Effects of Radiation damage on a scintillating fibre based ion Beam Profile Monitor

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Dipartimento di Fisica

Corso di Laurea Magistrale in Fisica

T

ESI DI

L

AUREA

M

AGISTRALE IN

F

ISICA

Effects of Radiation damage on a

scintillating fibre based ion Beam Profile

Monitor

Candidata:

Giulia MEO

Relatore:

Prof.essa Stephanie

H

ANSMANN

-M

ENZEMER

Relatore interno:

Prof. Giovanni P

UNZI

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Introduction

Plastic scintillating fibres have many uses in high energy physics. They can be used for the construction of tracking detectors, since they produce optical photons when a charged particle deposits energy in the scintillating material and they can be used to transport the optical photons to a read-out system. Moreover, they have many advantages: the spatial granularity is propor-tional to the fibre diameter, the scintillation decay time is typically on the order of a few nanoseconds and the deadtime is shorter than in other track-ing systems (as ionization chambers or multi-wire proportional chambers). In this thesis a prototype of beam profile monitor made of scintillating fibres is presented. All the measurements presented are conducted at the Heidelberg Ion Therapy Center (HIT), a radiation treatment facility located in the Univer-sity Clinic in Heidelberg (Germany). The development of a new beam profile monitor for the HIT could be an optimal replacement of the current system (made of ionization chambers and multi-wire proportional chambers) at the end of its lifetime. The facility provides protons and heavy ions in order to treat human cancers. In order to apply the exact dose in a tumor, the inten-sity, position and width of the beam must be monitored. Hence, the beam profile monitor should provide online measurements of the position, width and intensity of the beam. In particular, it has to be able to reconstruct the po-sition of the beam within a resolution less than 0.2 mm and the beam width with a resolution less than 0.4 mm.

The detector under study is made of four scintillating fibre mats. The mats are produced with the method as the LHCb Upgrade Scintillating Fibre Tracker, though with fewer layers and cut to shorter lenghts. Each mat is 13 × 40 cm2 and it is formed of two layers of fibres bonded with titanium dioxide. The diameter of a single fibre is 250 µm and the pitch is 275 µm between each fibre. The read-out system is made of four electronic boards with two 64-channel photodiode arrays for each board. Each channel has 0.8 mm of channel pitch. The boards are located at the end of each fibres mat.

The problem studied in this scintillating detector is related to the radia-tion damage. Indeed, it can degrade its light transmission. When a plastic scintillator is exposed to a certain dose of radiation, it suffers a damage, vis-ible as a reduction of the transmission light. The radiation hardness of two different types of scintillating fibre are investigated: SCSF-78 (blue fibres) and SCSF-3HF (green fibres), in order to use the one with more radiation hard-ness in this experiment. The damage in the scintillating fibre can cause an imprecise reconstruction of the beam profile for the tracking system (as the one presented), since a bias in the reconstruction of the beam position and beam width is introduced. In this thesis, the effects of the radiation dam-age in a beam profile monitor based on scintillating fibre are investigated. In

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particular, a special method to estimate and to quantify the damage in the scintillating fibre mats is presented. A toy model simulation is also created in order to further understand the effects of the damage in the scintillating fi-bres mat and to estimate the magnitude of the bias introduced by it where the experimental data is not available. A calibration method in order to remove the bias introduced by the radiation damage and other defects is also pre-sented and a comparison of the data before and after recalibration is made, in order to estimate the effect of the damage before and after data correction on the beam position and beam width.

Regarding the general structure of this thesis, the first chapter is dedicated to the description of the main processes of interaction of heavy ions and pro-tons in the matter, in order to give an overview of the interaction process of that particles when they pass a scintillating material. The second chapter presents a description of the scintillating fibre used in this experiment and the principles behind the scintillation process. A description of the working principle of the photodiode array is also presented. The third chapter will give a general introduction to the radiation damage and the causes behind it; hence why it is formed in plastic scintillators and the possible solutions to reduce it. A description of the detector and all its components is presented in the Chapter 4. Chapter 5 presents the radiation damage analysis and the results from the analysis. Chapter 6 is dedicated to the conclusion and the outlooks in order to improve the detector performances.

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Chapter 1 Background Information

Since in this thesis a proton beam that passes through different types of ma-terial is described, it is important to illustrate the predominant mechanisms of interactions of heavy ions and protons passing through a material. Some physical aspects and a general description of the facility used for the mea-surements is also presented.

1.1 Interactions of heavy particles in matter

Protons or other ions can interact with matter through several mechanisms: Coulomb interactions of ions with atomic electrons, Coulombic interactions of ions with the atomic nucleus plus other nuclear interactions. Protons or other heavy charged ions can lose kinetic energy via inelastic Coulomb in-teractions with the electrons in the material and since their mass is much grater than electrons they travel nearly in a straight line. However, a proton that passes near an atomic nucleus undergoes a repulsive Coulombic inter-action, deflecting the proton from its original straight-line trajectory. Also a non-elastic nuclear reaction between proton and the atomic nucleus could be possible and in this case the projectile proton entering the nucleus pro-duces secondary particles or nuclear fragments. Finally, Bremsstrahlung is theoretically possible, but at therapeutic proton beam energies this effect is negligible [1].

1.1.1 Inelastic Coulomb scattering

Inelastic scattering of protons and heavy ions with the electrons in the matter is one of the main sources of energy loss. The energy loss rate, defined by dE and dx, where E is the mean energy loss and x is the distance in which the particle loses energy, is well described by the Bethe-Bloch formula 1.1 (1930) [1]. S= − * dE dx + =Kz2_pρZt A 1 β2 " 1 2ln 2mec2β2γ2Tmax I2 −β 2₋δ 2− C Z # (1.1)

In this formula K=4πNAr2emec2is a constant with NAthe Avogadro’s num-ber, re the classical electron radius, me mass of an electron, c the speed of

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light; zpis the charge of the projectile; Ztis the atomic number of the absorb-ing material; A is atomic weight of the absorbabsorb-ing material; β = v/c, where v is the velocity of the projectile; γ = (1−β2)−1/2; Tmax is the maximum

kinetic energy which can be imparted to a free electron in a single collision; I is the mean excitation potential of the absorbing material; δ is the density corrections, a predominant term at higher energies and it derives from the shielding of remote electrons by close electrons; C is the shell correction item and this term is predominant only for low energies, where the particle veloc-ity is near the velocveloc-ity of the atomic electrons. The last two terms in the in the Bethe–Bloch equation involve relativistic theory and quantum mechanics and need to be considered when very high or very low proton energies are used in calculations.

FIGURE1.1: Mass stopping power(−dE_dx)for positive muon in copper in function of βγ= p/Mc (picture modified from [2]).

