Download Development of the readout for an innovative monitor chamber for

Università degli Studi di Torino
Dipartimento di Fisica
Tesi di Laurea Magistrale in Fisica
Development of the readout for an innovative
monitor chamber for Hadrontherapy applications
Candidato: Federico Fausti
Relatore: Prof. Roberto Sacchi
Coordinatore: Dott.ssa Simona Giordanengo
Anno Accademico: 2012-2013
Summary
Introduction ................................................................................................................................... 1
Chapter 1 ....................................................................................................................................... 3
Radiation therapy with heavy charged particles............................................................................ 3
1.1 Introduction ......................................................................................................................... 3
1.2 Physical Properties .............................................................................................................. 5
1.2.1 Interaction of photons and ions with matter ................................................................. 5
1.2.2 The Bragg peak width and energy spread .................................................................... 9
1.2.3 Spread Out Bragg Peak – SOBP .................................................................................. 9
1.2.4 The particle range ....................................................................................................... 11
1.2.5 Magnetic Deflection for Active Beam Shaping ......................................................... 12
1.3 Nuclear interactions........................................................................................................... 13
1.4 Biophysical Properties....................................................................................................... 15
1.4.1 Physical Dose ............................................................................................................. 15
1.4.2 Stopping Power and LET ........................................................................................... 15
1.5 The biological effects of the radiation............................................................................... 17
1.5.1 Relative Biological Effectiveness .............................................................................. 19
1.5.2 Oxygen Enhancement Ratio ....................................................................................... 21
1.5.3 Biological effective Dose ........................................................................................... 22
1.6 Biophysical models ........................................................................................................... 24
1.6.1 The Micro-dosimetric Kinetic Model (MKM) ........................................................... 25
1.6.2 The Local Effective Model (LEM) ............................................................................ 26
Chapter 2 ..................................................................................................................................... 30
Accelerators for hadrontherapy treatments ................................................................................. 30
2.1 Introduction ....................................................................................................................... 30
2.2 Accelerators requirements ................................................................................................. 32
2.3 Present accelerators for hadrontherapy ............................................................................. 33
2.3.1 The cyclotron.............................................................................................................. 33
2.3.2 The synchrotron.......................................................................................................... 34
2.3.3 Models and properties ................................................................................................ 35
2.3.4 Facilities under construction ...................................................................................... 38
2.4 New ion accelerators ......................................................................................................... 39
2.4.1 Superconducting cyclotron......................................................................................... 40
2.4.2 FFAGs - Fixed-Field Alternating-Gradient accelerators............................................ 42
2.4.3 High-frequency linacs for carbon ion therapy: the Cyclinac...................................... 44
2.5 Future perspective ............................................................................................................. 47
2.5.1 Rotating SC synchrocyclotron ................................................................................... 47
2.5.2 Dielectric Wall Accelerator ........................................................................................ 48
2.5.3 Turning Linac for Proton therapy............................................................................... 49
2.5.3 Laser-driven accelerators ........................................................................................... 49
2.6 A final remark ................................................................................................................... 52
Chapter 3 ..................................................................................................................................... 53
Gas Filled Detectors .................................................................................................................... 53
3.1 Introduction ....................................................................................................................... 53
3.2 Production of Electron-Ion Pairs ....................................................................................... 54
3.3 Energy resolution and the Fano factor .............................................................................. 56
3.4 Diffusion and Drift of Charges in Gases ........................................................................... 59
3.4.1 Diffusion in the Absence of Electric Field ................................................................. 59
3.4.2 Charge diffusion in the presence of electric field....................................................... 60
3.5 Drift of Charges in Electric Field ...................................................................................... 61
3.5.1 Drift of Ions ................................................................................................................ 61
3.5.2 Drift of Electrons........................................................................................................ 63
3.6 Effects of Impurities on Charge Transport ........................................................................ 65
3.7 Regions of Operation for Gas Filled Detectors ................................................................. 67
3.7.1 Recombination Region ............................................................................................... 68
3.7.2 Ion Chamber Region .................................................................................................. 68
3.7.3 Proportional Region ................................................................................................... 69
3.7.4 Region of Limited Proportionality ............................................................................. 69
3.7.5 Geiger-Mueller Region .............................................................................................. 70
3.7.6 Continuous Discharge ................................................................................................ 70
3.8 Ionization Chambers ......................................................................................................... 70
3.8.1 Current Voltage Characteristics ................................................................................. 71
3.8.2 The ionization current ................................................................................................ 72
3.8.3 Mechanical Design: parallel plate geometry .............................................................. 73
3.8.4 Choice of Gas ............................................................................................................. 77
3.8.5 Advantages and Disadvantages of Ion Chambers ...................................................... 77
3.9 Sources of Error in Gaseous Detectors.............................................................................. 79
3.9.1 Effects of contaminants .............................................................................................. 79
3.9.2 Recombination Losses................................................................................................ 82
Chapter 4 ..................................................................................................................................... 85
Collection efficiency: the ions recombination correction factor ................................................. 85
4.1 Introduction ....................................................................................................................... 85
4.2 Theoretical background ..................................................................................................... 87
4.2.1. Recombination rate ................................................................................................... 87
4.2.2 Collection efficiency for general recombination in continuous radiation beams ....... 88
4.2.3 Collection efficiency for general recombination in pulsed radiation beams .............. 93
4.3 The multiple gap ionization chamber ................................................................................ 97
4.3.2 Method for the determination of the collection efficiency ......................................... 98
4.3.3 Expected results........................................................................................................ 103
Chapter 5 ................................................................................................................................... 112
The read-out front-end chip characterization ............................................................................ 112
5.1 The TERA08 chip: Circuit architecture and operation mode.......................................... 113
5.2 Chip characterization....................................................................................................... 118
5.2.1 The experimental setup ............................................................................................ 120
5.2.2 The linearity test ....................................................................................................... 121
5.2.3 Count resolution ....................................................................................................... 128
5.2.4 Rest fluctuations ....................................................................................................... 134
Concluding remarks .................................................................................................................. 137
Acknowledgments ..................................................................................................................... 139
Bibliography.............................................................................................................................. 140
Introduction
The main goal of the radiotherapy is the local control of the tumor and of the
surrounding diffusion path. In order to reach this goal, a sufficiently high dose must be
delivered to the tumor in order to destroy it, while the surrounding healthy tissues must
be kept safe, so that they do not undergo serious or even irreversible damage or
complications [1] [2].
The main advantage of the hadrontherapy is that, when heavy ions cross the human
body they are few deflected, so that the tissue damage is reduced until these ions,
resting, release the main part of their energy as a peak. Taking advantage of this peak,
called “Bragg peak”, hadron therapy maximizes the dose delivered to the tumor sparing
the surrounding healthy tissue. The result is an increase of complication-free tumor cure
in comparison to conventional radiotherapy.
Nowadays the number of hadrontherapy centers for proton and carbon ions treatment
is constantly increasing. This type of therapy is not so widespread, principally because
of the high costs for building and operating the facilities. For this reason, the trend in
the new developments is towards the realization of smaller compact particle
accelerators. With these characteristics, an accelerator provides pulsed beam with a
much higher intensity in each pulse than conventional uniform beams for maintaining
the same released dose-per-treatment to the patient; therefore, also the related detectors
will have to cope with this high intensity pulsed beam structure.
The INFN in collaboration with the University of Torino, is developing an innovative
multi-gap monitor chamber, specifically designed for these applications. This detector
includes three parallel ionization chambers with independent anodes and cathodes
separated by a gap filled with nitrogen gas. The advantage of using different gaps is the
possibility to study and well estimate the effects of the ion recombination generated into
the gaseous detecting medium when a high ionization density occurs.
The read-out of the front-end is a critical part of the project. The core of this frontend electronics is the 64-channel ASIC, called TERA08 chip (developed by INFN and
University of Torino), consisting of a current-to-frequency converter followed by a
counter (the conversion is based on the recycling integrator principle [3]); the maximum
1
frequency of the converter is 20MHz. The ASIC was designed in CMOS 0.35 μm
technology. In previous applications of this chip, it was used with an input current range
well below the single channel frequency saturation. However, the high beam intensity
foreseen in the new compact accelerators will lead to an input current above the
saturation level of a single channel
The innovation for the read-out used in this project, are the parallel connection of the
entire chip channels and the use of one chip for each gap of the chamber. With this
setup, we expect a maximum input current 64 times higher, compared to the single
channel’s connection.
The contribution of this thesis mainly consists in:
•
the adjustment and the characterization of the chip TERA08, for the high
current range (the linearity of the current to frequency conversion, and a
study about the way the channels count).
•
the optimization of the electronic setup and the software for the data
acquisition;
•
the study of the collection efficiency for the multiple gap chamber (a
simulation with the aim to find the best configuration for the chamber, in
terms of voltages applied for the different gaps and thickness of the gaps,
with the aim to provide the best estimation for the collection efficiency).
The experimental setup that has been used to characterize the chips is based on a
FlexRIO FPGA module for a PXI platform National Instrument and Lab View software.
