Study of the Time-Of-Flight detector for nuclear fragmentation experiment FOOT in particle terapy

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Universit`

a degli Studi di Pisa

FACOLT `A DI FISICA

Corso di Laurea Magistrale in Fisica Medica

Tesi di laurea magistrale

Study of the Time-Of-Flight detector

for the nuclear fragmentation

experiment FOOT in particle therapy

Candidato:

Matteo Bertazzoni

Relatore:

Maria Giuseppina Bisogni

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Introduction

Nowadays, one of the most advanced methods for solid tumor treatment is represented by hadrontherapy, a high precision external radiotherapy tech-nique which applies collimated beams of protons or heavier ions to defeat radioresistant tumors and which has given a boost to the use of radiation in the fight against cancer. Compared to the standard X-ray based treatments, due to the profile of their released dose in tissue, charged hadron beams can be very effective in destroying the tumor and, at the same time, avoiding the adjacent healthy tissue. On the other hand, the use of accelerated particles requires appropriate methods to accurately evaluate the dose distribution inside and outside the planned target volume during the irradiation treat-ment. The most important difference between protons and heavier ions is the increased biological effectiveness of the latter, i.e., with heavy ions a lower physical dose is needed to obtain a given biological effect. Carbon ions are particularly attractive for hadrontherapy, due to the fact that their energy deposition is highly localized and their relative biological effectiveness (RBE) is high towards the end of the range, thus offering an additional advantage for slowly growing radioresistant tumors. However, when the carbon beam penetrates matter, the primary ions can be fragmented as a result of the collisions with the tissue atomic nuclei. The collisions along the carbon path lead to the attenuation of the primary beam intensity and the production of secondary fragments, such as neutrons and ions lighter than carbon (hydro-gen, helium, lithium, beryllium and boron isotopes). These lighter fragments have longer ranges and wider energy distributions than the primary particles and give rise to a characteristic dose tail behind the Bragg peak (BP). The biological effect of a certain type of ion radiation is dependent also on these secondary products, therefore, a detailed knowledge of the fragmentation process is essential to guarantee the appropriate treatment accuracy.

The determination of the RBE of the fragments by means of radiobiolog-ical experiments is difficult and, in the energy range of biomedradiobiolog-ical interest (up to 250 M eV for protons and 400 M eV /u for carbon ions), limited cross section data are available for the production of heavy recoils after proton

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adopts an inverse kinematic approach. To bypass the problems given by the management of a pure hydrogen target, projectile-nucleus data are extracted by subtraction of cross sections on C and C2H4 targets. The final FOOT apparatus will consist of a high precision tracking system in magnetic field (composed by silicon pixel trackers and silicon strip detectors), a Time-Of-Flight dE/dx measurement system (hereafter called TOF dE/dx detector) and a calorimeter. The beam monitoring system of the FOOT experiment will include a plastic scintillator detector to measure the incoming rate of the ion beam and a drift chamber to measure the incident beam direction and position.

The final TOF dE/dx detector will be composed by two orthogonal layers of 22 plastic scintillator bars each, and each bar will be readout at both ends by silicon photomultipliers (SiPM). This detector will be used to measure the Time Of Flight of the fragments (for the calculation of the β of the particle) and the energy released in the scintillator (for the calculation of the mass number A). The requirements of the FOOT experiment are: dE/dx resolution σE/E ∼ 2% and TOF resolution σt∼ 100 ps. In the development of the final TOF dE/dx detector, some critical parameters need to be taken into account. These are, for example, the thickness of the plastic scintillator bar, the efficiency of the light collection (i.e. the number of SiPMs at the ends of the bars and the type of connection among them) and the data acquisition parameters which are used to digitize the signal. Before developing the final detector, these parameters need to be studied and tuned. The aim of the present thesis is therefore the development and the characterization of a TOF dE/dx protoype that consists of a plastic scintillator bar coupled on both sides to SiPMs and to study how the time and energy resolution depend on factors such as the beam energy, the beam interaction position inside the scintillator bar, the SiPM applied voltage and the electronics sampling rate. In Chapter 1, the state of the art of hadrontherapy is introduced, fol-lowed by a description of the relevant radiobiological parameters adopted in Particle Terapy. Chapter 2 shows the measurements strategy and the

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exper-Introduction 3

imental setup adopted in the FOOT experiment. In Chapter 3, the structure of the TOF dE/dx prototype detector and the calculation of the time and energy information is explained. The preliminary results obtained with a TOF dE/dx detector prototype at the Proton Therapy Centre (PTC) of the Trento Hospital with a 70-230 M eV proton beam are presented and discussed in Chapter 4. In the final Chapter, the conclusions of the work are drawn and the future perspectives are outlined.

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factors that increase the possibility of certain cancers associated with afflu-ence. This effect combined with the growth and ageing of population, lead to expect over 20 million new cancer cases annually by 2025. However, the estimated cancer mortality is in a decreasing tendency: the 5-year relative survival rate for all cancers diagnosed during 2005-2011 was 69%, up from 49% during 1975-1977 [32]. The increase in the survival rate reflects both progress in diagnosis techniques and improvements of technologies. Nowa-days there are different techniques to treat neoplastic disease. The standard methods are surgery, chemotherapy, radiation therapy and, more recently, immunotherapy. Radiation therapy contributes to the cure of approximately 23% of all cancer patients, used alone (12%) or in combination with surgery (6%) or chemotherapy-immunotherapy (5%) [33] [34]. The percentage of pa-tients that are referred to a radiation therapy department for at least part of the treatment goes up to 70% in industrialized countries.

1.1 History of hadronterapy

The application of high-energy beams of heavy charged particles to radiother-apy was first considered in 1946 by Robert R. Wilson. He had worked in the Manhattan Project in Los Alamos and soon after the end of World war II de-cided to go back to Berkeley, where he found an inspiring academic research environment around Ernest Lawrence and collaborators. In the course of the

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1.1. HISTORY OF HADRONTERAPY 5

design of a new cyclotron he started to investigate the range of 150 M eV protons and the stopping characteristics in various shielding materials.

Two years later the synchrocyclotron at LBL Berkeley became available for experiments and the physical and radiobiological properties of proton beams were thoroughly investigated by Tobias and co-workers [35]. Patient treatments started in 1954 at LBL Berkeley, first with protons and later with helium beams. At the Harvard Cyclotron Lab (USA) more than 9000 patients were treated with proton beams (1961-2002), and also in Europe proton therapy begun in the 1950s and 1960s at laboratories in Uppsala (Sweden), Moscow and St. Petersburg. Radiotherapy with heavier ions was initiated by Tobias and co-workers at the BEVALAC facility at LBL. Many interest-ing facts about the development of hadrontherapy can be found in [36]. At LBL most of the patient treatments (1975-1992) with heavy ions were per-formed with20_{N e}_{ions (670 M eV /u) which at that time appeared to be most} attractive because of their high relative biological effectiveness (RBE) com-bined with a low oxygen enhancement ratio (OER) in the treatment target volume [9] [37]. The beams were delivered to the patients by passive beam shaping systems, including scattering devices and magnets for broadening the beam and a number of passive elements like ridge filter, range modulator and collimator [38]. Until its closure in 1992 the BEVALAC was the only facility worldwide using heavy ions for the treatment of localized deepseated tumors. In 1994 the Heavy-Ion Medical Accelerator (HIMAC) [39] dedicated to radiotherapy started with carbon ions at National Institute of Radiological Science (NIRS) at Chiba (Japan), using similar technical concepts as those pioneered at Berkeley. In Europe first treatments with 12_C _{ions started at} Gesellschaft f¨ur SchwerIonenforschung (GSI) Darmstadt in 1997.