The stopping power described by the Bethe-Bloch equation 1.1 is shown in Figure 1.1 for positive muons in copper and in the Figure 1.2 for heavy ions [3]. Figure 1.1 shows the energy loss per traversed material divided by the density of the material versus βγ. In the case of radiotherapy, a range of tissue up to 30 cm is desired and this corresponds to a specific energy for par-ticle type (more details in Table 1.1) with a velocity of β ≡ v_c ≈0.7. At these energies and velocities particles are below the minimum (MIP = minimum ionizing pint) of βγ≈ 4 and, hence, the energy-loss rate dE/dx is dominated by inelastic collisions with the target electrons (electronic stopping). The de-pendence 1/β2 leads to the maximum energy loss when the particles slow down and the maximum deposit of energy is in a small region before that the particles are completely stopped. This region is the so-called Bragg Peak (sec. 1.1.4). It is instructive to observe how the projectile’s characteristics govern its energy loss rate: energy loss is proportional to the inverse square of its velocity (1/v2classically and 1/β2relativistically) and the square of the ion charge (z = 1 for protons), and there is no dependence on projectile mass [1].

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1.1. Interactions of heavy particles in matter 5

The Bethe-Bloch describes the mean energy loss in a material of finite thickness; for a tiny layer of material the energy loss is described by the Lan-dau distribution. In this distribution, a peak describes the most probably energy loss and a long positive tail shows the contribution due to the delta electrons. These electrons are produced by the ionization process of a heavy particle in a material. Indeed, electrons and ions are produced by the ioniza-tion process, but usually their energy is really slow that they cannot produce further ionization. Anyway, periodically, a large amount of energy can be transferred to electrons, that can cause secondary ionization. These energetic electrons are called delta rays. Considering the material in the active area for the detector under study (more details in the Table 1.2), delta rays can be a ionization source.

The total path length of the particles in the material is named range R and it is expressed in function of the initial energy Ei:

R(Ei) = Z E_i 0 dE 0 dx −1 dE0 (1.2)

For heavy particles R(Ei) is close to the mean range R, because the particles do not scatter a lot inside the material and they travel almost on a straight line. Ranges of different ions beams in water are shown in the Figure 1.3

In the range of interest (from 1 mm to 30 cm in human tissue) the Bethe-Bloch formula can be approximated to the Bragg-Kleemann formula from which the range can be expressed as directly dependent from the energy:

R(E) = αEp (1.3)

where α is a material dependent constant, E is the initial energy of the proton beam, and the exponent p takes into account the dependence of the proton’s energy or velocity (for proton in water p=2.633×10−3and α=1.735 [4]).

1.1.2 Non-elastic nuclear reactions

Heavy ions or protons can also interact with the atomic nucleus via non-elastic nuclear reactions. The probability of the nuclear reactions between the heavy ions and the nuclei of the target material are smaller compared to the reaction of the ions with nuclear electrons of the material, but they have significant effects at large penetration depths with a high transferred energy in the last few µm of the particle path [3]. These nuclear reactions can lead to a complete disintegration of both projectile and target nuclei or in partial fragmentation. Some of the important effects of the fragmentation are:

• loss of primary ions

• production of secondary fragments moving with the same velocity of the primary ions, but they have longer ranges. The longer range is due to the z2_pdependence in the Bethe-Bloch equation 1.1 and for this reason they produce a energy deposition tail after the Bragg peak (see Figure 1.1.4).

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FIGURE1.2: Mean energy loss in wa-ter for protons and 12C with the re-spective range indicated on the top

[3].

FIGURE 1.3: Mean range of heavy ions in water [3].

• Secondary fragments could also produce a broadening of the lateral distribution of the deposited energy.

1.1.3 Elastic Coulomb Scattering

A non negligible scattering is the elastic Coulomb scattering of the heavy ions and protons with target nuclei. When a proton (or heavy ion) passes close to the target nucleus it is elastically scattered or deflected by the repulsive force from the positive charge of the nucleus. The proton loses a little amount of energy in this way, but its trajectory is deflected. Every single collision of a proton with a target nucleus is described by the Rutherford differential cross section into the solid angle [1]:

dσ

dΩ =z2pZ2tr2e

(mec/βp)2

4 sin4Θ/2 (1.4)

where zp is the charge of the projectile, Zt is the atomic number of the ab-sorber material, re is the classical electron radius, me is the mass of the elec-tron, c is the speed of light, β = v/c, p is the proton momentum, and Θ is

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FIGURE1.4: Energy deposition of 330 MeV/u12C ions stopping in water. In red it is possible to see the stopping power of the primary ions with the Bragg peak and in blue the secondary

fragments with the dose tail beyond the Bragg peak.[5]

the scattering angle of the proton. The dependence from the angle is given by the term 1/ sin4(Θ/2), i.e. the proton is scattered preferentially at small

angles for single scattering events. For a beam of heavy particles passing a medium, several of these scattering mechanisms take place and their cumu-lative effects are known as multiple Coulomb scattering.

Multiple Coulomb Scattering

The Multiple Coulomb scattering is well represented by the theory of Molière (1948), an analytical solution of the Bethe’s equation (1921). For small deflec-tion angles the Coulomb scattering distribudeflec-tion is roughly Gaussian. Assum-ing small deflection angles in the Coulomb scatterAssum-ing, the higher-order terms in the Molière equation can be neglected, so the distribution will be Gaussian with a standard deviation given by [3] (see also Figure 1.5):

σθ[rad] = 14.1MeV β pc zp s d Lrad " 1+1 9log10 d Lrad !# (1.5) with βc, p and zp the velocity, momentum, and charge number of the in-cident particle, Lrad the radiation length and d the distance of the particle in the medium. Projectiles passing a medium made of heavy particles have a larger Coulomb scattering distribution than projectiles passing a medium of light particles with the same medium thickness. The angular spread in-creases when the velocity of the heavy particles slow down, due to the term

β pcin the denominator of the formula 1.5.

1.1.4 Bragg Curve

As mentioned above, the Bethe-Bloch describes the energy loss rate. The Bragg curve describes the energy loss rate as a function of the distance in

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FIGURE1.5: Considering a particle passing a thickness x, ifΘ is the solid angle in which 98% of the beam is concentrated after the path x, projecting the solid angle on the plane, one can de-fine the projected angle θ0 = Θ/

√

2 as the angular dispersion

σθ[rad] defined by the equation 1.5. Figure modified by [6].

a medium. For protons and heavy ions, the deposit of energy is in a small region in the target before that they are completely stopped. Due to the term 1/β2 and the square of the nuclear charge zp in the Bethe-Bloch formula, when the particles slow down, a large amount of energy is released. For heavy charged particles it is possible to observe a clear depth-dose profile (Bragg Curve).

FIGURE1.6: Energy deposited by different particles in matter such as human tissue. Protons and carbon ions deposit most of their energy at a specific depth, instead photons used in con-ventional X-rays leave energy all along their path, damaging

healthy tissue. Figure from [7] (modified).

In Figure 1.6 a depth-dose profile for photons, electrons, protons and car-bon is shown. The dose deposited by photons is initially built up, mainly because of electrons scattered via Compton effect. In contrast to photons, for the dose profiles of protons and heavy ions is possible to distinguish the Bragg peak at the end of their path. The position of this peak can be precisely adjusted to the desired depth in tissue by changing the kinetic energy of the incident heavy particles. The main difference between the profile of the ions and protons is that ions have a dose tail behind the Bragg peak, due to the

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secondary fragments produced in nuclear reactions along the stopping path of the ions.

