These parameters are in fact fundamental to extract the characteristics of nuclear fragments (mass, charge, energy and direction) and calculate their energy deposition profiles. TPS are based on analytical models and validated through MC simulations. However, the models currently employed are based on approximated calculations of nuclear reaction cross sections, which eventually introduce a source of dose uncertainty in clinical treatment plans, as will be explained in the next section.

Figure 1.9: Contribution of projectile nuclear fragments to the depth-dose profile of a 330 MeV/u carbon ions beam impinging on a PMMA (PolyMethyl MethAcrylate) target. The graph has been obtained through a Geant4 MC simulation (from [17]).

1.2.2 DNA damage and Linear Energy Transfer

The basic principle of any type of radiotherapy is to use ionizing radiation to damage tumor cells. The aim is to kill these cells (directly or by apoptosis) or, at least, remove

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1.2. RADIOBIOLOGY IN CHARGED PARTICLE THERAPY 11 their clonogenic potential, i.e. their ability to reproduce. Thus, the actual target of radiotherapy is DNA. DNA damage is usually referred to as

• direct, when particles ionize the DNA molecule, breaking one or both of its chains. • indirect, when DNA gets damaged by chemical reactions with unstable molecules,

called free radicals, generated by the beam traveling inside cells.

The severity of the damage is directly linked to the type of lesion induced by the particles on the DNA helix. It is usually classified as

• Single Strand Break (SSB). The lesion is confined to only one of the two strands, breaking it into two pieces. This type of damage has low biological impact because cells are able to repair most of these fractures without consequences. SSBs are the main kind of breaks induced by X-rays.

• Double Strand Break (DSB). In this case both of the DNA strands are broken, either at the same level or at a distance of few DNA base pairs. These type of lesions are very difficult to repair and usually result in cell death. Heavy charged particles mainly cause DSBs when interacting with cells.

• Clustered damage. In this case, the beam induces multiple DNA lesions, but at a distance of few tens of base pairs. The outcome of these interactions mainly depends on the position of ionized DNA sites. [18]

The type of DNA lesions induced by radiotherapy beams is directly linked to Linear Energy Transfer (LET). LET is a quantity similar to the stopping power defined in Equa-tion 1.1, but with an important distincEqua-tion. While dE/dx includes all the electromagnetic losses, LET is defined as the energy released inside a medium per unit path length ex-cluding both radiative losses and δ-rays. It can be expressed as

LET= dE

dx

∆

(1.12) where ∆ is a cut-off value that excludes any higher energy loss. This means that LET only includes energy releases along the track of the particles. When considering indirectly ionizing radiation beams (photons or neutrons), LET refers to the stopping power of secondary particles. [19]

In clinical practice, radiations are usually characterized through their LET and divided i.e. sparsely ionizing (low-LET, ∼1 keV/µm) and densely ionizing (high-LET, ∼ 10−100 keV/µm). In particular

• Photons are usually referred to as low-LET particles (secondary electrons have low LET). Each photon entering the patient can interact with the molecules through photoelectric effect, Compton scattering or pair production. These processes have low cross section, meaning that photons usually undergo a single interaction inside the body. As a consequence, the number of ionizations produced inside a cell per incident photon is small.

• Heavy charged particles are considered high-LET radiation, since they have a very short mean free path inside a medium and ionize a high number of atomic electrons along their track. This means that hadrons produced a much higher ionization density and have better chances of interacting multiple times with the same DNA molecule.

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12 CHAPTER 1. CHARGED PARTICLE THERAPY As a consequence, CPT beams are more effective than X-rays in creating DSBs and, thus, in killing cells. The described interactions between DNA and different types of radiation are schematically displayed in Figure 1.10.

Figure 1.10: Visualization of low/high LET interactions and different types of DNA dam-age (from [18]).

1.2.3 Cell survival models

The link between radiation dose and cell survival has been studied for many years through in vitro experiments. In these studies, the “death” of a cell can be defined in different ways. For non-reproductive differentiated cells (like neurons), it is usually defined as the loss of a specific function. For reproductive and less differentiated cells (e.g. stem cells, bone marrow, etc.), death is normally defined as the loss of reproductive capabilities.