Data acquisition system (DAQ) is performed with a PC.
2
Chapter 1
Radiation therapy with heavy charged particles
1.1 Introduction
Since the beginning of clinical radiation therapy (RT), it has been the goal of
radiation oncologists to restrict the irradiated volume to the site and shape of the target
volume.
Several species of particles have been and are still the subject of intensive clinical
and radiobiological studies: neutrons, protons, pions, antiprotons, as well as helium,
boron, carbon and oxygen ions. Among all the different forms of external RT, ion
beams therapy is considered as the one getting closest to this goal. Currently, there are
30 facilities using protons for radiotherapy around the world and only few using carbonion beams. About 11 hadron therapy facilities (most of them using proton beams) are
planned for or are already under construction. The existing facilities are spread around
the globe, situated in North America, Russia, Asia, South Africa and Europe. According
to the patient statistics published by the Particle Therapy Cooperative Group (PTCOG),
108.238 patients were treated using hadron therapy by the end of 2012: 93.895 with
proton beams, 10.756 with Carbon ions, and 4.027 with other particles (Helium nuclei,
pions and other ions) [4].
The physical rationale to use protons and heavier ions in RT was conceived already
decades ago. In 1946, the Harvard physicist, Robert R. Wilson published his pioneering
paper on the radiological use of fast protons to “acquaint medical and biological
workers” with some of the physical properties and possibilities of ions [5].
As mentioned before, radiotherapy has two major goals: controlling disease and
reducing side effects. Taking into account these purposes, the reason of using hadrons in
radiotherapy is to deliver the dose to the target volume with a better localisation than
using conventional therapy with electron and photon beams (Fig. 1.1). In order to do
this, therapeutic ion beams offer the advantage of a depth dose distribution with a
3
pronounced maximum, named Bragg peak, and a sharp dose fall-off at large penetration
depth, in contrast to the exponential dose deposition of photons or neutrons, or the
broad maximum generated by electrons.
This is also known as an inverted dose profile and it allows a higher degree of dose
conformation to the target volume. The position of the peak as a function of depth is
dependent on the particle range and therefore on its initial energy. Since the peak width
is generally smaller than the tumour size, the beam needs to be modulated to obtain the
so-called "Spread-Out Bragg Peak" (SOBP), which allows to obtain a better
conformation of the dose to the target volume, with respect to conventional irradiation
(see Fig. 1.1). The spread-out Bragg peak (SOBP) is the result of several stacked
pristine Bragg curves and it can be obtained either with passive, or with active systems.
The former consist of absorbers of variable thickness, whereas the latter are based on
beam deflection by magnets and particle range variation by energy tuning [6].
Fig. 1.1: Schematic view of depth-dose distributions of photons and ions. (a) mega voltage
photon field, (b) spread-out ion beam, (c) depth–dose profiles of a and b along the central beam
axis [7].
The penetration depth of ions can be tailored precisely to coincide with the location
of the tumor to be treated. A finite path with maximum dose deposition close to the end
(Bragg peak) is an advantage shared by all ions as compared to photon irradiation. The
shallow entrance dose warrants that the radiation burden on the healthy tissue in front of
a deep-seated tumor can be kept low. The finite path limits the range of the radiation
field to the distal part of the tumor and spares structures beyond from radiation
exposure.
4
The carbon ions offer further advantages over protons or other lighter charged
particles: first, the lateral scattering in tissue is reduced roughly by approximately a
factor of 3. Second, carbon ions have an increased relative biological effectiveness
(RBE), especially in the stopping region at the Bragg peak, as it will be analysed in the
following sections.
1.2 Physical Properties
1.2.1 Interaction of photons and ions with matter
The different depth-dose profiles for ions and photons are due to the different way in
which they interact with the crossed medium.
When photons of short wavelengths (X or gamma rays) strike condensed matter, they
release electrons from the atoms stricken. The processes by which their energy is
transferred to the medium are stochastic events, such as inelastic or Compton scattering,
photoelectric processes and, at higher energies, pair production. Due to the statistical
nature of the absorption process and the fact that photons are strongly deflected
(scattered) during their interactions with atoms, a photon beam entering condensed
matter spreads rapidly and has no defined range.
The corresponding absorption curve of a photon beam reveals an initial build-up
domain, followed by a region of exponentially decreasing dose as shown in figure 1.2.
Fig. 1.2 Depth–dose distributions of various types of radiation in water [7].
5
In contrast to the indirectly ionizing electromagnetic radiation, radiation consisting of
charged particles (electrons, alpha particles, accelerated ions) is directly ionizing.
In classical mechanics, the transfer of kinetic energy is inversely proportional to the
square of the velocity v (dE/dx ~ 1/v2). Due to their low mass, accelerated electrons
reach rapidly high velocities close to the speed of light (at energies > 1 MeV); in this
situation, the energy loss per unit length becomes independent of the energy (dE/dx ~
1/c2). As a consequence, relativistic electrons deposit a constant energy dose per unit
length. In water with its density similar to tissue, this dose corresponds to approx.
2MeV/cm. The low mass renders electrons subject to strong lateral scattering.
Bremsstrahlung photons which are produced as a by-product of the stopping process of
the electrons in the field of the nuclei cause the low-intensity tail at the end of the
depth–dose curve (Fig. 1.2).
For protons and all heavier ions, the absorption curve in matter shows a slow initial
increase with penetration depth and a steep rise and fall towards the end of the particle’s
range (Figs. 1.1C and 1.2). Because of their much higher mass, ions experience
significantly less lateral scattering than electrons.
Atomic nuclei accelerated to the therapeutically relevant kinetic energy (approx. 50 –
400MeV/u) interact predominantly via coulomb forces with the target electrons of the
traversed matter. This leads to excitation and ionization of atoms along the track of the
traveling particle.
Quantitatively, the energy loss per unit path length, also called stopping power, of
these heavy charged particles is described by the Bethe-Bloch formula
−
2 m e c 2 β 2γ 2
dE 4πe 4 N A z 2 Z
ρ
ln
=
− ( relativistic _ terms )
dx
me c 2 β 2 A
I
(1.1)
where:
•
•
•
•
v
β = c , v is the speed of the particle and c the speed of light,
Na is the Avogadro’s number,
ze is the particle charge,
me is the rest mass of the electron,
6
•
Z, A, ρ and I are the atomic number, the mass number, the density and the mean
excitation energy of the medium.
For low particle velocity (v<<c, and β << 1), this formula can be reduced to
- dE/dx ~ Knoz2/v2 [ln (2me v2/I)].
(1.2)
where K is a constant, no the electron density of the target material. Under these
conditions, the stopping power varies mainly with z2/v2. With decreasing speed, dE/dx
thus increases. However, the projectile scavenges electrons, reducing its effective
charge Z. At E= 3Mc2 (M being the particle mass), the energy loss is minimal. For still
lower velocities, dE/dx increases logarithmically. Together, these effects produce the
sharp rise and fall at the end of the ion track (the Bragg peak) in the graphical
representation of energy loss or relative dose as function of penetration depth.
Most ion particles travel the same distance in a mono-energetic beam. But not all of
these do the same number of collisions. Their range is, therefore, somewhat different, as
explained in equation 1.3. This phenomenon is called straggling. In human tissues, the
straggling effect is of the order of 1% of the mean range for protons [8]. For heavier
ions, range straggling varies approximately inversely to the square-root of the particle
mass. This means that helium ions show only 50% and neon approx. 22% of the
straggle of protons (Fig. 1.3).
As the mass of the lightest ion, the proton (1H+), is already 1,836 times the mass of
the electron, a collision with an electron barely deflects the projectile ion from its initial
path. Still, multiple deflections result in lateral spreading or scattering and divergence of
the beam. In large parallel beams only the outer edges are affected.
In the centre, the number of particles scattering out is compensated for by others
scattering in. The central dose of narrow beams, however, decreases with depth, as
particles scattering out are no longer replaced (Fig. 1.4).
7
Fig. 1.3: Straggling as function of path length. Comparison of a proton, helium and neon beam
in water. Range straggling corresponds to the standard deviation σx of the range distribution of a
particle beam with mean range R. At first approximation, it varies inversely to the square root of
the mass of the particle.
Fig. 1.4: Lateral beam deflection as a function of path length. Data from LBL, Berkeley, USA
The transverse spread of an infinitely narrow proton beam amounts to approximately
5% of its initial range [8]. Just as for range straggling, the angular deflection from the
incident beam direction by multiple scattering decreases with increasing charge and
mass.
8
1.2.2 The Bragg peak width and energy spread
For a single particle, the maximum of its energy loss is much sharper according to
the Bethe-Bloch formula than the Bragg curve of a beam measured in an ionization
chamber. The width of the measured Bragg curve is caused by the multiple scattering
processes that yields an almost Gaussian energy loss distribution.