1.1.5 Dose

One important quantity that is taken into account is the Dose. The absorbed dose is defined as the mean energy de deposited in a mass element dm:

D = de

dm [1Gy=1J/kg] (1.6)

Always related to the dose, there is the Bragg peak for a particle passes through matter, the particle ionizes atoms of the material and deposits a dose along its path. Considering protons passing different materials (as polystyrene, Graphite etc...) with an energy in the range 50-200 MeV (range of energy used in radiotherapy) the depth dose distribution is similar to the one of the water (as shown in Figure 1.7). In general, we can assume that for low den-sity materials (liquid water, polystyrene, PMMA) the depth dose distribution of the protons passing through them is comparable to the one of the water. For high density material (Ti, Cu and Au as in Figure 1.7) the stopping power is greater than the one for protons in low density material, so a difference in the Bragg peak respect to the water is observed .

RBE= DX

Dre f

(1.7) The RBE depends on radiation type and energy, tissue irradiated and de-livered dose. For this reason one can talk about water equivalent properties,

FIGURE1.7: Bragg peak for a 100 MeV proton beam in different materials, as a function of the depth. [8].

because the dose deposition of protons at a certain energy in water and in low density material is similar.

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1.1.6 Water Equivalent Properties

Also in radiation therapy, water is used as a tissue reference medium, be-cause of the similarity with human tissue. The following quantities are refer-eed to the water:

Water Equivalent Thickness

The Water Equivalent Thickness (WET) (in g/cm2) is defined as the amount of water that causes the same energy loss of a beam in a medium m.

WET =tw =tmρm

ρw Sm

Sw (1.8)

with twand tmthe thickness of the water and the material, ρm and ρware the density of the material and the density of the water, Sm and Sware the mean values of mass stopping power for water and the material (from equation 1.1 divided by ρ). For polystyrene (material used in the experiment presented in this thesis), the value of the WER is 115.7 mm, using a proton beam energy of 200 MeV and tm =49.83 mm [4].

Water Equivalent Ratio

It is also possible to define the adimensional quantity Water Equivalent Ratio (WER) as: WER = tw tm = ρm ρw Sm Sw (1.9)

The quantity in this form is easy to compare with results from measurements. It is possible to compute the WER using different methods, as for example using the Bragg–Kleeman (BK) rule to estimate the stopping power Sm and Sw:

S= − dE

dρx = − E1−p

ρα p (1.10)

with α=2.545×10−3and p = 1.735 for protons in polystyrene [4].

1.2 The Heidelberg Ion Beam Therapy Center

All the measurements presented in this thesis were performed at HIT (Hei-delberg Ion Beam Therapy Center). The Hei(Hei-delberg Ion Beam Therapy center was the first dedicated particle therapy facility in Europe offering treatments with both protons and carbon ions. The center is located near the Heidel-berg Kopfklinik and it was built in 2009 [10]. The accelerator scheme is the following (see also Figure 1.8): three ion sources provide carbon, protons and helium in parallel and (under request) also oxygen ions (switching one

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1.2. The Heidelberg Ion Beam Therapy Center 11

FIGURE1.8: Overview of the HIT accelerator [9].

of three ion sources with the oxygen one). An injector linac (linear accelera-tor), a combination of a 400 keV/u radio frequency quadrupole (RFQ) and a 7 MeV/u IH drift tube LINAC ([9]-[11]), accelerates the ions to an energy of 7 MeV/u; after that the ions are accelerated in a compact synchrotron with a circumference of about 65 m. The particles are extracted slowly from the synchrotron, in order to have a precisely monitored and safe dose applica-tion. The extraction lasts usually 5 s, but can be extended to 12 s in case of applications needing with low intensity beam. After each extraction, there is a pause of 5 s in order to accelerate new particles.

The beam is transported to the four beam stations by the high energy beam transport line (HEBT). Three rooms are reserved for patient treatment (two horizontal fixed-beam rooms and a rotating ion gantry) and an addi-tional experimental area for technical and scientific research and quality as-surance. All the measurements presented in this thesis were performed in the experimental area (near the Beam Dump). Carbon ions and protons are mostly used for therapy, while helium and oxygen ions are used for experi-ments. The synchrotron provided different types of parameters for each type of beam. A summary of some of these parameters is shown in the Table 1.1.

The beam size is due to the multiple Coulomb scattering, since the beam passes through different materials before the isocenter; protons with a low energy (i.e. 48 MeV/u) have a higher angular (lateral) spread respect to the others particles (when they pass a material), according to the equation 1.5, respectively (for this protons with 48 MeV/u of kinetic energy, the beam size is 33 mm).

In the experimental area of the HIT, the user can set the desired beam conditions from a library of settings. The range of energies at HIT is divided

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Parameter Protons Carbon Helium Oxygen

Energy (MeV/u) 48-221 89-430 51-221 104-515

Intensity (s−1) 8·107-3.2·109 2·106-8·107 2·107-8·108 1·106-4·107

Beam size (mm) 8-33 3-20 5-27 4-22

TABLE1.1: Energy, Intensity and Beam Size (FWHM) at isocen-ter (isocenisocen-ter is the spot at 142 mm at the vacuum exit window, accelerators nozzle, in the beam direction) ranges for the four

different type of ion sources.

into 255 available beam settings where (for a proton beam) 48 MeV/u is the energy corresponding to the set level 1 and 221 MeV/u is the energy corre-sponding to the set level 255. The lowest and the highest level corresponds to a particle range in water of 2 cm and 30 cm, respectively (these are the penetration depths in human tissue that HIT wants to reach). Up to ten dif-ferent intensity levels and six difdif-ferent levels of the beam size can be also set. The beam size refers to the isocenter, that is 142 mm from the vacuum exit window (accelerator nozzle) in the z beam direction.

The position of the dose in X and Y is controlled by moving the beam using two fast dipole magnets, called scanning magnets, which deflect the beam over the detector. This tecnique is called raster-scanning [12].

The beam position, width and intensity are monitored online by ionisa-tion and multi-wire proporionisa-tional chambers (ICs and MWPCs), located next the scanning magnets.

The intensity over time at the beam target is called the spill. An example of such a spill is reported in the Figure 1.9.

FIGURE1.9: Carbon spill for an energy beam of 250.08 MeV/u [9].

The spill is not smooth and constant because of the intensity fluctuations on a time scale of the order 1 s and 1 ms. It is possible to notice also the

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1.2. The Heidelberg Ion Beam Therapy Center 13

typical 5 seconds of beam extraction.

1.2.1 Required performance of the HIT beam monitor

The new prototype of beam profile monitor with scintillating fibers should satisfy some requirements that are currently fulfilled by the current tracking system made of ICs and MWPCs. The Table 1.2 summarizes some of the requirements. In particular, one should be able to reconstruct the beam posi-tion with a resoluposi-tion < 200 µm and with a beam width resoluposi-tion < 400 µm. Moreover, the beam profile should be reconstructed at a given frequency of 4-8 kHz.