One of the most common models used in clinical radiotherapy to link radiation dose and cell damage is the linear-quadratic model

S= e−αD−βD2 (1.13) where D represents the physical dose and S the surviving fraction of cells. The α and β parameters, which can vary depending on targeted tissue and type of radiation, are used to define the radiosensitivity of the exposed region.

In particular, in conventional radiotherapy a high α/β ratio is typical of early respond-ing tissues (such as most tumors, α/β ∼ 10 Gy), whereas a low ratio is common in late reactive cells (e.g. normal tissues, α/β ∼ 2 Gy). This α/β variability is the rationale for treatment fractionation, since tissues with low α/β are less sensitive to low doses. On the contrary, in CPT the type of irradiated cells plays a less significant role due to the different behavior of hadrons inside the body. [20]

The linear-quadratic model showed to be quite effective in reproducing the experi-mental data up to a few decades of S. An example of some typical cell survival curves is displayed in Figure 1.11. The graph shows that the behavior of S strongly changes between low-LET and high-LET radiations. This is mainly due to the fact that the α

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1.2. RADIOBIOLOGY IN CHARGED PARTICLE THERAPY 13

Figure 1.11: Example of cell survival curves for different types of radiation. The quadratic “shoulder” is clear in the X-ray curve and negligible for high-LET radiations. The α/β ratio represents the dose value at which linear and quadratic damage have the same effect (from [20]).

and β parameters are linked respectively to DSB and SSB damage. Since this last one is almost absent for heavy charged particles, the linear term is always dominant and the curve can be described as

S = e−αD (1.14)

This is a reflection of the higher effectiveness of hadrons in cell killing and means that, in addition to the physical advantage, CPT also shows a significant biological advantage. The damage induced in DNA by high-LET radiation is much harder to repair, meaning that CPT beams have higher chances of killing the cells, especially in the BP region. Moreover, hadrons have lower LET in the entrance channel, which results in less severe lesions and higher cell survival rates than in the BP.

1.2.4 Relative Biological Effectiveness

A steeper survival curve also implies that heavy charged particles need to deposit a lower quantity of dose, with respect to photons, to produce the same amount of tissue damage. This characteristic is usually measured using a quantity called Relative Biological Effectiveness (RBE), defined as the ratio between the dose DX of a reference radiation

and the dose D of another type of radiation needed to achieve the same survival ratio S

RBE = DX D S (1.15)

Usually, DX is evaluated using photon beams (γ-rays from60Co decay), so RBE is defined

unitary for X-rays and higher for protons and heavy ions.

RBE depends on many different quantities, such as LET, dose, biological damage, fractionation, tissue type and it can also change along particle tracks. The typical be-havior of RBE as a function of LET of densely ionizing beams is showed in Figure 1.12. The curves obtained from experimental data show that RBE continuously grows as LET

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14 CHAPTER 1. CHARGED PARTICLE THERAPY becomes higher, up to a peak value for LET ∼ 100 − 200 keV/µm. After this peak, the RBE value starts decreasing because of overkilling effects, i.e. the damage induced in cells overcomes the amount needed to cause death and tissues receive some unnecessary dose. The actual position of the peak is particle-dependent and usually shifts to higher LETs for heavier ions.

Figure 1.12: 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]).

The idea of RBE is crucial in radiotherapy since it introduces the concept of RBE-weighted dose or biological dose, a key parameter in TPS. This quantity is usually mea-sured in Gy-RBE and is obtained multiplying the physical dose D deposited by the RBE of the utilized radiation. It expresses the conventional X-ray dose needed to obtain the same biological effect as the radiation of interest. Thus, RBE-weighted dose gives a clearer idea of the biological damage caused to each region of the body. In most of modern TPS, heavy ion treatments are based on this quantity, which is considered to be more reliable than physical dose. TPS usually include theoretical models that somewhat account for RBE variability of heavy ion beams along their path, mainly caused by high LET changes. Instead, currently the RBE of proton beams is set to a constant value of 1.1 in clinical practice, meaning that protons are considered 10% more efficient than photons along their entire track. The rationale for using a fixed value is that the LET of protons does not change as much as for heavy ions. However, different radiobiological studies have highlighted a non negligible increase in RBE both in the entrance channel and in the SOBP, with values ranging up to 1.6. [21]. Even though RBE dependency is less important in protontherapy, the choice of using a constant value could lead to an underestimation of the biological effect. In particular, research indicates that a treatment plan that includes RBE changes of protons may reduce the risk of complications at the edges of the treated region. [22]