Because this width depends on the penetration depth Δx of the particles, for greater
particle energies and longer penetration, the half width of the Bragg maximum becomes
larger and the height smaller. The value of the width of the Bragg maximum determines
the gradient of the distal fall-off of the dose distributions. For a typical tumor treatment
in the head, ranges of 10 cm in depth are used that correspond to a FWHM of 4 - 5 mm
or a gradient of half of this value which is very good.
However, in practice, range profiles are more affected by the density distribution of
the penetrated tissue than by the intrinsic straggling. For smaller penetration depths,
frequently the half width of the Bragg maximum has to be increased artificially: in
active scanning, the beam delivered to the target volume is dissected into slices of equal
particle range, spaced of the width of the Bragg maximum. If the Bragg maximum is too
sharp, too many slices are needed to fill the complete target volume. In this case it can
be very advantageous to enlarge the Bragg maximum by a passive absorber system of 23 mm thickness in order to reduce the overall treatment time.
1.2.3 Spread Out Bragg Peak – SOBP
Bragg peaks are usually not wide enough to cover most treatment volumes. The
Bragg peak must thus be spread out over the full depth of the tumour. This can be
achieved either by the interposition of an absorbing material of variable thickness in the
beam path (passive spreading) or by the active energy modulation of the extracted
beam.
9
Fig. 1.5: The intensity modulated Spread Out Bragg Peak for a deep seated large tumour
volume, compared with a photon beam (left). Superposition of Bragg peaks to form a Spread
Out Bragg Peak (SOBP): the highest weight is assigned to the peak defining the distal end
(right).
The highest energy ions define the distal extend of the irradiated tumour volume, but
they also deposit energy, at a lower rate, in the plateau upstream of the end of their
range. Therefore, less intensity is necessary in more proximal layers of the tumour
volume, as some dose has already been deposited there (Fig. 1.4). A uniform dose in the
SOBP is achieved in passive delivery systems by several types of dedicated filters
(rotating wedge or propeller, Ridge filter etc.). The transverse dose spreading is
produced by passive scatterers upstream the whole set up, and the field contours are
limited by collimators.
Fig. 1.6: Schematic representation of a purely passive spreading system. A set of scatterers
guaranties a flat transverse dose distribution over a large field. Starting with a Single Bragg
Peak (SPB) a Ridge filter (in combination with an energy degrader of uniform thickness as
range shifter) produces the SOBP with correct intensity for each depth. A special compensator
conforms the distal surface of the radiation field to the distal surface of the target.
10
For carbon ions the use of absorbing materials has a clear disadvantage: nucleon
fragmentation imposes severe limits in the use of the beam. Nuclear reactions cause a
loss of primary beam particles and a buildup of lower-Z fragments, these effects
becoming more and more important with increasing penetration depth. The secondary or
higher-order projectile like fragments moves with about the same velocity as the
primary ions. They have in general longer ranges and produce a dose tail behind the
Bragg peak. The angular distributions of fragments are mainly determined by reaction
kinematics and forward directed, but much broader than the lateral spread of the
primary ions caused by multiple Coulomb scattering.
The use of a dynamic beam delivery system is typically used as it produces a desired
radiation field using variable extraction energy of the beam from a synchrotron and a
lateral magnetic deflection system.
1.2.4 The particle range
The range of a charged particle is the distance it travels before coming to rest. The
reciprocal of the stopping power gives the distance travelled per unit energy loss.
Therefore, the range R(T) of a particle of kinetic energy T is the integral of this quantity
down to zero energy:
𝑑𝐸 −1
𝑅(𝑇) = � �− � 𝑑𝐸
𝑑𝑥
𝑇
0
(1.3)
The range in function of v results to be:
𝑅(𝛽) =
𝑀
𝐹(𝛽)
𝑧2𝑍
(1.4)
where the function F(β) depends only on the velocity of the particle.
The particle range for hadrons is always specified in water; if a maximum
penetration depth of 30 cm is required, the energies range between 60 MeV and 250
MeV for protons and between 120 MeV/u and 400 MeV/u for carbon ions.
The range in mm for carbon ions at different energies is presented in Table 1.1.
11
Table 1.1: Range in mm at different energies and FWHM at different penetration depth for
carbon ions.
1.2.5 Magnetic Deflection for Active Beam Shaping
The narrow Bragg peak of a mono energetic beam, which is only a few millimetres
wide, is exploited in specific radiosurgery procedures. For most practical irradiations,
however, it is necessary to spread the radiation field laterally and in depth to cover a
larger target area (Fig. 1.1). Originally this has been achieved by using passive beam
shaping devices, such as scattering foils and energy modulating absorber media, which
broaden the beam profile transversely and extend the Bragg peak dose from the distal to
the proximal end of the target volume, respectively. However, the charge of the ions
offers still another way to tailor the irradiated volume very precisely to the shape of the
tumor: a pencil-thin ion beam can be deflected magnetically in horizontal and vertical
directions to irradiate the tumor slice using a grid of points. By reducing the energy
stepwise and repeating the irradiation for each slice, a tumor of arbitrary shape can be
successively irradiated from its most distal to the most proximal part [9-10].
This irradiation technique, which is only possible with protons and heavier ions,
permits the ultimate in tumor-conform RT, minimizing the radiation burden on healthy
tissue. In addition, it facilitates the application of individualized treatments with local
boosts or other desired nonhomogeneous dose distributions. It can be applied to increase
the dose in the tumor as compared to photon irradiation without increasing the dose in
the entrance channel, or to reduce unwanted radiation in the beam entrance without
changing the overall tumor dose.
12
1.3 Nuclear interactions
When a charged particle crosses the medium, it can decrease its velocity by
scattering with electrons but also interacting with atomic nuclei.
Because this interaction is electromagnetic, through the Coulomb force, the
phenomenon is called multiple Coulomb scattering. The Coulomb scattering of the
projectiles is described very precisely in the theory of Moliere [Moliere 1948].
This kind of interaction of therapeutic particles with air and human tissue is often
negligible for carbon ions but it is of crucial importance for protons which have a mass
12 times smaller. For the clinical application, the lateral scattering of the beam is more
important than the longitudinal.
Because of possible range uncertainties, the treatment planning will avoid a beam
directly stopping in front of a critical structure. Therefore, tumour volumes close to
critical structures can only be irradiated with the beam passing by. How close the beam
can get is consequently determined by the lateral scattering.
Also the kinematics of nuclear fragmentation reactions contributes to the lateral
width of a beam, predominantly at the distal side of the Bragg peak where the primary
projectiles are stopped and the residual dose is made up of contributions of nuclear
fragments only [11].
Measurements of this scattering, named Gaussian multiple-scattering [12], confirmed
the Moliere theory and a parametrization [13] for small angle scattering having an
angular distribution 𝑓(𝛼):
f (α ) =
1
2πσ alpha
 α2
exp −
 2σ α



(1.5)
𝜎𝑎𝑙𝑝ℎ𝑎 =
1
14.1 𝑀𝑒𝑉
𝑑
𝑑
𝑍𝑝 �
�1 + 𝑙𝑜𝑔10
�
9
𝛽𝑝𝑐
𝐿𝑟𝑎𝑑
𝐿𝑟𝑎𝑑
(1.6)
where σα is the standard deviation, p the momentum, 𝐿𝑟𝑎𝑑 the radiation length and d the
thickness of the material.
13
The particle scattering is used in proton therapy to spread the pristine pencil beam in
order to obtain a larger and homogeneous dose distribution, similar to that used with
photons.
Consider a particle beam passing through various absorbers and scatterers and
stopping in a water tank. Some of the particles undergo nuclear interactions on the way,
either in the absorbers and scatterers or in the water. At any given point we call those
particles primaries which have only suffered EM interactions. Particles resulting from
nuclear reactions are secondaries.
Possible secondaries from non-elastic reactions at therapy energies are protons,
neutrons, heavy fragments such as alphas, X rays, and the recoiling residual nucleus.
Secondaries usually are emitted at large angles with the beam direction unlike primaries
which, even after multiple scattering, rarely exceed a few degrees. This means that
secondaries produced upstream in scatterers or absorbers will clear out of the beam for
purely geometric reasons before entering the volume of interest.
Because these nuclear reactions take place mostly at energies of several hundred
MeV/u, they can be approximated in a two steps process. First, the collision that takes
about 10-23 sec and generates partially excited pre-fragments which is followed by the
de-excitation by nucleon evaporation and the emission of photons, forming the final
number and size of fragments, that takes 10-21 to 10-16 sec.
For carbon ions, the small amount of nuclear fragmentation of the projectile and the
production of positron emitting carbon isotopes
10
C and
11
C that can be exploited for
verifying the delivered dose by the measurement in coincidence of the two
𝛽 + annihilation quanta.
An important consequence of the nuclear interactions is the activation which occurs
on the nozzle and also in the patient because of the neutrons produced in the irradiation.
The latter requires specific shielding and has to be reduced as much as possible to avoid
unwanted dose to the patient. One solution is to limit the elements along the beam lines
between the accelerator exit and the patient surface.
The fragments and nuclear effects should be evaluated explicitly and included in the
treatment planning, in particular when heavy ions are used. A simple solution adopted is
to use measured rather than theoretical Bragg peaks for the depth-dose.