Besides the great success of using proton beams for cancer therapy, carbon ions have shown to be an effective treatment modality as high-LET radiation with more than 10.000 patients treated worldwide (mainly in Japan). Helium ions indeed seem to be therapeutically very promising as they offer a good compromise between high-LET and low-LET radiation, combined with fa-vorable physical characteristics (much less scattering than protons). Clinical trials with He-ions are under preparation at the HIT facility in Heidelberg.

Up to now there are 68 clinical facilities operating with protons or heavy ions worldwide (Austria, Canada, Czech Republic, China, France, Germany, Italy, Japan, Poland, Russia, South Africa, South Korea, Sweden, Switzer-land, Taiwan, United Kingdom, Usa). Other 39 facilities are under construc-tion also in new countries (Denmark, Emirate of Abu Dhabi, India, Nether-lands, Saudi Arabia, Singapore, Slovak Republic) and they should be oper-ating in about two years [40].

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dm

In the international system of unit (SI) the dose unit of measurement is the Gray and 1 Gy corresponds to 1 J of absorbed radiation by 1 kg of mass (1 Gy = 1 J/kg) [7].

1.2.1 Linear Energy Transfer (LET)

A quantity closely related to the stopping power is the Linear Energy Transfer (LET) which refers to the energy deposited in the target medium per unit path length by the slowing-down particle and it is defined as:

LET = dE

dx (1.2)

The definition of linear energy transfer is very similar to the definition of the stopping power in Equation A.2, but in the dE/dx case it is considered at the energy given to the absorber (measured in keV /µm) instead of the energy loss by the incident particle.

When a charged particle traverses matter, several secondary electrons (usually called delta rays if their energy is high enough to ionize) are produced as a consequence of the process of ionization.

LET depends on the particle energy and type: normally, photons and protons are referred to as low-LET radiation for their typical sparse ionization density, while carbon ions are called high-LET particles due to their larger ionization density, as shown in Figure 1.1.

The higher the LET, the higher will be the biological effectiveness. In fact, high LET radiations produce more microscopic damages and more clus-tered lesions with respect to low LET particles. The distinction between low and high LET, for many cellular systems, is represented by the value of

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1.2. PHYSICAL ASPECTS 7

Figure 1.1: Schematic representation of the differences between High-LET and Low-LET radiation at the same total dose. Poins indicate the ionization events.

20 keV /µm [8]. In Table 1.1, a list of LET values for ions from hydrogen to oxygen (in the energy range corresponding to 200 MeV protons) is given. From Table 1.1, it must be highlighted that carbon ions have a LET higher than 20 keV /µm in the last part of their travel (40 mm from the stopping point) while at the beginning, in the so called ’entry channel’, their LET is smaller than 15 keV /µm. This means that at the end of their path the biological damage is high and difficult to repair, while it is reduced at the beginning of the path. This can be exploited in adrotherapy to treat deep lesion while preserving healthy tissue.

It is possible link the LET to the dose distribution as follows citelaitano:

D[Gy] = LET keV µm × F 1 cm2 × 1 ρ cm3 g (1.3)

For a parallel beam with fluence F (dN particles traversing a surface dS), which deposits a dose D in a thin slice of absorber material with mass den-sity ρ equal to Equation 1.3.

1.2.2 Energy Deposition

As explained in Appendix A, the energy released by the photons decreases exponentially with the depth of penetration, showing a peak between the first centimeters of tissue depending on the initial photon energy (Figure 1.2). In

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7_Li+3 _234.3 _3.7 _4.6 _6.2 _8.9 _40.0

11_B+5 _329.5 _8.5 _{10.0 13.5 19.0} _87.5

12_C+6 _390.7 _{11.0 13.5 17.5 24.5 112.0}

14_N+7 _430.5 _{14.5 17.5 22.5 31.5 142.0}

12_O+8 _468.0 _{18.0 21.5 28.0 29.0 175.0}

contrast, heavy charge particles have a particular deposition curve which follows the Bethe-Bloch formula (Equation A.2). This is characterized by a small amount of energy lost when the particle velocity is high (entry channel), while most of it is released into a very narrow portion of the path near the end of the particle range, the so-called Bragg peak (Figure A.4). In addition, being the range a function of energy, the depth of the Bragg peak within the patient can be varied and adjusted by changing the beam energy (as shown in Figure 1.3).

In Figure 1.4 is reported a simplified scheme of the dose release in ra-diotherapy: in (a) is presented the ideal dose-depth relation where only the tumor (pink box) is irradiated while in (b) the photon dose-depth relation in shown; in (c) and (d) the dose-depth profile is shown for protons and car-bon ions, respectively. From this simple scheme it can be easily understood that therapies with protons (c) or carbon ions (d) lead to achieve a higher conformity of the dose released to the target volume and the OAR receives a much lower dose with respect to photon therapy .

It has to be pointed out that the nuclear fragmentation of charged par-ticles interacting with target nuclei has to be considered for carbon beams (Section 1.3): the produced projectile fragments, due to the conservation of the projectile momentum, are responsible of an overdosage that is delivered to tissues beyond the tumor volume, due to a tail of the released dose after

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Figure 1.2: Comparison of the depth dose profiles of X-rays, photons, protons and carbon ions [9].

Figure 1.3: Carbon ions measured depth-dose distributions in water for different beam energies [10].

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Figure 1.4: Comparison between desired profile (with a single field (b), proton therapy (c) and carbon ion therapy (d) for a given tumor volume (pink box) in proximity to an OAR (yellow area) [45].

1.2.3 Lateral beam spread

The charged particle beam undergoes a diffusion due to the interaction with the patient body. As a consequence the beam is spread in the transverse direc-tion with respect to its original size. This spread is mainly caused by multiple scattering, i.e. elastic Coulomb interaction with target nuclei (Appendix A). Considering a proton and a carbon beam having the the same range P in a material (e.g. 150 M eV protons and 285 M eV /u carbon ions with P=15.6 cm), the lateral beam spread is expected to be three times larger for protons. An idea of this effect is given by Figure 1.5.

There are two distinguishable contributions to the overall multiple scat-tering: the contribution due to the interaction of the beam with materials before the patient as the beam pipe exit window, the external beam moni-tors, collimators and air and the contribution due to the interaction with the patient tissues. The former contribution dominates at low energies, while the latter dominates at high energies, when the beam range increases inside the patient.

Figure 1.6 show the beam spread for carbon ions and protons: the parallel particle beam of 5 mm FWHM, that passes through a nozzle (including a

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Figure 1.5: Image of the diffusion of protons (top) and carbon ions (bottom) as a function of depth in tissues [13].

thin vacuum window and beam monitors) and enters a water target placed at a distance of 1 m from the nozzle exit has been simulated. At low energies the beam width is mainly dominated by the scattering in the nozzle, while at higher energies the scattering in the target dominates. Carbon ions show a much smaller spread than protons for the same penetration depth

Figure 1.6: Calculated beam spread for carbon ions (red) and protons (blue) in a typical treatment beam line [13].

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out on a wide range of angles. In such a collision, virtually all nucleons in both colliding partners are participating;

2. Peripheral collisions, where the momentum and energy transfer are relatively small. Only a few nucleons in the overlapping area interact effectively during the collision and the number of participants’ nucleons is small.

Figure 1.7: Rapresentation of central and peripheral collision [5].