The source of RBE variability in protons is still under investigation at the moment but a viable explanation of this effect was proposed in [23]. When traversing the body, protons may interact with target nuclei and lead to their fragmentation. The resulting secondary particles can have very different kinetic energy and LET, depending on projectile and target characteristic. Still, target nuclei are usually heavier than protons, so there is a high chance of producing a short range, high LET (and RBE) fragment that will release

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1.3. THESIS OBJECTIVES 15 his entire energy in ∼10 − 100µm. Thus, these fragments can locally increase the actual RBE of the beam and play a significant role in the total dose distribution. The impact of nuclear fragmentation for a proton beam was simulated, obtaining the behavior displayed in Figure 1.13. The results show that only 60% of the primaries actually reach the BP. Even though the number of nuclear interaction is higher in the BP, target fragments account for only 2% of the biological effect in this region. Instead, their contribution is much higher in the entrance channel, where nuclear fragments are responsible for 10% of the biological effect. This also means that the actual dose-depth profile could flatten, diminishing the ratio between entrance channel and BP.

Figure 1.13: Bragg curve of a 220 MeV proton beam obtained from an MC simulation (FLUKA). The different contributions to the depth-dose profile are highlighted, showing the relevance of target nuclear fragmentation in the entrance channel (from [24]).

However, the actual contribution of target fragmentation is currently very difficult to evaluate. The lack of experimental cross section values represents a source of uncertainty for beam transport simulations. The available models are not accurate enough and a direct comparison with data is still impossible in most cases. Moreover, it is important to notice that, while target fragmentations are probably more significant in protontherapy, the impact of these processes needs to be correctly evaluated also for heavy ion beams.

1.3 Thesis objectives

To summarize, the main issues in CPT related to nuclear fragmentation are

• RBE variability, linked to an increase of absorbed dose in the entrance channel. This effect is mainly relevant in proton therapy, and it is caused by low energy heavy recoil nuclei produced in target fragmentation.

• Dose tails behind the SOBP caused by projectile nuclear fragments, relevant in heavy ion treatments.

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16 CHAPTER 1. CHARGED PARTICLE THERAPY An in-depth knowledge of nuclear fragmentation processes of both projectile and target nuclei could improve the accuracy of the models currently implemented in TPS and MC simulations. However, there is still a lack of experimental values for nuclear fragmentation cross sections in the energy range of CPT, especially concerning target fragmentation.

The aim of the FOOT (FragmentatiOn Of Target) experiment, described in the next chapter, is to perform a set of nuclear double differential cross section measurements at CPT energies and provide a significant portion of the values currently unavailable in nuclear physics databases (for example, [25]). During this thesis work, I have focused on the study of the detectors of FOOT used to perform the charge (Z) identification of nuclear fragments, based on energy deposition and Time-Of-Flight measurements. My main contribution has been the development of a data analysis procedure dedicated to the calibration of these detectors and the reconstruction of Z for the impinging particles.

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Chapter 2 The FOOT experiment

The FOOT (FragmentatiOn Of Target) experiment aims to measure the double dif-ferential cross section of nuclear inelastic reactions in the energy range of CPT (up to 250 MeV for protons and 400 MeV/u for 12C and 16O). The project has been approved and funded by INFN (Istituto Nazionale di Fisica Nucleare, Italy) and, as of now, it counts over 100 members. Currently, the FOOT international collaboration includes eleven INFN sections, 10 Italian universities, three foreign universities and three other research insti-tutions.

FOOT aims to create a portable system capable of performing measurements on both projectile and target nuclear fragmentation processes. The requirement of a portable setup is fundamental because the needed beams will be available in different facilities, which mainly are

• CNAO (Centro Nazionale di Adroterapia Oncologica) in Pavia (Italy), providing proton and 12_{C ion beams at CPT energies.}

• Heidelberg Ion Therapy (HIT) center in Germany, where 4_He, 12_{C and} 16_{O beams}

for CPT are available.