Any new detector should also improve some limitations of the current sys-tem. The most significant limitation is due to the time to measure the beam position, since it is related to the integration time of the MWPC, usually 1 ms with 150 µs of dead time, due to the drift time of ions produced in the gas. Integration times and signal latency also contribute. For this reason the intensity should be limited in order to have a measurement time of the beam position at least 1 ms. Improved speeds would reduce the uncertainties in the position of the target dose volume (for example internal motions of the patient, such as respiration which lead to uncertainties in the locations of the applied dose [13]). Treatment times could also be reduced.

Requirement Request Value

Beam Spot Size 1-33 mm

Beam Position Resolution <0.2 mm Beam Width Resolution <0.4 mm

Readout Rate 4-8 kHz

Dead Time <250µs

Material in active area <0.35 mm H2O eq./plane TABLE1.2: Requirements currently fulfilled by the HIT system

and required for the new tracking system [13].

The new detector should also have a minimal thickness of material in the active area (equivalent thickness in H2O <0.35 mm), since one wants to avoid the multiple scattering inside the material, that causes a broadening of the beam width; but also the production of secondary fragments inside the material of the tracking detector before reaching the target volume.

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Chapter 2 Scintillating fibers and

Photodiodes

In this chapter a description of the scintillating fibres and the main physics behind the scintillating fibres and scintillation process in organic scintillators are presented. A general introduction to the photodiodes and their working principle is also given. All these features there will be useful to understand the main working principle of the detector studied in this experiment.

2.1 Physical basis behind the scintillation

A typical organic scintillator is the plastic scintillator, that consists of several components, and hence, the production of scintillation light is typically a multi-step process. Organic plastic scintillators use ionization produced by charged particles (see the Section 1.1) to generate optical photons, usually in the blue and green wavelength regions. The basis of the scintillating plastics is a result of the general structure of aromatic hydrocarbons.

For organic plastic scintillator, the structure of the organic molecule is de-termined by the electronic configuration of the carbon atom. For the ground state of the carbon (Z=6) the electronic configuration is 1s22s22p2, but when a compound (for example benzene, chemical structure in Figure 2.1) is formed, one electron of the 2s state is excited into the 2p state and the electronic con-figuration becomes 1s22s12p3. The four valence electron orbitals, one 2s and three 2p, are mixed or "hybridized" in a particular configuration, in which one of the p orbital (say pz) is unchanged and three equivalent hybrid or-bitals are produced by mixing s, px and py. This sp2 are in the same plane (say X-Y plane) and they are inclined at equal angles of 120◦ to each other (Figure 2.2). The hybrid orbitals are know as σ-electrons and the bonds are named σ-bonds. The unchanged pz atomic orbital is mirror symmetric re-spect to the nodal plane X-Y and it is named π-electron[14]. In the benzene (C6H6) not only localized C-H and C-C σ bonds are presented, but also ad-ditional C-C bonds (called as π bonds) between the unchanged p orbital and the other unchanged p orbital of the neighboring carbon atom (as an example Figure 2.2). The six π electrons of the carbon molecules of the benzene inter-act to produce a common nodal plane and to form six π molecular orbital delocalized (Figure 2.1) [14].

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FIGURE2.1: σ bonds, six pz orbitals and delocalized π system

in the benzene molecule [15].

FIGURE2.2: Example of C-C bond and C-H bond in the Ethy-lene molecule C2H4.

The π electrons are responsible for the scintillation process, in particular the excited states of the π electrons are responsible of the luminescence pro-cess in the benzene ring. In the Figure 2.3 we can see a scheme of the energy levels of the π electrons. The electrons in the ground state S00 are excited in a higher energy level S10, S20, S30 etc by a incident charged particle (absorp-tion). Each principal level has also the corresponding vibrational levels (S01, S02, S03 for the ground state). The first principal level S10 has an energy of few eV above the ground state S00. All of the vibrational sub-levels are sin-glet states with a spacing of∼16 eV [16]. The direct transition between the ground state S00 to the triplet states Ti is spin forbidden. When a charged particle passes through an organic scintillator, the π electrons in the ground state are excited in a higher energy singlet state. The excited electrons then quickly relax to the bottom of the excited state by internal conversion (non ra-diative process). After that the thermal equilibrium is established (∼10−11s) and radiative transitions S1x →S0xcould happen in three different ways: flu-orescence, phosphorescence and delayed fluorescence. These are the ways in which the scintillating light is produced.

Fluorescence

The process of the fluorescence occurs with a radiative transition from the state S1to the state S0(Figure 2.3). The radiative lifetime is∼10−8−10−9s, greater than the period of molecular vibrations 10−12 s. The intensity of the fluorescence emission is described by an exponential law I = I0e−t/τ, with I0 intensity at time 0 and τ the fluorescence decay time [14]. This process involves transitions from the excited state S10 to the vibrational sub-levels of the ground-state S00, S01, S02 etc.

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2.1. Physical basis behind the scintillation 17

FIGURE 2.3: Scheme of the electronic levels of π electrons in a organic molecule with the different radiative transition

pro-cesses indicated [17].

Phosphorescence

Phosphorescence is the process for which wavelengths longer than fluores-cence and with a longer decay time (∼ 10−4s) are emitted, since in this pro-cess there is no immediate re-emission of the absorbed radiation. A fraction of the electrons excited in the singlet state go to the triplet state through a non-radiative transition, called inter-system crossing (Figure 2.3). After that, they are re-emitted in the ground state really slowly, since this process is spin-forbidden. Jablonski (1915) was the first to give this explanation. A schematic Jablonski energy diagram is in the Figure 2.4.

Delayed fluorescence

Delayed fluorescence process is the emission of a spectrum identical to the one of the fluorescence process but with a long decay time≥10−6s (intensity of the emission non-exponentially as in the fluorescence). In this case the decay time is bigger than in the case of the Fluorescence, since the fraction of the electrons in the triplet state could acquire over the time a certain thermal activation energy to return from the triplet state to the excited single state S1 (through a non-radiative process) and slowly they are re-emitted in the ground state (see also Figure 2.4).

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FIGURE2.4: Jablonski energy diagram for three processes: Flu-orescence, Phosphorescence and Delayed Fluorescence [18].

2.1.1 Ionisation quenching

Another important quantity which must be taken into account for the plastic organic scintillators is the scintillation efficiency, defined as the fraction of all incident particle energy which is converted into visible light. As we said, a particle that passes through the fibers excites the molecules into the fibers, but there are alternate de-excitation modes available to the excited molecules that do not involve the emission of light and in which the excitation is de-graded mainly to heat. All these process of radiationless de-excitation are so called quenching. It is also important in the fabrication of a scintillator to eliminate all the impurities, which degrade the light output by providing alternate quenching mechanisms for the excitation energy. Birks and Pringle have reviewed the energy transfer mechanisms in binary and tertiary organic mixtures (details in Section 2.2) together with their influence on scintillation efficiency and pulse timing characteristics [14].