The central collisions include the Complete Fusion (CF) and Incomplete Fusion (IF). The CF and IF cross section change as a function of the projectile energy and at high energies the CF probability is very low while the IF probability is very high. Instead at low energies, in the Bragg peak region, the CF probability reaches values of ∼ 40-50% or even more, depending also on the projectile mass. The peripherical collision can give rise to several phenomena:

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1.3. NUCLEAR FRAGMENTATION 13

• Quasi-elastic scattering • Nuclear fragmentation

The first is analogous to the Coulombian scattering just treated, except that it is mediated by strong nuclear force rather than by electromagnetic re-pulsion. Quasi-elastic scattering is a phenomenon formally similar to the previous one. The quasi elasticity is expressed in a non-conservation of the kinetic energy of the system, whereby the projectile provide energy to the target, which then reaches an excited and unstable state. The projectile then proceeds with altered direction and speed, while the target returns to the equilibrium state by emitting a photon of energy equal to that received. Nu-clear de-energizing photons are called prompt photons (or gamma) due to their emission in a short time since the occurrence of the interaction, and they can be emitted even in the case of nuclear fragmentation.

The peripheral collision fragmentation process can be described with the two-stage pattern that occurs in two different time scales [5]: the model of ablation-abrasion. This model is a simplification of core-core collision, and is schematically illustrated in Figure 1.8.

Figure 1.8: Schematic representation of abrasion-ablation model for the nuclear fragmentation due to peripheral collisions of projectile and target nucleus [5].

The first phase is abrasion, when a bullet hits a target nucleus, the nu-cleons inside the overlapping zone (fireball) interact with each other and are expelled from both the bullet and the target. Light particles are emitted at this stage. Bullet fragments follow the initial trajectory at about the same initial speed, while the recoil fragments slow it down.

In the second reaction stage, ablation, the system termalized and de-energized due to the evaporation of neutrons, proton and light nuclei, fission,

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where the dose is distributed randomly throughout the cells. This is schemat-ically explained in Figure 1.9.

Figure 1.9: (A) Schematic view of an undamaged part of DNA, (B) two separated single strand breaks, (C) a double strand break, and (D) a ’clustered lesion’. The (*) indicate a base damage [11].

Low doses lead from the undamaged double stranded DNA (A) first to separated single strand breaks and single base damages (B) which can mostly be repaired. Two single strand breaks occuring close to each other may lead to a double strand break (C), which in most cases can also be repaired by the cell. Only when the local dose becomes high enough that the produced damage cannot be sufficiently repaired a lethal event will result (D).

Therefore, the biological response which is quantitatively described by the cell survival S, is a non-linear function of dose and, for doses up to a few

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1.4. BIOLOGICAL ASPECTS 15

Grays, cell inactivation can be parametrized by spell the Linear-Quadratic (LQ) model [12], thus giving

S(D) = S0· e−(αD+βD

2₎

(1.4) where D is the absorbed dose and α [Gy−1_{] and β [Gy}−2_{] are} experimen-tally determined parameters characterizing the radiation response. The ratio α/β determines the trend of the survival curve and it gives an indication of the cellular repair capacity (Figure 1.10).

Figure 1.10: Survival curves for Chinese hamster ovary (CHO-K1) cells irradi-ated with X-rays (1) and carbon ions of different energies: (2) 266.4 M eV /u LET = 13.7 keV /µm, (3) 11.0 M eV /u LET = 153.0 keV /µm, (4) 2.4 M eV /u LET = 482.7 keV /µm [11].

Low α/β ratio is associated with a prevalence of repairable damage, while high ratio is related to a severe non repairable damage. Both cases are pre-sented in Figure 1.10: the curve associated with X-ray radiation shows a clear

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1.4.1 Relative Biological Effectiveness (RBE)

To calculate and to predict biological damage due to incident radiation, the Relative Biological Effectiveness (RBE) is used. RBE is the ratio of biological damage proportional related to the absorbed dose, induced by a reference radiation Dref (usually a beam of photons), and the absorbed dose induced by the radiation taken into account, Dtest. The RBE is therefore defined by Equation 1.5.

RBE = Dref Dtest

(1.5) To compare the biological effects of different types of radiation, and to evaluate RBE, cells survival curves are commonly used. These curves show the relationship between the fraction of cells that preserve reproductive in-tegrity and the absorbed dose (Figure 1.11). Relative biological efficacy is a complex quantity that depends on physical parameters (particle type, dose, LET), as well as biological parameters (tissue type, cell cycle phase, oxy-genation level).

It should be considered that the RBE may be different in different tissues or organs, and may also vary within the tumor itself. Each type of radiation is characterized by its own form with different corresponding RBE values relative to photons (RBE = 1.0). By fixing a survival level, in Figure 1.11, can be graphically determined the RBE values for a given type of radiation. Comparing the two survival curves, it is noted that the RBE of a radiation is not constant at different levels of cell survival.

1.4.2 Oxygen Enhancement Ratio (OER)

The presence of oxygen in cellular tissue can enhance the harmful effect of radiation due to the formation of free radicals. Therefore, a parameter

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1.4. BIOLOGICAL ASPECTS 17

Figure 1.11: Cell survival curves and RBE determination, for survival levels of 10% and 1% for light ion (red dotted line) and photons (black line - reference radiation) radiation [13].

to consider to estimate the biological efficacy of a treatment is the degree of oxygenation of the tissue to be treated. Indeed, numerous studies have shown that treatment is less effective in hypoxia [14].

This effect of enhancing the damage caused by the presence of oxygen is expressed by the Oxygen Enhancement Ratio (OER), defined as the ratio between the dose required to produce a certain biological effect in the non-oxygenated tissue (DnO) and the dose required to produce the same effect in a fully oxygenated tissue at atmospheric pressure (DO):

OER= DnO DO

(1.6)

The typical values of the OER vary between 1 (the damage produced by the radiation does not depend on the presence of oxygen) and 3 (the damage caused by the radiation is strongly affected the presence of oxygen). However, it has to be considered that the OER varies in relation to the type of radiation, since it is a decreasing function of the LET. In fact, high LET

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quired to achieve the same effect compared to highly ionizing radiations. For these reasons, charge hadron radiations are more effective in treating poorly oxygenated tumors. In Figure 1.12, the influence of the oxygen level on cell survival of human kidney cells for carbon monoxide at different energies is noteworthy and therefore different from LET.

Figure 1.12: Influence of oxygen level on cell survival of human kidney cells for carbon ions at different energies and therefore different LET: 33 keV /u (blue) and 118 keV /u (red) compared to X-rays (black) [15].

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1.5. BEAM DELIVERY TECHNIQUES 19

1.5 Beam Delivery Techniques

As previously reported light ion beams are a valuable tool in radiation ther-apy, in particular for those applications where photons are not giving positive results or surgery cannot be employed, e.g. for deep seated tumors surrounded by organs at risk. The difference between hadrons and photons in the dose release in tissues calls for a different way in planning the treatment. The narrow extension of the BP of the hadron beams asks for an accurate and precise positioning of this dose release maximum on the tumor region. Even-tual mistakes in the position of the BP on the tumor would imply at the same time overdosage of healthy tissues and underdosage of the tumor. Moreover, tumors have volumes of the order of centimeters, while the Bragg peak ex-tension is of the order of few millimeters and this difference in size must be taken into account in the clinical treatment. At the same time other im-portant aspects have to be considered, as the minimization of the impact of the intrinsic patient body movements, due for example to breathing, or the necessity to choose the best treatment angle to spare as much as possible healthy tissues.

1.5.1 Spread Out Bragg Peak (SOBP)

As previously stated the BP extension is of the order of few millimeters while usually tumor volumes are of the order of some centimeters. Then it is necessary to overlap many BP using beams with different energies to cover the entire tumor region. The result is the so called Spread Out Bragg Peak (SOBP) and an example is shown in Figure 1.13.