• GSI in Darmstadt (Germany), which can provide 4_He, 12_{C and} 16_{O and other ion}

species.

The main objective is to provide reliable inelastic cross section data in order to improve the quality of nuclear models currently implemented in the MC simulations inside TPS. The results obtained in FOOT could eventually be used to develop a new generation of biologically oriented TPS (BioTPS), based more on biological effect rather than dose or RBE-weighted dose.

To carry out the planned measurements, the experiment will include 2 different setups dedicated to the identification of different nuclear fragments:

• A setup based on electronic detectors and a magnetic spectrometer, dedicated to heavy fragments (Z ≥ 3) and with an angular acceptance of 10 degrees from the beam axis.

• An emulsion chamber spectrometer coupled with the interaction region of FOOT, dedicated to light fragments (Z ≤ 2) and with an angular acceptance of about 70 degrees.

The need for 2 setups is dictated by the difficulty in reaching a good angular acceptance while maintaining an effective tracking system of limited size. [26,27] As further specified in the following chapters, this work focuses only on a subset of the electronic setup.

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18 CHAPTER 2. THE FOOT EXPERIMENT

2.1 Cross section measurements and inverse kinematic

approach

To study the production yield and energy of the fragments, FOOT has been designed as a fixed target experiment. The idea is to send typical CPT beams (mainly He, C or O) on different target materials representative of human tissues and to characterize the produced particles, so targets will be mainly composed of H, C and O. The choice of using composite materials was dictated by the large amount of technical difficulties introduced by a pure gaseous target. Hydrogen and oxygen cross section values will be extrapolated indirectly, using the results obtained from two different acquisitions and subtracting the respective data.

Hydrogen cross sections will be obtained considering a pure carbon target and a polyethylene (C2H4) one and applying the formula

σ(H) = 1 4 σ(C2H4) − 2σ(C) (2.1) which is equally applicable to differential and double differential measurements. For Oxy-gen measurements, an additional PMMA (PolyMethyl MethAcrylate, chemical formula (C5O2H8)n) target will be used. A possible problem with this approach is that the

un-certainties on indirect cross sections are calculated as the quadratic sum of single target measurements, meaning that they can become quite large. This method has already been validated in previous works (see [28]), but constitutes a viable solution only if direct measurements achieve a good resolution.

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

data. Note the large resulting error bars (from [28]).

Another important issue in the measurements is represented by target fragmentation induced by proton beams, already addressed in Section 1.2.4. The expected characteristics of nuclear fragments produced by a typical protontherapy beam inside a human body are reported in Table 2.1. As can be seen,from this table, nuclear fragments have high LET and very short range, meaning that they will not be able to escape even targets a few mm thick. However, the lowest achievable target dimension is limited by different factors: a very thin target would be fragile, causing mechanical problems, and would highly reduce the reaction rate, implying very long data acquisitions.

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2.2. EXPERIMENTAL REQUIREMENTS AND DESIGN CRITERIA 19

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 [23]).

In the specific case of target fragmentation induced by protons, the solution proposed in FOOT is to apply an inverse kinematic approach. Instead of shooting protons on tissue-like nuclei, carbon and oxygen beams will be sent on hydrogen-enriched targets. If the beams have the same velocity (i.e. the same kinetic energy per nucleon), the two situations are simply linked by a change of reference frame, i.e. a Lorentz transformation. The only difference is that, in inverse kinematics, the fragments emitted are much more energetic and can easily escape the target and be detected by the FOOT apparatus. This approach requires a good accuracy in determining the trajectories of both projectile and fragments. In particular, the Lorentz transformation can be correctly applied only if the emission angles are measured with a maximum uncertainty of about a mrad. In this way, the only constraints on target thickness are determined by MCS and secondary fragmentations. To maintain these effects as low as possible, targets will need to be ∼ 2 − 5 mm thick and have a maximum mass thickness of the order of g/cm2 (very low chances of double nuclear interactions). [26,27]

2.2 Experimental requirements and design criteria

The design criteria of FOOT are mainly determined by the requested portability of the system and the desired accuracy on CPT beams measurements. The final objective has been set to a 5% maximum uncertainty on cross section values obtained with the electronic detector setup. The request on σinel resolution has been chosen considering the current

status of clinical TPS. Previous studies carried out through Monte Carlo simulations have shown that σinel data with higher uncertainty do not result in observable improvements

of state-of-the-art TPS.