For charged particles passing through a scintillating material, they inter-act negligiblely along their path, hence for fast electrons the scintillation re-sponse L (energy emitted mainly as fluorescence) is proportional to the par-ticle energy E dissipated in the scintillator material:

L =SE (2.1)

and in the differential form

dL dx =S

dE

dx (2.2)

with x is the range of the particle in the scintillating material, S is the absolute scintillation efficiency (that is the fraction of primary electrons converted in fluorescence photons), dE/dx is the energy loss and dL/dx is named specific fluorescence. The relation above has been verified for electrons in anthracene with an energy in the range 0.125-3 MeV and for electrons and µ mesons with an energy up to E=170 MeV. In the case of heavy particles or slow electrons (E<125 keV), L has not a linear dependence with E; it is observed that dL/dx is reduced below S for these particles in which energy loss dE/dx greater than the one for fast electrons. Hence, S depends on the type of particle and above

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2.2. Working principle of the scintillating fibers 19

all on the energy loss in the material. The scintillator response was observed for the fist time by Birk (1950), bombarding anthracene crystals with different types of particles.

Birks (1951) was the first to provide a semi-empirical solution for the non linear dependence of the light output L with the energy deposition E in a or-ganic scintillator. It proposed the following relation (2.3)1to describe the ion-isation quenching effect, assuming that the quenching is due to the high den-sity of excited molecules along the particle track which causes de-excitation without photon emission:

dL dx =

SdE_dx

1+kBdE_dx (2.3)

with kB the Birks constant. A typical value of kBis 10−4-10−2g/cm2MeV. For small dE/dx (as fast electrons) the relation (3.9) is found. For heavy particles, the dE/dx becomes larger and the equation (2.3) can be approximated to the equation dL dx = S kB =const (2.4)

For ions it is possible to express a quenching factor2as the ratio of the light yield (named as Lifor ions and Lefor electrons, both expressed as the integral form of the relation (2.3)) of the ions to that of electrons of the same energy:

Qi(E) = Li(E) Le(E) = RE 0 dE 1+kB(dE_dx)i RE 0 _1+k_BdE(dE dx)e (2.5)

In the relation above the term S disappeared and Qi(E) depends only on the parameter kB.

Tacking into account the relations (2.4) for heavy particles and (2.1) for fast electrons, the following approximations for the quenching ratio is ob-tained: Qi(E) = Li(E) Le(E) = Li(E)/E Le(E)/E ' dLi/dE dLe/dE ' 1 kBdEi/dx (2.6) from which important information are extrapolated:

• Quenching factor depends on energy, hence Qiis not constant. • Qiis minimal when dEi/dx is maximum.

• Qiincreases at low energies (consequence of the decrease of dEi/dx).

2.2 Working principle of the scintillating fibers

Scintillating optical fibers for tracking detectors (such as detector presented in this thesis) are used because of two main features:

1_{In the original relation the term k and B were treated as separated constants} 2_{named as the factor} α

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1. use the ionization energy deposited by charged particles to produce a proportional amount of optical photons;

2. the geometry, which is typically small in diameter and transports the optical photons to the read-out devices;

Because this thesis work studies the loss of signal due to the radiation damage, it is important to understand the production and transmission of the light.

2.2.1 Scintillation process in the fibres

A charged particle that passes through the fibre ionizes the molecules present in the core of the fibre (details about the structure of a fibre in the section 2.2.3); the deposited energy in the core by an ionizing particle first excites the electronic level of the base (usually polystyrene). Approximately 4.8 eV of deposited energy is required to excite a base molecule. The scintillation light yield of polystyrene is rather poor and for this reason an aromatic scintillator or primary dye (organic fluorescent) is added. This primary dye is chosen to have very high quantum efficiency (95%) and rapid fluorescence decay (few nanoseconds) and an emission in a specific wavelength. The intermolecular energy transfer between the respective quantum levels requires that the base emission band overlaps the added primary absorption band (Figure 2.9).

With a sufficient concentration of the primary dye the energy is trans-ferred between the base and the primary dye by means of a non-radiative dipole-dipole transmission (Förster transitions) [19], in which the molecules of the base absorb energy due to the excitation of incident light and the en-ergy is transfered to the molecules of the primary dye (if the base and the primary dye are close enough in order to do the non-radiative dipole-dipole transmission), so the base molecules are quickly relaxed to the ground state and the molecules of the primary dye are in a excited state. This system with a base and an organic primary fluorescent dye is named binary or two-component scintillator. The concentration of the primary dye in a binary system limits the length of the scintillating fibers, because of optical self-absorption of the emitted light by dye molecules (see Figure 2.9). Moreover, in a binary system, cross talk between the fibers are possible, because the light emitted from a primary dye can escape the fibre and excite the dye in the neighboring fibre.

In order to avoid this problem and to have more light output, there are several solutions; one of them is to add a second dye (or wavelength shifter) to the system with a large Stoke’s Shift [19]. This wavelength shifter (as TPB or 3HF used for the fibers in this experiment) absorbs the emission of the primary fluorescent dye and emits light in a wavelength region for which the transparent region of the base is improved, so the light emission is shifted in the transparent region of the base, where the base attenuation length reaches about 2.4 m and the Rayleigh scattering becomes unimportant (the Rayleigh scattering is the diffusion of the incident light due to scattering centers much smaller of the wavelength of the incidence light. In the case of the fibres it

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is basically due to the random fluctuation of the refractive index in the core, hence the inhomogeneity in the material during the fabrication process). In a fibre, the Rayleigh scattering becomes important for wavelength below 1.5 µm, in fact at this wavelength the Rayleigh scattering is higher than the other losses of light in the fibre. The intensity of the Rayleigh radiation given by a beam of light of wavelength λ and I0 intensity, that hits a little particle (scattering center) is:

I = I0(1+cos 2 θ 2R2 )( 2π λ ) 4₍n2−1 n2₊₂) 2₍d 2) 6 _(2.7)

in which n is the refractive index of the particle, θ is the scattering angle, d is the diameter of the particle, R is the distance of the particle. Treating par-ticles as molecules, hence point parpar-ticles,the Rayleigh intensity for a single molecule can be written as

I =I0(8π 4 α2 λ4R2 )(1+cos 2 θ) (2.8)

in which the refractive index is expressed in term of the polarizability α of the particle, thus the tendency of a molecule to create a dipole moment in the presence of an electric field induced by the beam light. As it possible to see from the previous relation, at lower wavelength the Rayleigh scattering increases (I∝ λ−4_{). The Rayleigh scattering will be also important for the} creation of light absorption regions, that cause the damage in the scintillating fibre (Section 3).

The system described above with the presence of a second dye is named ternary scintillator. Another solution could be related also to a binary scin-tillator, but with a fluorescent dye with a very low optical self absorption: in this way a large separation, or Stokes shift, between the absorption and emis-sion bands is presented. An example of such a dye is 3HF (3-hydroxyflavone), that fluoresces in the yellow-green region of the light spectrum (with a wave-length maximum of 530 nm). A third solution is to combine the two ap-proaches above in order to create a very efficient ternary scintillator with a high concentration of a primary dye and a low concentration of a secondary dye, usually intramolecular photon transfer (IPT) fluorescent dye. This sys-tems have many advantages, in fact using the IPT dye the optical attenuation length is longer because of the minimal self-absorption of the fluorescence emission, moreover this minimal self-absorption eliminates the problem of the cross talk and the long emission wavelength provides for improved re-sistance to the damage by radiation. An example of this efficient ternary scin-tillator is polystyrene doped with 1% by weight of paraterphenyl (PTP, the primary) and 1500 ppm of 3-hydroxyflavone (3HF, the secondary) [19]. This kind of ternary system is used in the experiment under study. In the next section 2.2.2 an explanation of the scintillating process in a ternary system is described.