In order to have a constant biological effect within the target volume, the planned treatment has also to take into account the RBE variation as a function of the penetration depth. As shown in Figure 1.13, hadron beams with different energies give different dose-depth distributions (black lines), each one with its RBE value. The sum of the contributions of traversing hadrons will led to the total dose deposition (red line), and so to the SOBP. Two main strategies are applied in PT facilities in order to homogeneously distribute the dose on the tumor area [13]: passive beam modulation and active beam scanning. The first technique generates the SOBP using passive field shaping elements, as schematically shown in Figure 1.14. The principal constituent elements are: the scattering system broadening the beam, the rangemodulator for energy modulation and the range-shifter to spread out the Bragg peak and shift it over the tumor volume, respectively. Then the narrow monoenergetic beam delivered by the accelerator is broadened by a scattering system followed by a range-modulator to modulate the beam

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Figure 1.13: Percentage dose distribution as a function of depth in water for a proton beam. The red line shows the SOBP as the result of the sum of different dose distributions (black lines) [41].

energy, producing different Bragg peaks in different positions; the collimator shields healthy tissues and the compensator adapts the SOBP to the distal contour of the tumor.

The limitations of this passive technique is the non negligible dose deliv-ered to normal tissues in the proximal part of the tumor due to the secondary particles that are produced in the interaction of the beam with the scattering system.

The active beam scanning technique, instead, splits the treatment volume in several iso-energetic slices, each one divided in an elementary volumes (voxels) grid. A scheme of this approach is outlined in Figure 1.15. After a slice selection, each voxel is irradiated by scanning the same energy beam using deflecting magnets, giving a typical zigzag scan path. After an entire slice has received its planned dose, the beam extraction is interrupted, the beam energy is changed and the irradiation of another slice can start. The main advantages of the active beam scanning are that no patient specific hardware for the treatment is needed, except for the immobilization, and the possibility to vary the deposited dose on each voxel, in order to create more specific planned treatments, theoretically permitting a specific irradiation also for irregular volumes. Moreover, the beam attenuation, scattering and fragmentation are reduced.

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Figure 1.14: Scheme of a fully passive modulation delivery system [13].

On the other hand, this technique requires more demanding control and safety systems with high accelerator performances on energy stability and beam exit position reproducibility.

For a long time the only two facilities that pioneered the IMPT approach were the Paul Scherrer Institute (PSI) in Switzerland and the GSI Helmholtz Centre for Heavy Ion Research (GSI) in Germany.

1.5.2 Gantries

A promising technique for the beam delivery proposes to improve the treat-ment quality introducing a rotational support, i.e. the gantry, in order to optimize the angles for the beam direction. Such a technique is commonly used in RT and allows for an almost free choice of the beam direction. On the other hand, such a freedom is not available in PT.

Considering protons, the high magnetic rigidity of the beam implies a bending radius of the order of 1 m. For carbon ions the situation is even worse (this is the reason why carbon ion facilities need larger accelerators). For example, for a 380 M eV /u carbon ion beam, having a range in water of 25 cm, the magnetic rigidity is ∼ 3 times the one of a proton beam with the same range. Moreover, a high precision on the rotating movement

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Figure 1.15: Left: GSI active scanning system working principle. The target volume is irradiated by moving a pencil beam with fast scanning magnets and the beam parameters are supplied synchronously to each pulse by a control system. Right: the entire tumor is divided in several iso-energetic slices (the slice being irradiated is expanded). During the irradiation each voxel (white dot) receives the planned dose; the green dots represent the pencil beam arrival points [13].

Figure 1.16: Left: 3D drawing of the HIT gantry treatment room [42]. Right: Gantry view from the accelerator room.

is required. Therefore, in hadrontherapy the need of the most preferable depth-dose profile in treating tumor volumes asked for a very challenging and expensive work of engineering. The first rotating isocentric gantry for carbon ions was built at the HIT center in Heidelberg (Germany). It is a gigantic

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steel construction, 25 m long, with a diameter of 13 m. The HIT gantry is in operation for both protons and carbon ions since 2012 (Figure 1.16).

1.5.3 Irradiation of moving organs

So far the organ irradiation with scanned beams has been performed only in stationary mode, where the patient is kept still by external supports. In this situation the target can be assumed to be fixed and the uncertainties due to patient motion (e.g. by breathing) are negligible.

The patient immobilization, with masks or special frames, is necessary in order to take advantage of the highly conformal dose deposition of PT. However, if the tumor is placed in an abdominal organ, breathing motion is absolutely not negligible. This could lead to variations in the path range of the beam in tissues, shifting the BP position with a high impact on the treatment quality, according to Figure 1.17 and Figure 1.18.

The breathing motion started to be considered as an important issue only recently in traditional radiation therapy, due to the low impact on photons, but for light ions therapy, the irradiation of moving targets is a very active re-search field. As can be observed in Figure 1.18, the breathing induced motion is almost negligible for photons (black and blue lines are almost overlapped), but it has a huge impact at the end of the range for carbon ions: considering the BP of the no-motion case (black line) over the tumor volume (in between the second two vertical red lines), a large amount of dose will be deposited outside the tumor volume

Some suggested options to take into account the patient motion are listed below:

1. Irradiation of planning target volume: the moving target is fully covered at any time. The limit of this technique is on the overall dose that can be given to the target volume, in order to minimize the dose released on healthy tissues.

2. Rescanning: if target motion and beam motion are considered uncorre-lated, the variance of the average dose decreases with a factor of 1/√N, with N the scan repetition times. Since the dose per scan has to be low-ered, the disadvantage of this technique is on the irradiation time which is extended. Moreover, the beam monitoring ionization chambers are not sensitive to low currents.

3. Gating: this system involves the radiation management within a par-ticular portion of the patients breathing cycle, referred to as the gate.

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Figure 1.17: Calculated dose deposition for a lung tumor (a) without and (b) with motion, leading to severe over or under dosage in the target volume. (c) and (d) show the carbon ions range modification during the breathing phase of inhaling and exhaling, respectively. Different iso-range curves are shown [42].

The position and width of the gate within a respiratory cycle are deter-mined by monitoring the patients respiratory motion, usually applied in relation to a flat minimum region at the end of the exhale phase. If the irradiation is limited to the gate, uncertainties due to target mo-tion can be reduced to less than 10% of the free breathing situamo-tion. The disadvantage of the gating system is the extended treatment time in order to ensure the delivered dose to be constant over the tumor volume.

4. Tracking: a synchronous three dimensional online motion compensation is required in order to allow the beam to follow the target movements at any time, leading, theoretically, to the same static case results. This tracking process presents some critical issues in technological develop-ment as the dynamic treatdevelop-ment planning and the beam delivery system

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1.6. PARTICLE THERAPY: STATUS AND PROSPECTS 25

Figure 1.18: The breathing induced motion produces a shift on the BP position for the same beam traveling thought different beam paths. The black line is relative to the no-motion case, while the blue line shows the absorbed dose in the motion case, the two vertical lines represent the tumor volume [42].

should be able to permit a lateral tracking and a fast range adaptation.

1.6 Particle Therapy: status and prospects

For both photon and charged particle therapy, the first step of the treat-ment configuration regards a pre-simulation of the therapy treattreat-ment: the description of the ’environment’ of the tumor (patient body) and the exact localization of the tumor are performed by using 3-D computed tomogra-phy (CT) or magnetic resonance (MRI) in order to create a 3-D image of the treatment area. The medical personnel decides the zones to be irradiated and the OAR that have to be spared as well as the treatment angles of the beam entrance inside the patient by means of a rotating couch or a gantry if this is available (Section 1.5.2). Exploiting both the radiotherapist prescription and the informations from the imaging, a complex software called Treatment Planning System (TPS) computes the treatment plan. The bidimensional iso-dose curves are then outlined.