To guarantee the requested accuracy, the performances that FOOT needs to achieve in heavy fragments identification (C, N, O) are

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20 CHAPTER 2. THE FOOT EXPERIMENT • Time-Of-Flight resolution σT OF lower than 100 ps.

• Kinetic energy resolution σ(Ek)/Ek around 2%.

• Energy deposition resolution σ(∆E)/∆E at the level of 2%.

These results need also to be achieved in a system as compact as possible. The final electronic detector setup will have a longitudinal dimension of 1.5-2 m, which allows it to be placed it in all the treatment chambers of the aforementioned CPT facilities.

A correct application of the inverse kinematic approach does not rely only on the already mentioned angular precision. The system also requires solid isotopic and identi-fication of the particles traveling through the setup. With the limited dimensions of the system, this criterion can be fulfilled through the redundancy of FOOT: the character-istics of the fragments are determined in different ways to limit as much as possible the possible systematic errors in the calculations. As an example

• The mass m of the particles can be determined with three different methods based on the measurements of kinetic energy Ek, momentum p and Time-Of-Flight T OF .

These quantities can be utilized two-by-two to calculate the mass through the equa-tions p= mβγ (2.2) Ek = mc2(γ − 1) (2.3) Ek= p p2_c2_{+ m}2_c4_{− mc}2 _(2.4)

where T OF is used to determine the Lorentz factors β = v/c and γ = 1/p1 − β2_.

Mass identification is expected to have resolution ranging from about 3% to 6%. • Charge identification is performed by means of the energy deposition ∆E in a thin

slab of plastic scintillator and T OF measurements. The atomic number Z of the particle is obtained from Equation 1.1 (substituting dE with ∆E and dx with the thickness of the scintillator slab). In the case of charge identification, redundancy can be achieved by also measuring the energy deposited in other detectors. With the above requirements on∆E and T OF accuracy, the final expected resolution on Z ranges from 6% for 1H to about 2% for16O nuclei.

2.3 Electronic setup

The FOOT electronic detector setup is dedicated to the identification of nuclear frag-ments heavier than 4He. The geometrical acceptance of the system has been chosen to match the region where particles with Z ≥3 are mainly emitted, within about 10 degrees from the beam direction. This value was found through a preliminary study with MC codes, leading to the results shown in Figure 2.2.

A schematic view of the electronic setup is reported in Figure 2.3. The system can be divided in 3 main regions: an upstream (pre-target) region, a magnetic spectrometer and a downstream region.

• The upstream region is dedicated to the monitoring of primary beam particles and is made of the first two detectors encountered by the beam: the Start Counter and the Beam Monitor.

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2.3. ELECTRONIC SETUP 21

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 [26]).

Figure 2.3: Schematic view of the electronic setup of FOOT for the detection of heavy ion fragments (from [27]).

• The magnetic spectrometer, placed right after the target, consists of three measuring stations (Vertex, Inner Tracker and Microstrip Silicon Detector) alternated by two permanent magnets. This portion of FOOT is dedicated to the particle tracking and momentum measurements.

• The downstream region is dedicated to the detection of the T OF and energy of particles. It includes two detectors placed at a variable distance from the target (1-2 m): the TOF-Wall detector and a BGO Calorimeter.

2.3.1 Start Counter

The Start Counter (STC) is a thin (250 µm) plastic scintillator and it is the first detector encountered by the beam. The STC has an active area of 5 x 5 cm2 and is placed 20-30 cm before the target. Figure 2.4a shows a technical drawing of the scintillator foil and its aluminum frame. Its main purpose is to provide the first time stamp of

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22 CHAPTER 2. THE FOOT EXPERIMENT the passage of primaries for T OF measurements. It also monitors the rate of primaries traveling through the system and generates a trigger signal for all the other detectors. The thickness of the scintillator foil was chosen in order to minimize its impact on the beam while keeping a good time resolution (60-70 ps). A detailed description of this detector is given in Section 3.2.1.