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FIGURE 2.5: Absorption and emission spectrum for different dyes. It is interesting to notice that the Stoke’s shift (difference in wavelength between the peak of emission and absorption) is not present in the 3HF dye (hence it is used as wavelength shifter); this means a lower self-absorption and a much longer

attenuation length compared to the others dyes.

2.2.2 Scintillation process in a ternary system

A schematic example of a ternary system is shown in Figure 2.6. The con-centrations of the primary dye, as previously mentioned, are rather small (<1% by weight) and for this reason the energy lost by incident particles is transferred completely to the base (solvent). The resulting primary fluores-cence (named γAin the Figure 2.6), due to the de-excitation of electrons from the excited state (the electrons will be in the lower excited state, since all the electrons in higher excited state will relax to the lower excited state through non radiative process) to the ground state of the base, is absorbed by the primary dye, itself an organic scintillator, through a non-radiative process (Förster process) with a time scale of 10−11s. Once that all the energy is trans-ferred to the primary dye, the electrons of the latter are in the excited state and they will relax in the ground state emitting photons (γB in the Figure 2.6). These photons will excite the secondary dye (wavelength shifter), that will emit fluorescence light with a certain wavelength (the choice of the dye is due in order to produce light within a wavelength to maximize the Stokes shift, and, hence, to avoid the self absorption).

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FIGURE2.6: Radiative transfer of energy from polymer base to primary and secondary dyes (fluors) in a ternary scintillator.

2.2.3 Optical Transport

When a charged particle passes through the fibre, light is produced in its core along the particle’s trajectory (the passage of the particle through mat-ter is described in the section 1.1). The photons are emitted isotropically (in all directions). In the detector described in this thesis the plastic scintillating fibers SCSF-78MJ are also used. They are produced by the company Kuraray in Japan (see Figure 2.7). They consist of a core with added organic scintilla-tors and two thin cladding layers. Polystyrene (PS), refractive index n=1.59, is typically used for the core and polymethylmethacrylate (PMMA), n=1.49 and fluorinated polymer (FP), n=1.42, for the claddings [20].

2.2.4 Capture Efficiency

The light that can be transported in a fibre is limited by the total internal reflection. This means that only the part of the light that undergo internal refraction is captured and transported, the rest of it is lost. The meridional rays, i.e those crossing the fibre axis (Figure 2.8), are reflected if their angle of incidence relative to the surface normal is greater of the critical angle3

θcrit =arcsin nclad

ncore (2.9)

In order to have total internal reflection for part of the incident light, the re-fractive index of the cladding is lower than the rere-fractive index of the core (nclad < ncore). Moreover, to maximize the relative amount of light, the vol-ume of the core should be as big as possible since the cladding is typically not scintillating. The fraction of the isotropically emitted photons transported to-wards the end of the fibre is named trapping fraction and it is given by

etrap ≥ dΩ 4π = 1 4π Z 90−_θ_crit 0 2πsinθdθ (2.10)

Assuming emission of scintillation light from a point source on the symme-try axis of a fiber with a circular cross section, the effective fraction of the light trapped by total internal reflection within the fiber in one direction is dΩ/4π =3.1% for single clad (ncore =1.59,nclad =1.49) and dΩ/4π =5.3% for multiclad fiber (n_clad,FP =1.42) [19].

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FIGURE2.7: Representation of the light transport in a scintillat-ing fibre . Figure from [21]

Double cladding fibres are typically chosen to maximize the collected light. In addition, the rays with helical paths (Figure 2.8), called skew rays, are also captured (rays emitted to the edge of the fibers within a polar angle

≤90◦). However these rays are attenuated faster along the length of the fibre due to the great number of reflections and longer path length. As such the trapping efficiency is more than 5.3 %.

(A)

(B)

FIGURE 2.8: Meridional rays passing near the center of the fibers (left) and skew rays originated outer rim of core (right).

(A) Front side of the fibre. (B) Later side of the fibre.

An important property of the scintillating fibers is the attenuation length which indicates the distance which the intensity of the light is reduced of 1/e due, in this case, to the reflection losses, absorption by polystyrene itself and self-absorption by a secondary dye (FP). In a simple model we can approxi-mate the intensity of the light as an exponential function

I(z) = I0e−z/Λatt (2.11) where I0 is the initial intensity, z is the traversed distance and Λatt is the attenuation length measured along the fiber axis. TheΛattdepends from dif-ferent wavelength and from the Rayleigh scattering it is clear that the shorter wavelengths are attenuated more strongly than the greater wavelengths [22] (the attenuation is due in part also to the skew rays that reach the end of the

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2.3. Photodiodes 25

fibre). For this reason in the spectrum of a fibre there will be attenuation for the short components and a shift towards the green and red component. For the SCSF-78 MJ fibre the attenuation length as measured with 4 UV-LEDs (390 nm) shifted along the fibre from 100 cm to 300 cm isΛatt = 3.7 m. The light is readout by a photospectrometer. These fibres produces several thou-sand photons per 1 MeV deposited energy. The decay time constant of the scintillation light signal is 2.8 ns and the emission spectrum extends from about 400 to 600 nm and peaks at 450 nm near the source [23] (see Figure 2.9).

FIGURE2.9: Light Intensity distributions measured at the end of a non-irradiated SCSF-78MJ fibre and for a SCSF-3HF fi-bre for excitations with a 370 nm LED between 100-300 cm. The light is readout by an intensity calibrated Hamamatsu

C10083CA-2050 photospectrometer [24].

2.3 Photodiodes

In the experimental detector described in the next chapter, the light output from the fibers mats is detected by photodiode array: a device by which the position and the intensity of the light is reconstructed. A photodiode is de-fined as a P-N junction diode that converts the light output into electric cur-rent.

2.3.1 Physics basis behind photodiodes

Photodiodes are made of semiconducting materials. Semiconductors are crys-talline materials. The outer shell of these materials have an energy band structure. The energy bands are regions of discrete energy levels, which have a really close spacing and for this reason they can be considered as a contin-uum; while the energy gap is a region that does not present energy levels. Due to the periodic disposition of the atoms in a crystal, which are close to each others, the energy band arises and as a consequence the electrons wavelength are overlapped. It is important to take in consideration that for the Pauli principle same electrons have to occupy different energy states; hence in the

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outer shell energy levels, the electrons will occupy many discrete energy lev-els slightly separated to each others. Instead, in the inner shell energy levlev-els, two electrons with opposite spin will occupy the same energy level. The en-ergy band more high is named conduction band. In this region the electrons are free and they can roam around the crystal. The lower region is named valence band. The electrons in this region have a tightly bound with the atoms of the crystal lattice. The probability of occupation of energy levels in valence band and conduction band is named Fermi level. In a pure semiconductor at absolute zero temperature the number of holes in the valence band and the number of electrons in the conduction band are the same, so the probability of occupation of energy level in conduction and valence band is equal, so the Fermi energy level lies in the middle of the energy gap, hence the pure semiconductor acts as an insulator (see Figure 2.10). The concentration of the holes, named p, in the valence band is given by:

p= NVe−(EF−EV)KBT _(2.12)

while the electrons concentration is given by: n= NCe

−(EC−EF)