In photon therapy, the patient positioning is verified before and during the treatment with the so called radiotherapy localization and radiotherapy verification methods, respectively. These techniques use proper photographic films in order to obtain the patients image: during the localization the

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im-be somehow overcome by fractionating the total released dose: in this case, the human cells are able to repair the DNA damages caused by radiations exposition. For the solid epithelial tumor, the provided total dose of about 60-70 Gy can be delivered in 30-35 daily fractions of 2 Gy each [42].

Taking into account that, especially for PT techniques, the dose released to tissues surrounding the tumor volume is anyway lower than the dose re-leased over the cancer area, where the highest destructive power of radiations is concentrated, the rate of the DNA repairs is thus higher for healthy cells than for cancer cells. Moreover the DNA repair is less effective in cancer cells than in normal cells.

The hypofractionation, a treatment schedule in which the total dose of radiation is divided into large doses, is today considered as a viable option in photon and charged particle therapy: the possibility to reduce the total number of treatment sessions from ∼ 30 to 4-5 sessions implies a clear advan-tage for the patient quality of life and a more effective use of the treatment centers [48].

Concerning the technological challenges required by the PT, this new and very conformal irradiation technique asks for sophisticated treatment plans, as well as for techniques able to keep under control during the treatment the beam position and dose delivered, the absorbed dose by tissues and finally the patient positioning.

In spite of the intrinsic complexity of the PT treatment, a clear example of the advantage with respect to the modern and effective conventional RT (IMRT) is given in Figure 1.19 where the comparison of a treatment plan for photon therapy and particle therapy is shown. The tumor volume sited in the skull base is irradiated with two fields of carbon ions (left) and nine fields with IMRT (right). As can be observed, despite for both therapies the maximum dose is localized over the tumor area, the delivered dose to the surrounding tissues is much more extended in photon therapy than in particle therapy.

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Figure 1.19: Treatment plans comparison for a target volume sited in the skull base irradiated with two fields with carbon ions (left) and nine fields with IMRT (right) [43].

1.6.1 Protons and

12

C ions

As explained in Appendix A, light ions can undergo nuclear fragmentation when interacting with the target nuclei (fragmentation in air has a much smaller impact). Low Z fragments are then produced, leading, from a therapy treatment point of view, to several drawbacks: fragments have longer range, different directions and different RBE with respect to primary particles.

The result of the nuclear fragmentation is visible in the Bragg peak tail, shown in Figure 1.20 for carbon ion therapy. On the other hand, protons nuclear fragmentation is a negligible effect and the relative depth-dose curves show an almost sharp fall off.

Another physical aspect that has to be taken into account when com-paring protons and carbon ions is the multiple scattering. As described in Section 1.2.3, the multiple scattering deflection angle is inversely proportional to the incident particle mass. Therefore, carbon ions suffer much less lateral beam spread than protons (Figure 1.5 and Figure 1.6). Figure 1.21 shows the comparison between a treatment plan with carbon ions (left) and pro-tons (right). A lower beam spread expresses a more localized dose deposition and hence a particle therapy with carbon ions will follow more precisely the tumor volume conformation.

Another advantage of carbon ions with respect to protons is the high RBE. Carbon ions are characterized by so dense ionizing tracks, that the probability of double ionizations on both DNA strands is much higher when

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Figure 1.20: Bragg curve as a function of the depth in water for a 400 M eV /u carbon ion beam. The experimental data (dots) and the FLUKA calculation (solid line) are shown. The dose contribution from primary12_C_{ions (red line)}

and secondary fragments (blue line) is also reported [44].

Figure 1.21: Treatment planning comparison for carbon ions (left) and protons (right). Carbon ions shows a more accurate tumor conformation dose depo-sition and normal tissue sparing due to lower multiple scattering effect with respect protons [44].

compared to sparsely ionizing proton tracks, making light ions more effective in tumor cells killing [46]. Even the OER is enhanced for light ions than for protons, reaching a value of ∼ 1 when the radiation is close to the BP region. Figure 1.22 shows the RBE as a function of the LET for different kind of

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particles: carbon ions appear to have a RBE behaviour well suited for tumor treatment, with low RBE at high energy (in the healthy tissues) and high RBE when particles stops inside the tumor region (Section 1.4.1).

Figure 1.22: Relative biological effectiveness as a function of the linear energy transfer [13].

However, when a comparison between proton and carbon therapy is made, the cost and the equipment size must be taken into account: the major ad-vantage of proton therapy is the lower cost proton facility with respect to a carbon ion accelerator. The magnetic rigidity, defined as R = p/q, with p the particle momentum and q its charge, is twice larger for carbon ions than for protons (being the carbon mass twelve times the proton mass and the carbon ion charge six times the proton one), as mentioned in Section 1.5.2. This means that carbon ion accelerators need a larger radius than proton accelerators. Therefore, to reach typical hadron therapy treatment energies, cyclotrons (normal or super conducting) that can be easily fit into a hospital environment are usually used for proton therapy. Carbon ions need much bigger (and so expensive) facilities such as synchrotrons (with a diameter of tens of meters).

Nowadays, other light ions are under study for future PT applications, such as helium and oxygen ions:4_He_{beams suffer less the multiple scattering} effect with respect to proton beams and have a RBE value between protons and carbon ions RBE;16_O_{ions have a greater RBE with respect to}12_C_{due to}

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As previously stated, both a beam delivery problem or even a mismatch between the patient physiology and the CT time with respect to the treat-ment time can easily take to overdosage of healthy tissues and underdosage of the tumor region. Considering that in PT all the beam is absorbed in the patient body, techniques based on secondary particles produced in the in-teraction of the charged particle beam with tissues should be developed and operated in a clinical environment.

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Chapter 2 FOOT Experiment

Nowadays there is a lack of experimental measurements of the nuclear re-action cross sections for the fragments produced by protons with energies between 60 M eV and 250 M eV , which are the typical energies adopted in proton hadrontherapy. The available data for the projectile fragmentation in the heavy ion treatment framework are derived only by the GANIL ex-periment (with measurements of carbon ion at 95 M eV /u and 50 M eV /u [16]). There is not available measurements regarding carbon and oxygen ion at 300-350 M eV /u.

The FOOT experiment aims at measuring cross sections useful fragmen-tation to improve Treatment Planning System (TPS) in charged particle therapy. The project has two main goals:

1. the mesurement of target fragmentation in the collisions of protons against, mainly C and O nuclei (to be performed in the inverse kine-matic approach) for proton energies in the range 150-250 M eV , 2. the measurement of projectile fragmentation of C and O nuclei at

200-300 M eV /u against tissue-equivalent targets.

Through FOOT data, an interface will be implemented between the clin-ical TPS and the one developed in the research field, thus enabling the use of variable RBE models for the recalculation of clinical plans. Software im-provement for TPS will allow a significant reduction of dose release to healthy surrounding organs. The patient will eventually have access to more effective treatment, with fewer post-treatment problems.

This chapter describes strategies used for fragmentation measures, the experimental setup of the experiment and the requirements for effecting mea-surements of cross sections.

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Fragment E (M eV ) LET (keV /µm) Range (µm) 15_O _1.0 ₉₈₃ _2.3 15_N _1.0 ₉₂₅ _2.5 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 8_Be _6.4 ₄₀₀ _15.7 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

Thus, given a fragment produced by a proton projectile somewhere in the target, the ion can cross and leave the target only if it has been produced at a distance less than few micrometers from the exit surface of the target material. Otherwise the fragment deposits all its energy locally and can not be detected. Therefore a thick target must be excluded. On the other hand, also a very thin target provides a great amount of issues: first at all it is technically difficult to create and handle item with such a small thickness (µm). Moreover, the rate of fragmentation is extremely reduced, so it becomes excessively onerous to achieve a significant amount of data.