14
1.4 Biophysical Properties
1.4.1 Physical Dose
The physical absorbed dose is defined as the energy absorbed per unit target mass:
𝐷≡
𝑑𝐸
,
𝑑𝑚
1𝐺𝑦 ≡ 1
𝐽
≡ 100𝑟𝑎𝑑
𝐾𝑔
(1.7)
The energy absorbed by the target material may be less than the energy lost by the
radiation. Protons, for instance, have nuclear interactions which produce neutrons
among other secondaries. The neutrons, because of their lower interaction, will usually
stop in the shield walls of the radiation therapy facility. This lost energy typically
amounts to a few percent.
The following equation relates physical absorbed dose to fluence ϕ (particles per unit
area) and stopping power:
𝑑𝐸
𝛥𝑥 𝑁
𝑑𝐸
𝐷≡
= 𝑑𝑥
𝑑𝑚
𝑑𝑚
that means
𝐷=𝜙
(1.8)
𝑆
𝜌
(1.9)
𝑆
where 𝜌 is the effective mass stopping power derived from a measured Bragg peak.
1.4.2 Stopping Power and LET
The linear energy transfer or LET is a measure for the energy deposited by an
ionizing particle traveling through matter. The LET [keV/μm] changes with the charge
and energy of a projectile along the particle track. Its depth dependence yields the
characteristic Bragg maximum. It is closely related to the stopping power described in
Equation (1.1). While stopping power can be seen as a material property (depending on
electron density), which describes the energy absorbed by matter, LET describes the
energy transfer to the medium, and so, it describes what happens to the particle.
15
If all the secondary electron energies are considered, LET, numerically, equals stopping
power.
For charged particles the LET increases when:
•
the particle velocity decreases (LET ̴ 1/ v2)
•
the particle charge increases (LET ̴ Zeff2), Zeff is the effective particle charge.
The LET of photons and ions in tissue obeys different physical processes leading to
totally different depth dose profiles. While in the MeV domain the depth profile of
photons is dominated by hard collisions absorbing a large fraction or the entire energy
of the incident photon, the energy loss of ions is caused by a large number of soft
collisions (Fig 1.7).
The dose density along the track for different ions, i.e., the number of secondary
electrons produced, changes. According to Equation (1.1), the deposited dose increases
with decreasing velocity and with the incident ions effective charge square. As heavier
ions can have higher charge states than the singly charged protons, they can also have
higher ionization densities.
Fig. 1.7: The linear energy
transfer from photons to tissue
is dominated by one single
reaction per photon (a). This
leads basically to an exponential
attenuation function (b). For
ions only a small fraction of the
projectile energy is transferred
to an individual electron and the
final absorption is dependent on
the high number of free
electrons, such that the range is
nearly a deterministic function
of the incident energy. Note that
the angular deflection is
dominated by scattering on the
target nucleus, with a very small
amount of energy transfer only.
16
the LET is related with the Dose through the following relation:
Dose (Gy) = 1.6 ∗ 10−19 LET
ϕ
ρ
(1.10)
where ϕ is the fluence (particles/cm2); ρ is the density (g/cm3). Because the physical
and biological properties of proton beams differ significantly from those of heavier
particles, hadron therapy can be divided in proton therapy characterized by low LET,
and heavy-ion therapy with high LET properties.
1.5 The biological effects of the radiation
When ionization radiation interacts with matter, a fraction of its energy, quantified
through the absorbed dose, goes into the excitation and ionization of the atoms in the
matter. In the living matter, the absorbed energy causes chemical and biological effects
at the cells which propagate up to the tissue level. Cells are highly complex structures,
systems of many thousands of different molecules that can be damaged during the
ionizing process.
It is known that dividing cells are more sensitive to radiation than non-dividing cells.
It has been also discovered that radiation will kill dividing cancerous cells more readily
than healthy cells, which are less likely to be undergoing mitosis; therefore controlled
amounts of radiation, directed at concentrations of cancerous cells, do more damage to
the cancer than they do to the residual normal cells of the patient body.
The primary ionization processes in living organism trigger a large number of events
that eventually lead to chemical transformations in some important biomolecules,
alterations which can cause mutation, transformation or cell apoptosis. For small
amounts of doses only small targets become damaged. This implies non-fatal damage in
the cell, which allows for regeneration after some time. Conversely, if one was to
overcome this limit, cells then become unable to regenerate, as a result, they will perish.
The loss of reproductive integrity is caused by radiation through ionization that
damages the DNA, contained into the main sensitive structure of the cell, its nucleus.
The break of one of the two strands which compose DNA (Single Strand Break, SSB) is
generally not sufficient to cause cell inactivation, since it is readily repaired using the
17
opposite strand as a template. On the contrary, the break of both strands within a few
DNA base-pairs (Double Strand Break, DSB) represents a more serious damage, hardly
repaired, which is strongly correlated to cell inactivation (Fig. 1.9) [14], [15].
Fig. 1.9: A schematic representation of the particle interaction with the cellular tissue. The
heavy ions have higher probability to perform a double strand break than protons.
From a biological point of view a cell is in apoptosis if it has lost its capacity for
sustained proliferation or has lost its reproductive integrity. This means that a cell may
still be physically present in the biological system and apparently intact, but it has lost
the capacity to divide indefinitely and to produce a large number of progeny. Cell
survival to ionizing radiations is a relevant biological endpoint to plan radiotherapy and
hadron therapy treatments since it can be linked to the probability of tumour control.
Generally, cell survival is estimated by in vitro measurements of cell-survival curves,
which draw the survival probability expressed as a function of the dose delivered by the
irradiation facility (Fig. 1.10).
18
Fig. 1.10: Characteristic cell survival curve as a function of dose for low-LET x-rays and highLET charged particles. Higher LET radiations increase the slope of the cell survival curve,
resulting in a larger RBE per unit dose. The shoulder of the x-ray curve is probably due to repair
processes.
1.5.1 Relative Biological Effectiveness
Even though LET is not a good parameter to describe the full spectrum of biological
radiation effects, it is still a widely used quantity to categorize ion-induced damage. The
limitations of LET become particularly prominent when ions of different atomic number
are compared. In particular for LET values greater than 100 keV/μm, different
biological responses can be observed for particles of the same LET but different atomic
number.
A coefficient of relative biological effectiveness (RBE) is introduced to take into
account the dissimilarity in the effect of radiations of various types for the same
physical dose. RBE is defined [16], [17], as the ratio between the absorbed dose of a
reference radiation, typically X-rays, and that of the radiation used, required to produce
the same biological effect S:
𝑅𝐵𝐸𝑆 =
𝐷𝑋
𝐷𝑇
(1.11)
The difference in radiobiological effectiveness between X ray and ion irradiation
arises from the different ionization pattern they produce. In fact, photons are sparsely
ionizing particles, since generate ionization events which are well separated in space
along the track (Fig. 1.9). Conversely, ions are densely ionizing in virtue of the dense
19
column of ionizations produced around the ion path. Thanks to the high ionization
density, ions are usually more effective in producing DSBs than photons. Therefore, the
survival probability that corresponds to an ion irradiation is, for the same dose,
generally lower than that obtained with X rays and steeper S(D) curves are observed
(Fig. 1.10). The RBE is a rather complex quantity as it depends on linear energy transfer
(LET), dose per fraction, the amount of projectile fragmentation, the cell or tissue type
irradiated as well as on the selected biological endpoint.
For several biological end points, a characteristic relation is observed between the
change in LET and the RBE of a specific particle beam. For protons for example, the
biological effect increases throughout the Bragg peak, reaching a maximum near the
distal edge of the peak.
As the particles' velocity continues to decrease and LET to increase, the killing
efficiency per unit dose decreases. Figure 1.11 shows the relation between LET and
biological effect for different ions. The LET at which the maximum RBE is observed is
particle specific. Carbon exhibits a maximum RBE, over a larger LET range than
protons
Figure 1.11: RBE measurements performed using different ions and a wide range of LET
values. There is not a single RBE- LET relationship for all the ions: the maximum of ion
effectiveness shifts towards higher LET values for heavier ions and height of the peak decreases
for heavier ions.
The decreasing RBE for too large LET is due to an overproduction of local damage
(“overkill-effect”) resulting also in an effective saturation. The increased RBE can be
explained by the increased ionisation density which causes a cluster of produced
damages.
20
1.5.2 Oxygen Enhancement Ratio
Oxygen acts as sensitizer, rendering cells more susceptible to radiation damage.
When cells are irradiated with photons or low-LET ions, they can undergo different
survival behaviour, depending on the presence or absence of oxygen (Fig. 1.12).