KBT _(2.13)

where KB is the Boltzmann constant, T is the absolute temperature of the semiconductor, NCis the density of the states in the conduction band and NV is the density of the states in the valence band (they can be calculated from the Fermi-Dirac statistics), EV and ECare the energy levels of the valence and conduction band, EF is the energy of the Fermi level. As said before, for a pure semiconductor the concentration of holes and electrons is the same, so

p=n=ni (2.14)

with ni = 1.5×1010cm−3 for Si at T = 300 K and the Fermi energy level can be written as:

EF = EC+EV

2 (2.15)

Substantially, materials can be divided as insulator, semiconductor and con-ductor (metal). In insulator the energy gap is large, this means that the differ-ence in energy between the electrons in the valdiffer-ence band and in the conduc-tion band is too large and it is impossible for an electron to pass this energy in order to be transfer from the valence to the conduction band. Basically the electron are all in the valence band and the thermal energy to excite the electrons in the conduction band is not sufficient. In the case of a conductor material, the energy gap does not exist and the electrons are free to move in the conduction band and participate in conduction. In a semiconductor the energy gap is small enough such that the electrons in the valence band are excited by thermal energy in the conduction band. Hence, in presence of an electric field, a small current travels from the valence to the conduc-tion band. However, if the semiconductor is cooled there will be not enough thermal energy for the conduction of the electrons. An example of a semi-conductor materials are silicon or germanium. In the lower energy state a

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2.3. Photodiodes 27

silicon atom has four valence electrons; under the effect of thermal energy at normal temperature the valence electrons are excited in the conduction band and they leave a hole in the original position. This process is repeated for all the electrons in the material. Considering the charge of the holes as positive compared to the negative charge of the electrons, at the end two sources of current there will be: a negative current of electrons from the valence band to the conduction band and a positive current of the holes in the valence band. Moreover in this case the same number of electrons and holes will be cre-ated. Usually, in a semiconductor crystal, a dopant can be added in order to create a doped semiconductor. This dopant have a certain amount of valence electrons in the outer orbital. If a pentavalent dopant (five valence electrons) in the silicon atom (four valence electrons) is added, only four electrons will occupy the four holes in the valence band of the silicon; the fifth will be lo-cated in a discrete energy level in the energy gap. This level is close to the conduction band, so the electrons will be excited in the conduction band, in-creasing the conductivity. In this system the current will be generated mainly by the electrons and this type of semiconductor is named n-type. If a triva-lent dopant is added to silicon, now a valence electron is missed, because the electrons of the impurity dopant will occupy three holes in the valence band of the silicon, but there will be an excess of one hole. The trivalent impurity creates this time another level in the energy gap near the valence band, so electrons in the valence state are excited in this level, leaving an excess of holes. This excess of holes will decrease the concentration of free electrons in the material and for this reason the charge (hence the current) will be transported mainly by the positive holes. This kind of semiconductor transporting a positive current is named p-type. P-type semiconductors are also named "acceptors", because of the excess of holes that accept free elec-trons. N-type semiconductors are named as "donors", because of the excess of electrons they will donate a negative charge to the lattice.

FIGURE 2.10: Scheme of the energy band structure for metal (conductor), semiconductor and insulator.

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2.3.2 P-N Junction Diode

A P-N junction is a piece of silicon with two terminals (see Figure 2.11). One terminal is doped with a P-type dopant (i.e boran) and the other one with a N-type dopant (i.e. phosphorus). The n-type and p-type semiconductors are electrically neutral, but merging them together their behavior is really different. Since the different concentration of electrons and holes in the two

FIGURE2.11: P-N junction and the junction diode symbol with the current flow indicated.

materials, there will be a flow of electrons towards the p region and a flow of holes towards the n region. The charge transfer of electrons and holes across the PN junction is named diffusion. Hence, the part of the junction in the p region will become negative because of the excess of electrons and part of the junction in the n region will become positive because of the excess of holes. This process creates an electric field gradient, that stops the diffusion process and creates a region of immobile space charge. A potential difference will be created because of the electric field, called as contact potential (this potential is generated from the electrostatic force of attraction between the opposite charges). The contact potential is 1 V generally. Because of this potential, a depletion zone is formed and it inhibits any further electron transfer, unless a voltage is introduced on the junction. If no external potential are applied to the PN junction, the diode is connected in a Zero Bias condition. When a photon (for example a photon from the scintillation process) strikes the photodiode, it excites an electron in the photodiode, thereby creating a mo-bile electron and a positively charged electron hole. This mechanism is also called inner photoelectric effects. If the absorption of the photon in the diode occurs in the junction’s depletion region, these carriers are swept from the junction by the inbuilt electric field of the depletion region. Photodiodes in Zero Bias mode are used in the experiment. The photodiodes array used to detect the scintillating light are described in the chapter 4. More information about the operational modes of photodiodes can be found in the A.

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2.3. Photodiodes 29

FIGURE2.12: Schematic example of a diode in a Zero Bias con-dition [25].

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31

Chapter 3 Radiation in organic scintillators

An important effect due to the exposure of a plastic scintillator to a certain dose of radiation has to be considered termed radiation damage. It is well known that radiation damage produces a deterioration in scintillation effi-ciency, this means worsening in the transmission properties of the scintilla-tor and a loss in the intrinsic scintillation light output (see also Figure 3.3). Typically, the light output of a scintillator decreases exponentially with the dose received [26].

L(D) = L0e−D/C (3.1)

where L(D) is the light output in a scintillator that receives a certain dose D, L0is the light output before irradiation and C is a constant that depends on the material in which the scintillator is constructed.

3.0.1 Radical Production from Ionization

The cause of the formation of the radiation damage in a scintillator material is due to behavior of molecules inside the material when they are bombarded by a certain dose of radiation. The energy deposited in the polymer by parti-cles not only excites the luminescence centers, but also breaks chemical bonds and, as a consequence, the properties of the polymer are drastically modified at high dose exposure. Indeed the C-H bond in the polymer are split and hydrogen and free radicals (the name radicals is used for atoms, molecules or ions with an unpaired valence electron) are released, while the free carbon bonds are left in the residual material. The carbon bonds act as color centers in the polymers, thus regions in which the fluorescence light is absorbed. For this reason, after the exposure of a certain dose, many plastic scintillating materials, like polystyrene, have regions with a yellow or brown color. It is also well known that, when the irradiation process is made in the air (or the scintillating material was exposed to the air before the irradiation, so oxygen molecules were already present into the material), the oxygen molecules dif-fuse in the scintillating material and react with the radicals R ·, producing peroxide radicals RO2·(the symbol·is used to indicate the radicals)[27]:

R· +O2 →RO2· (3.2)

The peroxide radicals can react in turn in the following ways:

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RO2· +RO2· →RO2·R+O2 (3.4) When oxygen is not present during irradiation, the following reactions take place:

R· +RH→RH+R· (3.5)

R· +R· → X (3.6)

in which RH is used to indicate the polymer molecules and X as the result of the radicals annihilation process. Other reactions to the (3.2) could also happen when oxygen is present during irradiation, but the (3.2) is the faster one, hence one can assume that in presence of oxygen, free radicals are not available. The reactions (3.3), (3.4) and (3.6) are the final reactions in which an irradiation process is concluded (concerning the peroxy radical (RO2·), it is unstable at room temperature and decays within hours following the reaction (3.3) and (3.4)). The damage is generated by the presence of the radicals in the scintillating sample (eq. (3.3)-(3.4)-(3.6)).