2.3.2 Beam Monitor

The Beam Monitor (BM) is an Ar/CO2 (80/20%) drift chamber, filled with 12 layers

of alternating horizontal and vertical wires. Each plane consists of 3 rectangular drift cells of 16 x 11 mm2 with the long side perpendicular to the beam direction. Consecutive layers are also staggered by half cell to avoid left-right ambiguities. The total dimensions of the BM are 11 x 11 x 21 cm3_.

The aim of the BM is to accurately measure the initial position and direction of primaries, fundamental for particle tracking and rejection of pre-target fragmentation events. Since the momentum of primaries is fundamental for the Lorentz boost, the BM should achieve a resolution of about 140 µm for position measurements and ∼ mrad for angular data. Since it is placed between the STC and the target, the BM was designed as a drift chamber also for its low impact on the primaries.

(a) (b)

Figure 2.4: Technical drawings of the (a) Start Counter in its aluminum frame (from [29]) and (b) Beam Monitor (from [26]).

2.3.3 Magnetic spectrometer

The tracking system of FOOT is a magnetic spectrometer placed right after the target and it includes three measuring stations alternated with two permanent magnets. This section of FOOT is dedicated to the evaluation of the momentum of particles, obtained by studying the bending of beam trajectories inside a magnetic field. Moreover, the spectrometer will also give information about the interaction point of particles inside the target. The overall design of the spectrometer is mainly dictated by the requested momentum resolution and its portability. The accuracy of p measurements increases as transverse momentum variations ∆pT become larger. For a particle of charge q moving

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2.3. ELECTRONIC SETUP 23 in a magnetic field B of length L, ∆pT is given by

∆pT = q

Z L

0

Bdl (2.5)

This means that p resolution depends mainly on B and L. A preliminary feasibility study with MC simulations led to the configuration shown in Figure 2.5, where the z axis represents the beam line.

(a) (b)

Figure 2.5: (a) Schematic view of the permanent magnets in Halbach configuration and (b) simulated transverse magnetic field along z at x = 0, y = 0. Both graphs were obtained with the dimensions mentioned below (from [26]).

The permanent magnets are made of Sm2Co17 (Samarium-Cobalt) modules assembled

in Halbach configuration. The material was chosen for its strong resistance to radiation damage, while the configuration has the advantage of a nearly uniform magnetic field along transverse (x − y) planes. Precisely, the field is uniform at the percent level up to a distance of 3 cm from the centers of the magnets. Figure 2.5b also displays the longitudinal profile of the magnetic field, which can be approximated with the sum of two Gaussian functions.

A good trade-off between p resolution and portability is reachable with the configura-tion in Figure 2.5a. The magnets cover a longitudinal distance of about 15-20 cm and the modules are ∼ 10 cm thick with an internal radius of ∼ 4 cm. The resulting magnetic field at the center of the Halbach rings reaches a maximum of 0.9 T. The final magnets will weigh 200-300 kg, which means that a robust mechanical frame is mandatory to exploit the best possible resolution (∼ 10µm) achievable by the tracking system. Moreover, the design of the three measuring stations has been chosen in order to minimize MCS and secondary fragmentations, while keeping a good p resolution and geometrical acceptance. Vertex

The Vertex (VTX) is the first detector of the tracking system. It is made of four layers of MIMOSA28 (M28) chips developed by the Strasbourg CNRS PICSEL group. [30] The M28 comes from the family of CMOS Monolithic Active Pixel Sensors (MAPS), already in use in X-ray imaging and charged particle detection. Each sensor includes 928(rows) x 960(columns) pixels of 20.7 µm pitch, corresponding to a total active area of 20.22 x 22.71 mm2, and is50µm thick. The VTX is placed at ∼ 0.5 cm from the target and will be divided in two substations at a distance of 10 mm from each other. Each substation is made of two planes at a 2 mm distance. With this setup, the VTX has a geometrical

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24 CHAPTER 2. THE FOOT EXPERIMENT acceptance of ∼40 degrees with respect to the target. The aim of the VTX is to identify the vertices of the trajectories, i.e. the points where primaries interacted with the target. The particles passing through this detector produce a signal inside different pixels and their hit positions on the planes can be reconstructed. The accuracy required for these values is at the level of few µm.