The oxygen enhancement ratio (OER) of radiation is the dose D required to produce
a certain biological effect E in the absence of oxygen (anoxic conditions) to the dose
required to produce the same effect in the presence of oxygen (oxic conditions),
𝑂𝐸𝑅 =
𝐷𝑎𝑛𝑜𝑥𝑖𝑐 (𝐸)
𝐷𝑜𝑥𝑖𝑐 (𝐸)
(1.12)
For X-rays, the OER ranges from 2.5 to 3 which means, a 2.5–3 times higher X-ray
dose is required to kill oxygen-deprived cells rather than the same cells under aerobic
conditions. Many independent studies have shown that the OER-value begins to
decrease at LET values of ≥ 100 keV/μm approaching unity between 150 and 300
keV/μm depending on the biological system used [18] [19].
For many biological systems the oxygen dependency of radiation response increases
up to an oxygen pressure of approx. 20mmHg (2.700 Pa). Well vascularized normal
tissues exhibit oxygen pressures of ≥ 40mmHg. They should, therefore, be fully
radiosensitive as far as the oxygen effect is concerned.
In experimentally-induced animal tumors hypoxic cells have routinely been found.
For human tumors, the existence of hypoxic cells is recognized but their clinical
significance is debated. The fact that severe anemia during RT is associated with worse
local control in a variety of cancers underlines the importance of sufficient oxygen
supply [19].
21
Fig. 1.12: Cell survival curves of human kidney T1 cells after irradiation with ions or X-rays in
air or nitrogen atmosphere, respectively.
But considerable intra- and inter-individual variations in oxygenation among tumors
of the same clinical stage and grade make general statements difficult.
It was found that the minimum OER is lower for heavier ions such as carbon or neon
than for light ions e.g., helium. It is supposed that, the potential higher radiation damage
of ions by direct hits compared to indirect radical-induced hits reduces the oxygen
effect. Along with a reduction of the OER the RBE is further enhanced in the SOBP.
Therefore, heavy particles such as carbon ions offer enormous potential for curing
tumors with hypoxic regions.
1.5.3 Biological effective Dose
Cell inactivation is a crucial issue in radiation-induced biological damage, since it is
the main aim of the radiotherapy. In principle ionising radiation can kill the cells of any
tumour tissue, if the provided doses are sufficiently high. However, the maximum dose
that can be delivered to a tumour is limited by the tolerance of the normal tissues
surrounding the tumour itself. The simultaneous maximisation of Tumour Control
Probability (TCP) and minimisation of Normal Tissue Complication Probability
22
(NTCP) is the main goal of treatment planning, especially for tumours located in close
proximity of critical organs/tissues [20].
As opposed to most of the therapeutic radiation beams (excluding neutrons), owing
to the strong dependence of the biological response on the energy of carbon ions in
clinical applications it is common to use a biological effective dose instead of a physical
dose:
𝐵𝐸𝐷 = 𝐷𝑃ℎ𝑦𝑠 . 𝑅𝐵𝐸
(1.13)
The unit of measure for this quantity is named Sievert or Gray Equivalent, which has
the same dimensions as the Gray (J/kg) but it measures a different quantity. Due to the
RBE, the BED varies with depth, and the type of tissue so, the lack of uniformity of the
physical dose distribution in the SOBP being obvious. The difference between the
distributions for different types of tissues can be seen in Fig 1.16.
For protons, a global RBE value of 1.1 is commonly adopted. Although there are
experimental data showing that the RBE may increase up to 2 at the distal edge of the
Bragg peak, this is not considered to be clinically relevant. As the RBE for protons is
assumed to be a constant factor, it has no impact on the dose optimization algorithm.
For carbon ions, the RBE increases strongly with LET and hence depth. A more
detailed RBE model is therefore required. To achieve a homogeneous biologically
effective dose within the target volume, the absorbed dose must decrease with
increasing depth. Due to the nonlinear dependence of the RBE on absorbed dose, this
optimization process is more difficult than for protons, especially for the simultaneous
optimization of multiple fields.
23
Fig. 1.13: Biological effective depth dose distributions for a clinical carbon-ion beam calculated
for different tissue types.
As one can see from figure 1.13, a uniform damage of tumour cells is not obtained
by simply requiring a constant physical dose delivery on the target, because a flat dose
SOBP does not necessarily correspond to a flat biological effect. In fact, the information
of delivered dose alone is not sufficient to determine the biological effectiveness of a
carbon-ion beam: a beam composed by ions of low kinetic energy is more efficient in
inactivating cells than another beam depositing the same dose but with ions of higher
kinetic energy. To account for these differences, several biophysical models have been
developed which are described in the following.
1.6 Biophysical models
The beam characteristics (distribution of kinetic energies and ion species) change
during tissue penetration due to the energy loss, straggling and fragmentation. For these
reason in each point treated, a superposition of many beams is needed. A Treatment
Planning System (TPS) is used to compute the inactivation probability relative to the
cells in a certain location on the basis of the statistical knowledge of how many and
which particles have passed by. In other words, the TPS computes in an efficient way
the biological effectiveness of treatment beams, on the basis of biophysical models.
24
Two widely used models are subsequently described: the Kinetic Micro-dosimetric
Model and the Local Effect Model (LEM), developed at GSI Darmstadt and is currently
used at HIT Heidelberg (Germany).
1.6.1 The Micro-dosimetric Kinetic Model (MKM)
The MKM has been developed since 1994 by Roland B. Hawkins, a Medical Doctor
of the Radiation Oncology Center in New Orleans, Louisiana. Recently, this model has
been adopted by the researchers of the Tokyo Institute of Technology and of the
National Institute of Radiological Sciences (NIRS) in Chiba, Japan [21], [22]. The
MKM descends from the pre-existing Theory of Dual Radiation Action (TDRA) [23].
The MK model extends the fundamental assumption of the TDRA model by
considering that lethal (non-repairable) lesions are due not only to the association of two
sub-lethal lesions, but also due to some of a sub-lethal lesions not being repaired after a
certain amount of time (a number of completed mitotic cycles) (see Fig. 1.14).
The MK model proposes the following mathematical expression for the average
number of lethal lesions after that z sub-lethal lesions are created in a domain d:
𝜀(𝑧) = 𝐴𝑧 2 + 𝑘𝑧 2
(1.14)
Since the effect produced by a single track should be proportional to dose D while
two-track action should be proportional to the square of the dose, the dose-effect
relationship for this model should be of this form:
𝜀(𝐷) = 𝑎𝐷 + 𝑏𝐷 + 𝑐𝐷2 = (𝐴 + 𝐵)𝑑 + 𝑐𝐷2
(1.15)
where a, b and c correspond to the probabilities of occurrence of a non-repairable 1
track-SSB, 1 track-DSB and 2 track-DSB respectively. It can be derived that the
corresponding dose-effect relationship obtained from the previous equation is:
𝜀(𝐷) = (𝛼0+ 𝛾𝛽)𝐷 + 𝛽𝐷2
(1.16)
25
in which: α0 = the probability associated with 1 track-DSB damage, γβ = the probability
associated with 1 track-SSB damage; β = the probability for 2 tracks-DSB damage.
Fig. 1.14: Interaction types considered in the MK model. The upper figure represents a single
strand break whereas the others, represent a double strand breaks (left) and two single strand
breaks (right).
The terms α0 and β can be expressed as a function of kinetic parameters, while the
parameter γ is related to the dimensions of the domains within the cell nucleus that
contains the critical targets and also to the LET of the radiation used to irradiate them:
𝛾=
0.229
. 𝐿𝐸𝑇
𝑑2
(1.17)
where d represents the domain’s dimension (in μm); the LET is expressed in keV/μm.
1.6.2 The Local Effective Model (LEM)
The LEM is a model proposed by Scholz and Kraft of the GSI Biophysical
department, with the aim to determine the RBE values in the treatment planning
process, for patients undergoing ion therapy at GSI Darmstadt (Germany).
The principal assumption of the LEM is that the local biological effect, i.e. the
biological damage in a small sub-volume of the cell nucleus is determined only by the
expectation value of the energy deposition in that sub-volume and is independent of the
particular radiation type leading to that energy deposition. This is similar to the microdosimetric approach, but is applied to much smaller volumes at the nm scale as
26
compared to the μm scale of micro-dosimetry (let’s remember that, the human cell
diameter is 10-100 μm). For a given biological object, all the differences in the
biological action of charged particle beams should then be attributed to the different
spatial energy deposition pattern of heavy charged particles compared to photon
irradiation, i.e. on track structure at the nm scale. Moreover, for a given radiation type,
differences in the photon (X-rays) dose response curve for different biological objects or
tissues should also lead to corresponding differences in the RBE. In fact, while for X
rays the expectation value of the energy deposition in small volumes is constant over
the cell nucleus, in the case of ion irradiation it is sharply peaked and dependent on the
traversal position of ions. Then for X rays the local dose-effect curve coincides with the
global dose-survival curve, whiles for ions a double averaging, over the cell nucleus
volume and over the statistics of traversals is included in the global survival curve.
The three main ingredients of the LEM are the following:
•
Photon survival curve: The linear-quadratic (α, β) model serves as the
parameterization of the dose–effect curve after photon irradiation.
Above a cell specific threshold dose Dt, the survival curve is assumed to be
purely exponential.