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2.1. TARGET CHOICE 33

the end of the chapter) typically implies the management of a pure gaseous hydrogen target. However this can not be achieved in clinical centres. To overcome the difficulties of using a liquid H target, an enriched target with hydrogen can be used, for example polyethylene (C2H4) and a graphite target (C), and then get the fragmentation cross section of hydrogen can be obtain subtracting the impact sections of the two targets:

σ(H) = σ(C2H4) − 2 · σ(C)

4 (2.1)

This approach was validated in an experiment conducted at Ganil [16] (Figure 2.1). In fact, polyethylene and graphite targets are easy to produce and manage. Using these targets, it is also possible to measure the cross section for carbon targets at therapeutic energy of interest (60-250 M eV for protons).

Figure 2.1: Combination of the carbon and CH2 angular distribution to

de-termine the hydrogen angular distribution for alpha fragments. The angular distribution for the hydrogen target is the difference between the CH2 and

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1. the emission angle of the (heavy) fragments;

2. the angular separation between two fragments emitted in the same events.

The first item determines the angular acceptance while the second rules the granularity of the detector. An example of the Monte Carlo prediction calculation is given in Figure 2.2 where the angular distribution of different fragments produced by a 200 M eV /u16_O _{beam impinging on a C}

2H4 target, and their angular separation are shown.

Figure 2.2: MC calculation of angle separation between different fragments pro-duced by a 200 M eV /u 16_O _{beam impinging on a C}

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2.2. EXPERIMENTAL SETUP 35

As one can notice, all the particles with Z > 2 are produced in the forward direction with θ < 10◦_{, instead helium ions and protons can be produced at} θ 10◦_{. A similar distribution would be obtained for carbon incident beam} with the same energy. Due to the different physical effects, including the angular distributions, of heavy (Z > 2) and light (Z ≤ 2) particles, it has been decided to adopt two different experimental setups focus for the two species of particles.

2.2.1 Detection of heavy ion particles

The first experimental setup is dedicated to fragments with Z > 2, whose cross section data are missing in the literature. The hypothesized experiment arrangement from left to right is shown in Figure 2.3:

Figure 2.3: Schematic view of the FOOT apparatus [17].

Start Counter The Start Counter (SC) has been already used in the FIRST experiment [18], and it is made by a 250 µm thick scintillator disk, a EJ-228 fast scintillator foil, with a radius of 26 mm, sufficient to cover the typical beam transverse size. As shown in Figure 2.4, the light produced in the scintillator is collected radially by 160 optical fibers grouped in four bundles and readout by fast PMT.

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Figure 2.4: Details of the SC: the thin scintillator foil and the optical fibers grouped in four different arms [18].

The thickness of the scintillator was minimized to reduce the pre-target particles interaction probability, less than 5% with respect to the on-target one, assuming a 2 mm thick graphite target. The SC, placed 20-30 cm up-stream of the target, provides the trigger signal to the whole experiment and the measurement of incoming ion flux to be used for the cross section measurement. The SC provides the reference time for all the other detectors and allows the TOF measurement in combination with the ∆E scintillator detector.

Beam Monitor The Beam Monitor (BM) is a drift chamber designed for the reconstruction of charged particle trajectories. This detector gives the impact point of the beam on the target. Moreover, BM can provide important information on possible pre-target fragmentation of the projectile [19]. In fact, if a fragmentation event occurs before the target, the BM detects more than one track, it provides two orthogonal profiles of the beam by mean of six planes of three cells (see Figure 2.5), for a total of 36 sense wires horizontally and vertically alternated for each view. In order to resolve the left/right ambiguity, the consecutive layers of each beam view are staggered by half a cell. Each cell has a rectangular shape with dimensions of 10 × 16 mm2 _with the long side orthogonal to the beam (Figure 2.6);

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Figure 2.5: Layout of the Beam Monitor drift chamber [19].

Figure 2.6: BM cell layout [19].

Target Polyethylene and graphite targets are used. The thickness of the target is chosen to be about 2 mm, avoiding both the fragment trapping effect and the excessive drop of the nuclear interaction rate;

Silicon Pixel trackers A telescope of pixel tracks provides the vertex re-construction and the initial tracking of the produced fragments, following the experience gained in the FIRST experiment [30]. Between the two magnets, the fragment direction is measured by two additional layers of silicon pixel trackers. The stack of sensors is placed as shown schematically in Figure 2.7: this arrangement guarantees an acceptance at the level of about ±40◦ _{for the}

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Figure 2.7: Target and vertex tracker geometrical scheme [20].

Magnets Two permanent magnets to supply the necessary curvature for the charged fragments in order to perform the momentum measurements. The cylindrical geometry provides a transverse magnetic field with a maximum of 0.8 T at the centre, as displayed in Figure 2.8;

Silicon Trip Detector The Microstrip Silicon Detector (MSD) tracking, of fragments monitors, the fragments of the magnetic volumes, that is essen-tial to measure the time and to match traces rebuilt with the shots of the TOF scintillator and the calorimeter;

TOF dE/dx detector The TOF dE/dx detector is composed by two lay-ers of 22 plastic scintillator bars each, coupled at both ends to 3 × 3 mm silicon photomultipliers (SiPM) via optical glue. Each scintillator bar is 40 cm in length, so to cover all the angle in which fragmentation product are scat-tered. Plastic scintillator have been choosen over inhorganic ones beacause of their faster rise time, while SiPM detectors have been preferred over Photo Multiplier Tubes (PMTs) due to lower voltage requirements. A picture of

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Figure 2.8: 3D model of the magnet [21].

a single bar is shown in Figure 2.9. The two layers are arranged orthogo-nally to identify the two-dimensional interaction position of the particle in the detector. (Figure 2.10). A prototype of this detector will be explained in Chapter 3.

Calorimeter The FOOT calorimeter is the most downstream detector. It is designed to measure the energy of projectile fragments produced in the target. Since FOOT will work at a relatively low beam intensity, the ideal material for a calorimeter is a dense crystal with high light yield, without strict requirements for the response speed. The calorimeter is composed by 360 elements of BGO crystals (Bi4Ge3O12) with a density of 7.13 g/cm3 and acceptance area of 2 × 2 cm are arranged to assemble a cylindrical detector with 20 cm radius.

2.2.2 Detection of light charged particles

To characterize the production of low Z fragments, an emulsion spectrome-ter has been included in the FOOT setup as described in Section 2.2.1. In Figure 2.11 the arrangement of the Emulsion Spectrometer (ES) inside the

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Figure 2.9: Picture of the dE/dx detector prototype.

Figure 2.10: dE/dxTOF detector and BGO calorimeter [17].

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and the Beam Monitor.

Figure 2.11: Emulsion spectrometer setup inside the FOOT detector [17].

Among all tracking devices used in particle physics, nuclear emulsion particle detectors feature the highest spatial resolution (sub-micrometric) for tracking ionizing particles. Emulsion chambers integrate target and detector in a very compact setup and provide a very accurate reconstruction of the interactions occurring inside the target. Moreover, no power supply or any readout electronics is required and this helps to keep the emulsion setup compact and without angular limitations.

In the OPERA experiment the emulsion technique has been already ex-ploited to study the fragmentation of carbon ions in polycarbonate (Lexan) [22]. In this experiment, a detector made of nuclear emulsion films alternated to lexan plates (to simulate the human tissue) has been exposed to a 400 M eV /u 12_C _{beam to identify the secondary nuclei produced by fragmentation [23].} By analyzing the grain density along the particle track, the fragment charge could be assessed with a very high efficiency (above 99%). The discrimina-tion of Hydrogen, Helium, Lithium, Beryllium, Boron and Carbon can be achieved at least at two standard deviations, depending on the track length of the detected particles. In a second step of the investigation, total charge-changing cross section was also obtained by analyzing the carbon interaction

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Figure 2.12: Scheme of the emulsion spectrometer (ES) composition for the FOOT experiment [17].