Inner Tracker

The Inner Tracker (IT) is the second station of the spectrometer and is placed in the region between the two magnets, at ∼20 cm from the target. Its purpose is to measure the direction and transverse position of particle tracks. The detector is made of 2 planes of 8 M28 chips (the same of the VTX) each. The chips (50 µm thick, active area of 2 x 2 cm2_{) are equally divided in four ladders similar to the ones implemented in the PLUME}

project. [31] These modules are made of a Kapton FPC (Flexible Printed Cable), where the chips are glued, and have a total thickness of ∼ 100µm. The distance between each chip is confined to a maximum of 30 µm. The 4 ladders are fixed to an aluminum frame covering a total area of 8 x 8 cm2. To maximize the active surface, the two planes are also staggered laterally to avoid the superposition of dead areas between chips. Note that, even if the IT is placed inside the magnetic field (see Figure 2.5b), the performance of M28 chips should not be significantly affected. [32]

Microstrip Silicon Detectors

The Microstrip Silicon Detectors (MSD) represent the final station of the tracking sys-tem, placed at about 35 cm from the target. Its purpose is to provide the last information on trajectories in order to calculate the momentum of particles and match the tracks with TOF-Wall and Calorimeter hits. It can also provide a measure of the energy released dE/dx, which can be exploited to obtain a redundant measure of the charge of impinging particles (the main detector employed for charge identification is the TOF-Wall). The detector includes three 150 µm thick layers of alternatively orthogonal silicon microstrips. Each layer will have an active area of 9 x 9 cm2, enough to cover the 10 degrees accep-tance, and a microstrip pitch of 125 µm. With this setup, a < 35µm spatial resolution can be achieved.

2.3.4 TOF-Wall detector

The TOF-Wall (TW), or∆E-T OF detector, is the first component of the downstream region. This detector is made of 40 bars of plastic scintillator arranged perpendicularly in two consecutive layers. Each bar has an area of 2 x 44 cm2 _{and is 3 mm thick. Figure 2.6}

shows a picture of one of the bars. The aim of the TW is to provide a measurement of dE/dx and the last time stamp of particles T OF . The thickness of the bars has been chosen to ensure a good resolution for both time (70 ps) and energy (2-3%) measurements. The detector can also identify the hit position of fragments in the downstream region, allowing for a complete track reconstruction. The detector has been entirely developed by the University and INFN section of Pisa (hereafter called Pisa group). Detailed description of the TW is given in Section 3.2.2.

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2.4. FOOT MONTE CARLO SIMULATIONS 25

Figure 2.6: Picture of one of the bars in the TOF-Wall detector. Note the darkening tape around the bar used to shield the scintillator material from background light sources (from [26]).

2.3.5 Calorimeter

The last detector of the electronic setup is a BGO (Bismuth Germanate) Calorimeter (CALO). The purpose of this detector is to stop the impinging fragments and measure their kinetic energy. The final CALO will include 32 modules of BGO crystals arranged in a pointing geometry, as shown in Figure 2.7b. Each module is made of 9 crystals encased in a 3D-printed plastic support (Figure 2.7a), which was designed to hold the crystals from the back and leave only air and BGO in the first 12 cm of the detector. This is made possible by the shape of the crystals, i.e. a truncated pyramid with 2 x 2 cm2 and 2.9 x 2.9 cm2 _{surfaces and a length of 24 cm. The choice of BGO was dictated by}

its high density and light yield. Since FOOT will work at relatively low rates, the slow response of the material should not represent an issue. However, a possible problem is the significant production of neutrons, which can then escape the Calorimeter. BGO can partially limit this effect since it also has a high neutron capture cross section (σ = 1.47 barn), but a possible underestimation of the measured kinetic energy has to be taken into account. Some preliminary tests have shown that the crystals can reach an energy resolution ranging between 1-3%.