•
(b) Radial dose profile: Within an inner core of 10 nm around the track centre,
the dose is supposed to be constant. For higher radii, the dose decreases with 1/r2
up to a cut-off radius given by the maximum energy of delta-electrons.
•
(c) Target geometry: The cell nucleus is assumed to be a cylinder with radius rn
determined by measurements.
For photon radiation the density of lethal events VX(D) in the cell nucleus can be
defined as follows:
𝑉𝑋 (𝐷) =
��������
𝑁
−ln 𝑆𝑋 (𝐷)
𝑋 (𝐷)
=
𝑉𝑛𝑢𝑐
𝑉𝑛𝑢𝑐
(1.18)
27
where VNuc is the volume of the cell nucleus, D is the dose, NX(D) represents the
average number of lethal events produced by photon radiation in the nucleus by a dose
D and SX(D) denotes the cell survival probability at a dose D.
Given the complete local dose d(x, y, z) distribution, according to the impact
parameters of a given set of impinging ions, the average number of lethal events
induced per cell by heavy ion irradiation can be obtained by integration of the local
event density υion(d(x, y, z)):
�������
𝑁𝑙,𝚤𝑜𝑛 = � 𝑣𝑖𝑜𝑛 �𝑑(𝑥, 𝑦, 𝑧)�𝑑𝑉𝑛𝑢𝑐
(1.19)
The fundamental assumption of the LEM is that the local biological effect is
determined by the local dose, but is independent of the particular radiation type leading
to a given local dose:
𝑣𝑖𝑜𝑛 (𝑑) = 𝑣𝑥 (𝑑)
(1.20)
Thus, equal local doses correspond to equal local biological effects:
�������
𝑁𝑙,𝚤𝑜𝑛 �
− ln 𝑆𝑋 (𝑑(𝑥, 𝑦, 𝑧))
𝑑𝑉𝑛𝑢𝑐
𝑣𝑛𝑢𝑐
(1.21)
The Equation 1.21 clearly shows the theoretical link between the biological effect of
photon radiation and ion radiation. The integrand is fully determined by the low-LET
response of the object under investigation; the particle effect is ‘hidden’ in the
inhomogeneous local dose distribution d(x, y, z). This formula is the most general
formulation of the local effect model; it does not rely on any particular representation of
the photon dose response curve. It can be applied even if only numerical values of
SX (D) are available. However, for practical reasons, a linear-quadratic approach for the
low-LET dose response curve is generally used.
In this case the average number of lethal events is parameterized as:
2
��������
𝑁
𝑋 (𝐷) = − ln 𝑆𝑋 (𝐷) = ∝ 𝐷 + 𝛽𝐷
(1.22)
28
Since at high dose, for many biological objects a transition from the shouldered to an
exponential shape of the dose response curve is observed, a modified version of the
linear–quadratic approach is used. This transition is described by a parameter Dt (Fig.
1.15), representing the transition dose to the exponential shape with slope
smax = α + 2βDt, so that the dose response is finally given by:
α x D + β x D 2
− ln S = 
α x Dt + β x Dt 2 + Smax ( D − Dt )
D ≤ Dt
D > Dt
(1.23)
Usually, the dose Dt cannot be directly derived from experimental data, since
survival curves can be measured only down to 10-3 for most mammalian cell lines; Dt
represents thus a semi-free parameter of the model. In general, Dt values in the order of
15–30 Gy allow consistent descriptions of the experimental data.
The Local Effect Model (LEM) has been heavily criticised, the principal objection
being the very fundamental assumption of the model, i.e. that equal numbers of local
deposition events implies that a low-LET survival curve can be used to obtain the effect
produced by high-LET radiations. This proposition may be true within the cell nucleus
at the nano-scale, but when considering the entire nucleus volume, and therefore a
higher value of the hit cross section, the probability of successful hits are entirely
different for X-rays and ions and, subsequently, for their effect too.
Fig. 1.15: The modified version of the linear-quadratic surviving curve used by LEM [24].
Recent developments of the LEM taking clustered DNA damage into account were
introduced [25], significantly enhancing the accuracy of the predictions.
29
Chapter 2
Accelerators for hadrontherapy treatments
2.1 Introduction
From 60ties to the mid 80ties of the 20th century particle radiotherapy was based
exclusively on accelerator facilities developed for nuclear physics, with beam-lines and
treatment rooms adapted to the needs of radiotherapy.
An essential occurrence in particle therapy was the beginning of the construction and
installation of dedicated accelerators in hospital–based clinical centers. The first was the
MC60 62.5 MeV proton cyclotron, delivered by Scanditronix, operating at the
Clatterbridge Oncology Centre (UK) since 1989. This cyclotron has been used for fast
neutron radiotherapy and proton therapy of eye melanoma and is still used (2014) for
treatment of ocular tumors. The next major step was the installation at Loma Linda
University (California, USA) of a dedicated 250 MeV proton synchrotron, developed by
FermiLab, in 1990. It was the first dedicated clinical facility equipped in three rotating
gantries.
Another essential improvement was the application of scanning beams, which allow
“painting” the dose within the tumor volume. The first scanning systems were
developed in the research facilities at PSI (Villigen, Switzerland) for protons and GSI
(Darmstadt, Germany) for carbon ions and have been used to treat patients since 1996
and 1997, respectively. More recently scanning beams have started to be used on a
routine base in several clinical facilities, such as at the Rinecker Proton Therapy Center
in Munich, the Heidelberg Ion-Beam Therapy Centre (HIT), the Centro Nazionale di
Adroterapia Tumorale (CNAO) in Pavia, and at Hessen, Darmstadt.
In Fig. 2.1 is reported a graph, representing the evolution of the number of proton
therapy centres in the world between 1950 and 2015.
Fig.2.1: Evolution of the number of proton therapy centres in the world between 1950 and 2015.
30
In Fig. 2.2 and 2.3, is showed in detail, the worldwide distribution of proton and
carbon ion centres, with the related number of treated patients.
Fig. 2.2: Proton (red-orange) and C-ion (green) centers active worldwide. The size of the spot is
proportional to the number of patients treated as indicated in the figure legend. Detailed maps
for Europe and Japan are given in Fig. 2.3.
Fig. 2.3: Proton (red-orange) and C-ion (green) centers active in Europe and Japan. The size of
the spot is proportional to the number of patients treated as indicated in the figure legend.
31
In the first part of this chapter, are described the cyclotron and the synchrotron as the
currently most used accelerators for therapy with heavy ions. Subsequently, there is a
description about the characteristics and the technology of new ions accelerators
developed: the superconducting cyclotron, the Fixed-Field Alternating-Gradient
accelerator and the cyclinac.
In the final part of the chapter, we talk about the future perspective in this field: the
rotating synchrocyclotron, the Dielectric Wall Accelerator, the Turning Linac for Proton
Therapy and the Laser-driven accelerator.
In the entire chapter, the characteristics and the properties of these accelerators, are
correlated to the various projects already developed or under development.
2.2 Accelerators requirements
The overall goal of an accelerator for therapy with protons and heavier ions is to
produce a beam that penetrates 26-38 cm in human tissue. Translated in particle energy,
incident protons of 215 MeV are required on the patient surface and the beam emerging
from the accelerator must have energy between 200-250 MeV. For carbon ions the
beam energy at the accelerator exit must be between 300-400 MeV/u. In addition beam
must have sufficient intensity to allow therapeutic doses to be delivered within few
minutes. Typically beam intensities of between 1.8 x 1011 and 3.6 x 1011 particles per
minute are required if doses of 2 Gy/min are delivered uniformly to target volumes of
one litre [26].
The physical process of particle acceleration is described with the Lorentz force
laws:
𝐹� = 𝑞𝐸� 𝑎𝑛𝑑 𝐹� = 𝑞𝑣 𝑥 𝐵� .
(2.1)
This formula explains that an electric field 𝐸� increases the energy of a particle with a
charge q while a magnetic field 𝐵� describes its motion.
A particle accelerator used for radiotherapy, has to produce beams with sufficient
energy to reach the deepest tumors and conventional linear accelerators (LINACs) do
not produce sufficient electric field to build a compact system for hadron therapy.
32
Therefore, in order to accelerate charged particles in a compact machine, it is effective
to reuse the electric field, like a circular accelerator does.
2.3 Present accelerators for hadrontherapy
Nowadays 35 cyclotron or synchrotron based-facilities all around the world, offer
proton therapy and 6 synchrotron-based centres provide carbon ion therapy.
One of the main reasons why the hadrontherapy is not widespread is the high costs
for realization. Let’s consider that, for typical energy used in hadrontherapy, a 200-250
MeV protons beam is provided by a 4-5 m diameter cyclotron or by a 6-9 m diameter
synchrotrons whereas, a 400 MeV/u carbon ions beam is provided by a 18-25 m
synchrotron. Despite these dimensions entail high costs, about one third of the total
investments of a therapy system is used for the accelerator, the rest is for the building,
equipment, etc.
A detailed description of the cyclotron and the synchrotron, are presented in the
following sub paragraphs.