1. Vertexing and tracking detector (∼ 4 cm), composed by several el-ementary cells made of Carbon or C2H4 layers (1 mm) alternated by emulsion films (300 µm). The beam will interact with the cells and orig-inate secondary fragments. The detector emulsion structure will track the fragments and reconstruct the interaction vertex position with a micrometric resolution. The thickness of the layers is defined by the interaction length, in order to obtain a sufficiently high number of in-teractions fully contained in the detector.

2. Ionization detector (∼ 1 cm), composed by emulsion films only, with the aim of identifying the atomic numbers of low charged fragments (proton, helium and lithium).

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2.3. MEASUREMENTS AND REQUIREMENTS 43

3. The momentum measurement (∼ 4 cm, dedicated to the momentum measurements), is made of emulsion films (300 µm thick) interleaved with 1 mm thick lead plates as passive material. The momentum will be evaluated with the range technique: measuring the length of the whole particle track, its kinetic energy will be estimated on the basis of the correlation between range and momentum, using data supplied by NIST [25]. The section length will be set according to the incident beam energy; the number of lead plates will range between 10 and 50.

2.3 Measurements and requirements

To introduce a new proton RBE model, which includes the effects of nu-clear interactions, the FOOT experiment has to accomplish measurements of fragment energy spectrum (dσ/dE) with an energy resolution of the order of ∼ 1 M eV /u and measurements of the heavy fragment (Z > 2) produc-tion cross secproduc-tion, with a maximum uncertainty of ∼ 5%. In order to meet the aforementioned uncertainty levels, it is necessary to identify the nuclear charge number Z with a precision of ∼ 2%-3% and the nuclear mass number A within the ∼ 5%. These requirements regarding the knowledge of the frag-mented particles created by incident protons can be met once the measures of momentum, energy and Time of Flight have a resolution of : σp/p ∼ 5%, σEk/Ek of ∼ 2% and σt of ∼ 100 ps respectively.

2.3.1 Measurements of Time of Flight T OF

As presented in Section 2.2, the TOF of the particles is computed from the time measured from the scintillator read in coincidence with the trigger-time supplied by the start counter. Thought the measurement of the TOF is possible to calculate the β factor of the incident particle with Equation 2.2,

β = 1 c ·

L

T OF (2.2)

where L is the distance between the start counter and the TOF detector. This measurement of β is very important for calculating the charge and the mass of the fragments. TOF measurements and energy release in the scintillator (dE/dx) will be treated in Chapter 3.

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Z is the charge of the fragment and β is the velocity of fragment calculate with Equation 2.2. The charge of the fragment can be calculated measuring the energy released in the scintillator and by calculating β from the TOF measurements, inverting Equation 2.3 is derived the charge of fragment.

2.3.3 Measurements of momentum p

The momentum measurement is performed by the tracking detectors (Front Silicon Pixel Traker, Rear Silicon Pixel Traker, MSD) placed beyond the target combined with the magnetic field (B = 0.8 T ). The three tracking detectors are placed in different spots compared to permanent magnets, in order to estimate the particle position before (Silicon Pixel Trackers), in the middle (Silicon Pixel Trackers) and after (Silicon Strip Detectors) permanent magnets. In this way it should be possible to determine the track of a particle. The permanent magnets deviate the ion trajectories according to their impulse to charge ratio (p/Z). The curvature radius, derived from the Lorenz force, is in fact

R= pB

Ze (2.4)

where e is the electron charge, B is the modulus of the applied mag-netic field, R is the curvature radius calculated by knowing the trajectory of particles in the magnetic field and Z is the charge of particle calculated as explained in Section 2.3.2.

2.3.4 Measurements of kinetic energy E

k

The particle energy is measured by the calorimeter at the end of the beam line. By measuring the energy released into the BGO, it is possible to deter-mine the kinetic energy Ek of the fragment.

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2.3. MEASUREMENTS AND REQUIREMENTS 45

2.3.5 Mass identification A

The fragment mass m and the mass number A can be evaluated by combining two of three following quantities: particle momentum, kinetic energy and TOF.

1. Using TOF and moment particle p

p= mγβ ⇒ p= mβ

p1 − β2 ⇒ m=

p ·p1 − β2

β (2.5)

where the γ definition is used (Lorentz factor) γ = _√1

1−β2. Dividing

the mass m for atomic mass unit u, the mass number A is obtained

A= m u = 1 u · p ·p1 − β2 β (2.6)

where β is calculated with Equation 2.2. 2. Using TOF and kinetic energy Ek

p2 = E2 tot− m

2 _⇒ _m2_γ2_β2 _{= (E}

k+ m)2− m2 (2.7) where p = mγβ and Etot = (Ek+ m).

m2γ2β2 = E2 k+ 2mEk+ m2− m2 m2γ2β2− 2mEk+ E_k2 γ2_β2 = E 2 k+ E_k2 γ2_β2 mγβ − Ek γβ 2 = E2 k 1 + 1 γ2_β2 mγβ = Ek s 1 + 1 γ2_β2 +Ek γβ m= Ek γβ 1 γβ p γ2_β2_{+ 1} + 1 m= Ek γ2_β2 1 +p1 + γ2_β2

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E_tot2 = p2_+m2 _⇒ _(E k+m)2 = p2+m2 ⇒ m= p2_{− E}2 k 2Ek (2.9)

where Etot definition is used: Etot = (Ek+ m). Dividing the mass m for atomic mass unit u, the mass number A is obtained

A= m u = 1 u p2 − E2 k 2Ek (2.10)

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Chapter 3 TOF dE/dx prototype

As discussed in Section 2.2.1 it is important that the TOF dE/dx detector satisfies the reqirements of 100 ps time resolution and 2% energy resolution. In order to meet these requests, a TOF dE/dx prototype has been built. This device has been tested with proton beams at different energies (from 70 to 230 M eV ) at the Proton Therapy Centre (PTC) of the Trento Hospital (Trento, Italy) to evaluate its time and energy resolution.

3.1 Structure of prototype

The TOF dE/dx prototype is composed by:

• a plastic scintillator bar (EJ212, produced by Eljen Technology [49]), with dimensions 20 cm × 2 cm × 0.2 cm wrapped with teflon and cov-ered by a black vinyl. The specifications of the scintillator are reported in Table 3.1.

• 4 SiPMs photodetectors produced by AdvanSiD [50] of size 3 mm × 3 mm. Two SiPMs are set at each extremity of the scintillator bar so to reach a lateral coverage of the scintillator of about 30% (this means that about 70% of the photons producted inside the scintillator is not revealed). The SiPMs detectors of each couple are connected in series, so that their joint output signal accounts for all photons revealed by the two. The used SiPMs are of the Near UltraViolet (NUV) kind (Figure 3.2), with the features described in Table 3.2 (figures of merit in Appendix B).

• a layer of optical grease (Saint-Gobain BC-630) to couple the the scin-tillator bar to the SiPMs.

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Figure 3.1: Picture of TOF dE/dx prototype. Table 3.1: Properties of EJ212 scintillator [49].