Permanent and temporary damage

From different studies, it is well known that the diffusion of the atmospheric oxygen into the material during irradiation increases the amount of the dam-age in the polystyrene sample. In particular, a distinction of two different kinds of damage can be done: temporary damage, in which the color cen-ters go away after a certain time period that depends on the concentration of oxygen and temperature; a permanent damage, in which the color centers are stable. In the case of oxygen, it tends to create permanent damage in a scintillating material (during irradiation). The formation of the permanent absorption centers rise linearly with the dose during irradiation and they re-main constant after irradiation. This proportionality can be written as [27]:

∆µp(λ) = d∆µp(λ)

dD ·D (3.7)

in which∆µp(λ) = µirr(λ) −µunirr(λ)is the value of the permanent induced absorption (defined as the difference between the absorption coefficient µ of the irradiated and unirradiated sample) and D is the applied dose. The per-manent absorption centers are, hence, more visible at high dose rate. Two different kinds of temporary absorption centers could be observed accord-ing to the presence or absence of oxygen duraccord-ing irradiation and dependaccord-ing also on the scintillating dyes used. Indeed the presence of the dyes in the polystyrene base of a plastic scintillator can generate temporary absorption centers. It is known that the radicals observed in a free oxygen ambient inside a scintillating material are really stable, in fact they can persist for months or years. But these kind of radicals are not the primary products generated dur-ing irradiation. From studies about electron spin resonance (ESR) of PS and PMMA conducted in a temperature of 77-300 K, it is clear that the radicals produced in a first step are unstable and decay rapidly with an increase of the temperature. For this reason, the irradiation of scintillating material at

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Chapter 3. Radiation in organic scintillators 33

room temperature and with no oxygen produces not only longlived radicals, but also shortlived radicals. Due to their short live component, these radicals are also difficult to detect after irradiation (all the investigation about the ra-diation damage are done after irrara-diation). Finally, three types of absorption centers can be defined:

• P: permanent absorption centers; • RL: longlived absorption centers; • RS: shortlived absorption centers;

The respective radiation induced absorption can be express as:

∆µ =∆µP+∆µR_L+∆µR_S (3.8)

in which∆µP is the non anneable and∆µR_L is the anneable part of the radi-ation damage. ∆µR_S is the contribution of the shortlived absorption centers. The concentration of the shortlived absorption centers can be written as [28]:

d[RS(t)]

dt = gS·ρ·D˙ + dRS_

dt (3.9)

The first term describes the formation of these absorption centers and the second term describes the decay of these centers. ˙D is the absorbed dose rate,

ρis the density of the scintillator, gSis the chemical yield for the formation of RS, i.e the number of the shortlived absorption centers per absorbed energy [27]. In order to solve the differential equation, the term dRS_/dt should be known. It can be considered as:

dRS_ dt = −

[RS(t)]

τ (3.10)

for a first order process (RS → Y); while for a second order (also named biomolecular) process (RS +RS →Y0) it can be considered as:

dRS_

dt = −kS[RS(t)

2_] _(3.11)

which kS is a reaction constant for the decay and RS(t)2the square of the con-centration of the shortlived absorption centers. Assuming that the molecule Y and Y0do not absorb light, the value of the shortlived induced absorption ∆µS can be written as [27]:

∆µS(λ) = [RS(t)]σS(λ) (3.12)

with σS(λ) is the cross section for the interactions between photons with a

certain wavelength λ and RS the shortlived absorption centers. ∆µS is the difference between the absorption coefficient for the irradiated and unirradi-ated sample materials (at low rate, there is the saturation of R2 and the con-tribution of ∆µP and ∆µL can be neglected), ∆µS(λ) ≈ ∆µ(λ) = µirr(λ) −

µunirr(λ), respectively;[RS] is the concentration of the temporary absorption

centers. The transmission of the light decreases until when the saturation of the RS is achieved (∆µS(λ) → ∆µS,sat(λ)). This value of the saturation

corre-sponds to the equilibrium when the number of the decays and formations of shortlived absorption centers are the same ( dS(t)/dt = 0 in eq. (3.9)).

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3.0.2 Transmission loss

The optical transmission given by RScould be measured using the following expression:

Tirr(λ) Tunirr(λ) =e

−∆µS,sat·d _(3.13)

where d is the thickness of the sample (path length of the light in the irra-diated part of the fibre) and Tunirr(λ)and Tirr(λ)are the transmission of the

fiber before and after irradiation. Hence, the transmission of the light de-crease exponentially in presence of the absorption centers.

FIGURE3.1: Transmittance spectra of pure polystyrene (PS) for the irradiation in different material: (a) immediately after the high dose irradiation at 10Mrad; (b) after full annealing in the

air (recovery process) [29].

Permanent absorption centers are created during the collision between particles and polymers or during annealing process as described in the equa-tions (3.4) and (3.6). Radicals (RL) can be considered stable under the con-dition that no oxygen is applied (considering low dose applied and ambient temperature). They will strongly absorb the blue and UV light. If there is no oxygen in the scintillator material , the same amount of radicals will decay

Effects of Radiation damage on a scintillating fibre based ion Beam Profile Monitor

T

ESI DI

L

AUREA

M

AGISTRALE IN

F

ISICA

Effects of Radiation damage on a

scintillating fibre based ion Beam Profile

Monitor

Candidata:

Giulia MEO

Relatore:

Prof.essa Stephanie

H

-M

Relatore interno:

Prof. Giovanni P

Contents

Introduction

Chapter 1

Background Information

1.1

Interactions of heavy particles in matter

1.1.1

Inelastic Coulomb scattering

1.1.2

Non-elastic nuclear reactions

1.1.3

Elastic Coulomb Scattering

1.1.4

Bragg Curve

1.1.5

Dose

1.1.6

Water Equivalent Properties

1.2

The Heidelberg Ion Beam Therapy Center

1.2.1

Required performance of the HIT beam monitor

Chapter 2

Scintillating fibers and

Photodiodes

2.1

Physical basis behind the scintillation

2.1.1

Ionisation quenching

2.2

Working principle of the scintillating fibers

2.2.1

Scintillation process in the fibres

2.2.2

Scintillation process in a ternary system

2.2.3

Optical Transport

2.2.4

Capture Efficiency

2.3

Photodiodes

2.3.1

Physics basis behind photodiodes

2.3.2

P-N Junction Diode

Chapter 3

Radiation in organic scintillators

3.0.1

Radical Production from Ionization

3.0.2

Transmission loss