2.3.1 The cyclotron
In the cyclotron charged particles move in an outgoing, spiral trajectory. A highfrequency alternating voltage applied across the gap between the two halves ("dees"
electrodes) alternately attracts and repels charged particles. A magnetic dipole field
covers both the "dees" so, a perpendicular magnetic field (passing vertically through the
"dees" electrodes), combined with the increasing energy of the particles, forces the
particles to travel in such spiral way.
With no change in energy the charged particles in a magnetic field will follow a
circular path. In the cyclotron, energy is applied to the particles as they cross the gap
between the electrodes. The polarity of the electric field is switched at the exact time
when the beam reaches the gap to ensure acceleration of the beam and not deceleration.
The radiofrequency (RF) of the electric field, needed to synchronize the path of the
charged particle with the phase of the electric field, is given by the cyclotron equation:
33
𝜔=
𝑞𝐵
𝑚
(2.2)
where 𝜔 is the angular frequency of the electric field, q and m are the charge and the
mass of the particle and B is the transverse magnetic field. Since the magnetic field B is
nearly constant, the radius of the circle increases and so the maximum energy depends
on the Cyclotron dimension. Cyclotrons for hadrontherapy have relatively few
adjustable parameters, and produce continuous wave beams.
Fig. 2.4: A schematic representation of a cyclotron
2.3.2 The synchrotron
In a synchrotron, both the magnetic field and the frequency of the electric field
change. By increasing these parameters appropriately as the particles gain energy, their
path can be held constant as they are accelerated.
The beam is injected in the synchrotron ring by, typically, a LINAC with energy of 3
to 7 MeV. To achieve acceleration, the magnetic field and the frequency of the
accelerating electric field increase must be synchronised. Because of the finite time
required to cycle the magnets, synchrotrons produce a pulsed output. Typically the
beam acceleration cycle takes ~ 200 ms to 4 s and beam extraction occurs over a similar
period. The pulse repetition rate is therefore typically 0.5-2 Hz.
When the beam reaches the desired energy it is extracted and directed to the
treatment room through the beam transport system.
34
Fig. 2.5: A schematic view of a
synchrotron. Beam bending and
focusing are accomplished with
magnetic fields. Dipole magnets
bend the beam in a closed orbit.
Quadrupole magnets (grouped as
quadrupole lens sets) focus the
beam. Sextupole magnets are
usually included to increase the
tolerance of the focusing system to
beam energy.
2.3.3 Models and properties
In the 90s, the idea was that the best accelerator for proton therapy was a
synchrotron, however today most of the proton therapy centres are using cyclotron
technology (IBA, Varian, Still Rivers…).
In these 15 years users appreciated the advantages of cyclotrons:
• Simplicity
• Reliability
• Lower cost and size
• Rapid and accurate proton beam current modulation.
The greater handicap in using cyclotrons is that they deliver a fixed energy beam and
so absorbers are needed to change the beam energy during the treatment. By contrast, a
synchrotron can provide all the required energies delivering a pulsed beam, achieving
some important benefits:
• variable energy operation
• easy dose management
• ion beams for treatment.
35
About the latter advantages, worldwide few proton therapy centers use the
synchrotron technology (for example Hitachi and Mitsubishi) while all ion (p, C) beam
centers use synchrotron to perform both proton and carbon ion treatments with the same
accelerator.
The cyclotron is a simpler and easier to use accelerator and produces a continuous
beam suited for active beam scanning, but the energy is fixed and the required beam
energy degraders introduce an extra momentum spread. Additionally, the recent
superconducting design allows a very compact accelerator but the magnet is weighty,
difficult to manage and the time for maintenance could be long. On the other hand, the
synchrotron requires expensive injectors and sophisticated controls but the techniques
are well known and the repair times are short.
Fig. 2.6: representation of the Heidelberg Ion Therapy (HIT) centre. This synchrotron
accelerates protons and helium, oxygen, carbon ions. The gantry consists of a beam line that
directs the beam onto the patient at whatever angle is required for the treatment plan
optimization.
Example of a commercial cyclotron
The most used particle accelerator for proton therapy is the C-235 isochronous 230
MeV proton cyclotron produced by IBA (Ion Beam Application, a spin-off of the
accelerator physics development from the Louvain-la-Neuve University). The first
cyclotron of this type was installed at Harvard Medical School in Boston and it is
currently used in 13 hadron therapy centres around the world. The cyclotron is coupled
with a degrader and energy selector, which aims to reduce the 230 MeV mono energetic
(ΔE/E < 0.7%) proton beam extracted from the cyclotron to an arbitrary energy down to
36
70 MeV. The beam passing through a carbon or beryllium degrader increases its
momentum spread, which is next reduced by system of splits and magnets. However,
decreasing of proton energy leads to the reduction of the proton current up to two orders
of magnitude, which might be inconvenient for some application such as e.g. eye
treatment. A superconducting 250 MeV cyclotron developed by ACCEL Instruments is
now offered by Varian Medical Systems. These cyclotrons are currently used at PSI
Villigen and the Rinecker Proton Therapy Centre, while a few more are currently being
installed and constructed for centres in the USA. This cyclotron is equipped with a
similar degrader and energy selection system as the IBA C235 cyclotron.
Fig. 2.7: IBA’s C235 cyclotron.
Example of a synchrotron
The first commercial synchrotrons for proton and carbon ion therapy were produced by
Mitsubishi (12C 70 - 380 MeV/u and protons 70 - 250 MeV). This is a high intensity
machine (6 x 1010 protons/pulse, repetition rate 0.5 Hz). It is currently installed in 7
therapy centres in Japan.
A significant contribution to the development of synchrotrons for hadron therapy
came from accelerator physicists in Europe. The synchrotron at CNAO is a prototype
resulting from the research in high energy physics made possible through the
collaboration of CERN (Switzerland) with the Istituto Nazionale di Fisica Nucleare
(INFN, Italy), GSI (Germany), LPSC (France) and the University of Pavia (Italy).
37
Fig 2.8: Overview of the synchrotron ring of CNAO (Pavia).
Another version of this synchrotron is now under installation at MedAustron therapy
centeer in Wiener Neustadt in collaboration with CERN. It will produce both proton and
carbon ions, with intensity ≤ 1 x 1010 per pulse for protons and ≤ 4 x 108 per pulse for
carbon ions, energy of protons: 60-250 MeV (up to 800 MeV for research) and carbon
ions 120-400 MeV/n, repetition rate: 0.5 Hz and extraction time 0.1-10 s.
2.3.4 Facilities under construction
At the beginning of 2013, 27 new proton therapy centers around the world were
under construction or in the commissioning phase [27]. In Europe 5 new centres with
C-235 cyclotrons and scanning gantries are being installed or commissioned (Trento,
Kraków, Dresden, Uppsala, Dymitrovgrad). In 2014 MedAustron in Wiener Neustadt
will be completed. In Nice the acceptance of a superconducting 250 MeV
synchrocyclotron ProteusOne with IBA compact gantry is scheduled for 2014. A proton
therapy centre at the St. Petersburg Centre of Nuclear Medicine of the International
Institute of Biological Systems in Russia, built by Varian, is in the planning stage. In
Poznań, Poland the PTC is planned to be completed at the end of 2016. Two centers are
planned for 2017 in Great Britain: Christie NHS Foundation Trust in Manchester and
University College London Hospital (UCLH). In the Netherlands several proton therapy
centres with a total treatment capacity of 2200 patients per year are being planned; first
patient treatment should take place in 2017. Four locations are proposed: Amsterdam,
Delft, Groningen and Maastricht. In addition to several new Proton Therapy Centers in
38
USA and Japan, new centres are planned in India, China, Korea, Taiwan and Saudi
Arabia.
According to the report of CSIntel [28], 255 treatment rooms for hadrontherapy will
be in operation worldwide by 2017, while by 2020 this numbers is expected to increase
to about 1,000.
2.4 New ion accelerators
A well-known goal of development in charged particle radiotherapy is to realize
compact, reliable accelerators with advanced beam performance. These characteristics
would facilitate the access to hadrontherapy to more patients.
A more compact accelerators means a reduced radius of the accelerating structure
� has to increase in order to keep particles in the correct
therefore, the magnetic field 𝑩
� makes the focalization worse; to overcome this problem,
orbit. The increasing of 𝑩
radio frequency accelerating systems are used.
RF cavities can be structured like beads on a string, where the beads are the cavities
and the string is the beam pipe of a particle accelerator, through which particles travel in
a vacuum.
To prepare a RF cavity to accelerate particles, a RF power generator supplies an
electromagnetic field. The RF cavity is modelled to a specific size and shape so that
electromagnetic waves become resonant and build up inside the cavity. Charged
particles passing through the cavity feel the overall force and direction of the resulting
electromagnetic field, which transfers energy to push them forwards along the
accelerator.
The field in an RF cavity is made to oscillate at a given frequency, so timing the
arrival of particles is important. The ideally timed proton, with exactly the right energy,
will see zero accelerating voltage when the accelerator is at full energy. Protons with
slightly different energies arriving earlier or later will be accelerated or decelerated so
that they stay close to the energy of the ideal particle. In this way, the particle beam is
sorted into discrete packets called "bunches".