Light yield 104 _photons/MeV Visible light attenuation length 250 cm

Rise time 0.9 ns Decay Time 2.4 ns

Density 1.023 g/cm3 Polymer base Polyvinyltoluene Refractive index 1.58

3.1.1 Data acquisition

The SiPM output is amplified and sent to a fast-digitizer, which can sample the signal at a maximum rate of 5.12 GSample/s with a dynamic range of 1 V , adjustable according to the polarity of the detector output signal. The data acquisition, called WaveDAQ, is based on the DRS Application Specific

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3.1. STRUCTURE OF PROTOTYPE 49

Figure 3.2: Picture of an AdvanSiD NUV SiPM. Table 3.2: Properties of the SiPM AdvanSiD NUV SiPM [50].

Effective active area 3 mm × 3 mm Number of cells 5520

Breakdown voltage ∼26 V Gain (at 5 Vover) 3.25 · 106

Dark count rate ∼900 kHz Crosstalk probability 22% Afterpulse probability <4 %

Integrated Circuit (ASIC) [51] developed at the Paul Scherrer Institute (PSI) and on the Mu to E Gamma (MEG) Data DAQ [52] designed in collaboration by PSI and Istituto Nazionale di Fisica Nucleare (INFN). Detector signals are connected to a custom board called Wave-DREAM Board (WDB) which provides 16 channels with variable gain amplification and flexible shaping through a programmable pole-zero cancellation (Figure 3.3).

Switchable gain amplifiers and programmable attenuators allow an over-all input gain from 0.5 to 100. Moreover, the WDB can also supply SiPMs thanks to an onboard power supply. The input signals are digitised by both the DRS and and ADC (80MHz - 12bit) whose stream is received and used by an FPGA to perform some online reconstruction which is eventually finalised by higher level trigger board connected by means of Gb serial links. Contri-butions to the time measurements come from the DRS chip time calibration

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Figure 3.3: WaveDREAM Board.

and the reference clock distribution jitter between the different digitisers. This has been measured to be ∼10 ps, well below the experimental require-ments. The baseline fluctuation has been measured to be from 1 mV to 5 mV depending on the gain.

An example of the SiPM signal coupled to the scintillator with the setup described in Section 3.1 with a sampling rate of 5 GSample/s with a VOV=5 V (see Appendix B) is shown in Figure 3.4-left and an example of PMT wave-form coupled to the scintillator with the same sampling rate is shown in Figure 3.4-left. Each signal is composed of 1024 points whose time width depend on the sampling rate selected. Table 3.3 shows how signal time width depends on the sampling rate used.

3.1.2 Experimental setup

The prototype described in Section 3.1 has been tested in the Proton Therapy Centre of the Trento with proton beams at different energies. This facility can provide beams of protons at different energies. In particular the TOF dE/dx prototype has been tested for energies ranging from 70 to 230 M eV . The beam line has been arranged in the following order (Figure 3.5):

1. TOF dE/dx detector,

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3.1. STRUCTURE OF PROTOTYPE 51

Figure 3.4: Example of a SiPM waveform (on the left) and an example of a PMT waveform (on the right).

Table 3.3: Signal width as a function of sampling rate.

Sampling Rate Signal width 5 GSample/s 200 ns 4 GSample/s 250 ns 3 GSample/s 333 ns 2 GSample/s 500 ns

3. STS2 : plastic scintillator coupled to a PMT,

As shown Figure 3.5, the two SIPMs placed at a negative x value will be identified as SIP M 1 while the two SIPMs placed at a positive x value will be identified as SIP M 2.

This experimental apparatus provides us with 4 different data acquisition channels: the TOF dE/dx right and left outputs, the STS1 and STS2 signals. The STS1 and STS2 detectors have been used as triggers for the TOF dE/dx measurements (sometimes only the STS1 has been exploited).

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Figure 3.5: TOF dE/dx detector position on the beam line.

3.2 Timing performances evaluation

The procedure for the identification of the timestamp measured by a given channel is the following (Figure 3.6):

1. Choose a threshold that is a percentage fraction of the maximum signal (Figure 3.6(1))

2. Consider two points before and two points after the threshold (Fig-ure 3.6(2))

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3.2. TIMING PERFORMANCES EVALUATION 53

3. Perform a linear fit (Figure 3.6(3))

4. Intersect fit with the threshold and find t[ch](th) where the th refers to the threshold value used and the pedex ch indicates the channel. (Figure 3.6(4))

This process is repeated with different threshold values, over all data sets provided by the 4 data acquirement channels for each event recorded.

By performing a 4 points linear fit it is avoided the risk of considering points belonging to the baseline (for low thresholds) and points after the signals peak (for high thresholds).

Figure 3.6: Timestamp identification for one event recorded by SIPM1 channel with threshold value 5%.

3.2.1 Timestamp threshold choice

To find the best threshold the occurancy of the following quantities has been plotted:

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tII(th) = µ(tST S1(th), tST S2(th)) =

tST S1(th) + tST S2(th)

2 (3.2)

iii. the signal of the STS1 (tST S1), that is

tIII(th) = tST S1(th) (3.3)

By this procedure, for each threshold value, 3 histograms with approximately a bell-like shape have been obtained. As the distribution of optical photon arrival times on the SiPM is a gaussian, each histogram has been fitted with a function of the type:

y= a · e(x−b)22c2 (3.4)

where a is a costant, b is the mean and c is the standard deviation. In this way, for each threshold, the following fitted parameter values are obtained: aI(th), bI(th), cI(th), aII(th), bII(th), cII(th) and aIII(th), bIII(th), cIII(th). To obtain the optimal threshold value, a scan in the range of 5% and 95% (with 5% step) has been performed and the standard deviation obtained in each distribution as been evaluated.

Figure 3.7 shows the values as a function of the studied thresholds. As can be seen, the threshold values that minimize standard deviation are:

i. 5% for the two signals of the TOF dE/dx detector ii. 30% for the two signals of the STSs

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3.2. TIMING PERFORMANCES EVALUATION 55

Figure 3.7: Standard deviation of the time histogram as a function of threshold.

iii. 30% for the signal of the STS1

All these optimal thresholds values, have been obtained from data col-lected by setting the beam energy at 100 M eV , the beam position at centre of the bar, the SiPM overvoltage at 5 V and sampling rate at 5 GSample/s. It can be said with enough confidence that the optimized threshold values do not change significantly under a different settings of the aforementioned parameters because the shape of the plot in Figure 3.7 displays a particulary low inclinacy on the both sides of the minimum. So, the threshold values cal-culated above have been used even for those measurements that have been performed under different settings of the beam energy, beam position, SiPM overvoltage and sampling rate.

Study of the Time-Of-Flight detector for nuclear fragmentation experiment FOOT in particle terapy

Universit`

a degli Studi di Pisa

Study of the Time-Of-Flight detector

for the nuclear fragmentation

experiment FOOT in particle therapy

Contents

Introduction

1.1

History of hadronterapy

1.2.1

Linear Energy Transfer (LET)

1.2.2

Energy Deposition

1.2.3

Lateral beam spread

1.4.1

Relative Biological Effectiveness (RBE)

1.4.2

Oxygen Enhancement Ratio (OER)

1.5

Beam Delivery Techniques

1.5.1

Spread Out Bragg Peak (SOBP)

1.5.2

Gantries

1.5.3

Irradiation of moving organs

1.6

Particle Therapy: status and prospects

1.6.1

Protons and

C ions

Chapter 2

FOOT Experiment

2.2.1

Detection of heavy ion particles

2.2.2

Detection of light charged particles

2.3

Measurements and requirements

2.3.1

Measurements of Time of Flight T OF

2.3.3

Measurements of momentum p

2.3.4

Measurements of kinetic energy E

2.3.5

Mass identification A

Chapter 3

TOF dE/dx prototype

3.1

Structure of prototype

3.1.1

Data acquisition

3.1.2

Experimental setup

3.2

Timing performances evaluation

3.2.1

Timestamp threshold choice