2.4 FOOT Monte Carlo Simulations

Monte Carlo (MC) simulations are a fundamental tool in the study of the setup and physics of FOOT. The code chosen to simulate the setup is FLUKA, developed by INFN and CERN and based on the FORTRAN (77 and 95) language. [33, 34] FLUKA is a general purpose, theory driven MC code capable of simulating particle transport through complex geometries. FLUKA has been widely validated with experimental data for a large range of different particles and materials. The code has also proven to be able to simulate CPT treatment plans and can handle data obtained from Computed Tomography scans to accurately reproduce the body of the patients. [35] Moreover, the Flair graphical interface has been developed for a more user-friendly usage of the code. [36] Flair is mainly used for geometry implementation and debugging, but also permits to compile and run the

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26 CHAPTER 2. THE FOOT EXPERIMENT

(a) (b)

Figure 2.7: Technical drawing of the BGO Calorimeter: (a) 9-crystals module prototype showing housing box and DaQ system (8 x 8 mm2 SiPMs, 15 µm microcell pitch) and (b) geometry of the full detector (from [26]).

input files. A comprehensive list of the interaction models included inside FLUKA can be found in [37] and [38].

As already mentioned, MC simulations have been a fundamental tool to develop the design of FOOT. The entire geometry of the electronic setup has been extensively studied in the FLUKA framework in previous works (see [27] as an example). Figure 2.8 displays an image (obtained with Flair) of the geometry of the electronic setup implemented in FLUKA. In this thesis work, MC simulations were used to extract the expected T OF and

Figure 2.8: Geometry of the electronic setup of FOOT implemented in FLUKA: section on the x-z plane (V15 of the simulations)

∆E values and utilize them to calibrate the scintillators (STC and TW) of FOOT. This was achieved by reproducing the geometry and primary beams of the two experimental setups taken into account. Both of these were subsets of the detectors in the electronic setup and are described in Section 3.3.1 and 3.3.2.

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2.5. CURRENT STATUS AND RESEARCH PROGRAM 27

2.5 Current status and research program

The FOOT apparatus is currently under development and no measurements have been performed with the full system yet. The first data taking session with the entire electronic setup is scheduled for late 2021, but R&D studies on single detectors and partial setups have been already carried out through dedicated test beams.

As of today, many of the components of the electronic setup are under construction, such as the CALO and most of the magnetic spectrometer. Moreover, some detectors are able to acquire data but still need to be included in the total DAQ system. An-other tool currently under development is the general software of FOOT, called SHOE (Software for Hadrontherapy Optimization Experiment), which is meant to eventually perform the entire reconstruction of the events needed for double differential cross section measurements.

The scintillators (STC and TW) are the detectors closest to their final designs. They are both currently operative and no major modification is scheduled. The STC and TW are the two detectors studied in this thesis, with particular attention to the latter. As shown in the next chapters, these components of FOOT already proved to be accurate enough to meet the experimental requirements on charge identification of nuclear frag-ments.

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Chapter 3 Materials and methods

3.1 Overview

The FOOT scintillator detectors (STC and TW) were tested during two test beams performed in 2019 at CNAO and GSI. The goals were to set-up and test a calibration procedure for the detectors and validate it. In this thesis I have performed a detailed analysis of the data sets acquired with the STC and TW during those test beams. To this aim, I have contributed to develop a software framework to correctly handle data at the raw waveform level. A basic scheme of the entire analysis workflow is given in Figure 3.1. A list of the principal features of the data processing routine that I have developed and a brief user guide of the software are provided in Appendix A. The corresponding code covers all the procedures explained in Section 3.5, starting from the decoded waveforms and returning the first uncalibrated results for energy deposition and T OF measurements. The developed data processing routine is currently an integral part of the stand-alone software utilized by the Pisa group. Energy and T OF calibrations have been carried out through a comparison of raw data with MC simulation results in other dedicated scripts. All of the framework was written using the ROOT programming language developed at CERN. [39].

Figure 3.1: Scheme of the analysis workflow (the decoding of binary data is not treated in this work, since it was already provided).

Charge identification of nuclear fragments with the Time-Of-Flight detectors of the FOOT experiment

University of Pisa