39
During the energy-boosting process the protons in the bunches shift collectively to
see an overall acceleration on each passage through the cavities, picking up the energy
needed to keep up with the increasing field in the accelerators powerful magnets.
High-power klystrons (tubes containing electron beams) drive each RF cavity on the
accelerator.
2.4.1 Superconducting cyclotron
The fundamental advantage in the application of superconductivity is to make use of
the much higher current-carrying capacity of superconductors as compared to normalconducting (e.g., copper) wires. Superconductors at low temperatures carry high
currents without resistive or “Ohmic” losses, whereas such losses in a resistive magnet
coil need to be compensated for by powering the system continuously. This advantage
can be quantified by comparing the achievable current densities Jc of superconductors
versus normal-conducting materials like copper or aluminium. The Jc of copper is
around 3A/mm2 with no active cooling, and can be brought up to about 10 A/mm2 when
being water-cooled. The values for aluminium are very similar. In contrast to this, an
SC NbTi-filament can carry current densities of more than 3.000 A/mm2 even in
magnetic fields of about 4–10 T (Aubele A, Bruker-HTS, Personal communication,
2010), which is the relevant field range for the accelerators to be considered.
Despite some technical limitations, it is safe to say that for the low-field regime the
relative current densities of superconductors are at least a factor of 10–30 higher than
for normal-conducting wires. High current densities provide high magnetic fields,
which mean higher magnetic forces to bend and focus charged and heavy particle.
The main issue for clinical use of a SC accelerator concerns the reduced accessibility
to the elements of such a piece of equipment.
Thinking of accelerator vacuum chamber and devices installed at a temperature of
4K, some issues exist considering the time needed for operational changes or routine
maintenance. “Cold parts” would indeed impose unacceptable operational restrictions
like time-consuming warm up and cool-down procedures for maintenance purposes.
However, the considered accelerator is using SC coils housed in their cryostat, which
provides all the necessary transitions between low temperature and room temperature
40
within a few centimetre distance from the coils such that all the conventional parts of
the accelerator are kept at room temperature. Neither the RF cavities nor the ion source
or the extraction elements are cold. Instead, they are accessible as in a normal
conducting cyclotron.
The MEVION S250 is the first superconducting synchrocyclotron developed for
proton therapy system by Mevion Medical Powered. Four of such systems are under
installation in USA. ProTom comes in the market with compact 330 MeV synchrotron,
primarily developed at Russia and the Radiance 330 PT system.
The C400 is an IBA 6.3 m-diameter cyclotron, endowed with superconducting coils.
This cyclotron is based on the design of the ‘old’ 235 MeV IBA proton therapy
cyclotron and will be used for therapy with proton, helium or carbon ions.
4
12 6+
C
and
He2+ ions will be accelerated to 400 MeV/u by two cavities located in two opposite
valleys and extracted by an electrostatic deflector with an 80% efficiency. He2+ ions will
be accelerated to the energy 260MeV/u and extracted by stripping. The two extraction
channels join outside the cyclotron.
Fig. 2.9: A representation of the IBA C400 with the main parameters of the accelerator.
As for all cyclotrons, the energy is fixed and a 18 m long Energy Selection System is
needed to obtain the desired energy. Up to now, this is a standard, even if bulky and
radioactive, component of all the proton therapy centers based on cyclotrons, but it is a
novelty for carbon ions. For this reason specific Monte Carlo calculations have been
performed to check its performances. In 2007, IBA decided to build the prototype of
this machine close to GANIL (Caen) in the framework of the ARCHADE project. This
will be a research facility aiming, among other activities, to gather physical and
biological information for the development of a biologically optimized ion treatment
41
planning system to be pursued in collaboration with INFN, Dresden University,
ARCHADE and the company CMS-Elekta.
Fig. 2.10: Schematic view of the 250MeV super conducting cyclotron of Accel/Varian. Main
components are the iron yoke with its motorized pole caps (the upper one is in open position),
the supply cryostat and the coil cryostat clamped between the flux return yoke rings.
2.4.2 FFAGs - Fixed-Field Alternating-Gradient accelerators
A major clinical issue and great challenge to protons and above all for carbon ions
beam delivery technology is still the organ motion during treatment. Assuming that
instrumentation will be able to track transversal and longitudinal changes, scanning
systems can provide rapid corrections for the transverse motion. However, longitudinal
corrections require rapid energy changes, on the same order of time as provided by the
scanning system. Millisecond energy changes are not possible with the existing
accelerators. A fixed-field alternating gradient (FFAG) accelerator is under
development which might provide this energy flexibility.
Early design studies envision the possibility to accelerate carbon beams up to 400
MeV/u, with a repetition rate of 200 Hz, using compact or superconducting structures.
Such a system would allow for the fast energy variation required for the treatment of
moving organs.
These FFAGs thus, operates as synchrocyclotrons since the magnetic field is fixed
and the radio-frequency system is modulated so that the output beam is pulsed.
42
The magnet is subdivided in sectors, each one made of triplet shaving strong radial field
gradients: the central magnet bends the circulating beam outwards while the two
external ones bend it inwards.
This system has the disadvantage that an injector is needed. Since the first proposal,
it took more than 40 years to see the first Proof of Principle (PoP) 1 MeV proton FFAG
built in Japan [29]. The same group [30], has built in total five FFAGs; the largest one
accelerates protons to 150MeV, a suitable energy for cancer treatment. These machines
are of the ‘scaling’ type, i.e. during the acceleration the wiggling orbit increases in
average radius but maintains the same shape. ‘Non-scaling’ FFAGs require magnets
which are smaller in the radial direction but have the inconvenience that, during
acceleration, many resonances are necessarily crossed (see Fig. 2.11).
Fig. 2.11: Difference between scaling and non-scaling FFAGs (left). Cells of a non-scaling
linear field FFAG, which is tune-stabilized for medical therapy (right).
A facility proposed for carbon ions by Keil et al. [31] used three concentric FFAGs
in a dense doublet lattice to accelerate protons to 250 MeV (rings 1 and 2) and Carbon
to 400 MeV/u (rings 2 and 3).
43
Fig. 2.12: Triple-cascade radial-sector FFAG accelerator.
The proton and carbon rings are one inside the other and have 22 and 45 m
circumferences, so that, to reach 400 MeV/u, more than 60 m of focussing and
accelerating structures have to be built. At the beginning of 2010, a proton tunestabilized non-linear non-scaling FFAG, injected by a 30 MeV cyclotron and running at
1000 Hz, has been designed. The length of the proton medical FFAG is 40 m long
because it is made of 12 triplets with 1.7 m insertions where the RF cavities will be
installed. The variable energy extraction is done in the vertical plane. A 20 MeV
electron non-scaling FFAG (EMMA) is under construction to test the non-scaling
scheme in the easier relativistic regime [32]. While EMMA and the proton FFAG are
well advanced, the design of the carbon ion FFAG is still under development and it will
require a 7 MeV/u RFQ-linac injector that it will be about 55 metres long as a typical
carbon ion synchrotron of the same energy.
2.4.3 High-frequency linacs for carbon ion therapy: the Cyclinac
In 1989, Lennox [33] published the first design of a 24 m long 3 GHz proton linac
for cancer therapy. The main problem hits is the effective treatment of organs, which
move during the irradiation, mainly because of the respiration cycle. Three strategies
can be used:
(1)
the dose delivery is synchronized with the patient expiration phase
(respiratory gating);
(2)
the organ movement is detected by a suitable system and a set of feedback
loops compensates with on-line adjustments of the transverse and longitudinal
locations of the following delivered spots (3D feedback);
44
(3)
the tumour is painted many times in three dimensions so that each delivery
gives a small contribution to the local dose and any possible delivery error can
be corrected during the following ‘visits’ to the same voxel (repainting).
An optimal delivery mechanism should be such as to allow the use of any
combination of these three approaches, the most effective one being the combination of
a 3D feedback with repainting. The needed instruments are fast-cycling accelerators
(with repetition rates in the range 100–1000 Hz) with a pulse-by-pulse energy
adjustment. As discussed in the previous section, the novel FFAGs should have these
characteristics as well as the well-known ion linacs. In 1993 was introduced the
‘cyclinac’ concept, i.e. the combination of a high frequency proton linac (having the
standard 3 GHz frequency) and a 30 MeV cyclotron injector [34]. The main argument
was that the fraction of a continuous beam transmitted by a linac is very small, of the
order of 10-4 or less. Typically, this is the product of a-10-3 duty cycle and a 10%
capture rate of the practically continuous cyclotron beam. In the case of hadrontherapy,
such a small overall acceptance does not pose any problem because, as mentioned
before, very small protons and carbon ion currents are required: 1 and 0.1 nA,
respectively. These very small currents are easily obtained from a linac placed
downstream of a commercial cyclotron, which can produce without problems 105 times
larger currents.
In the last few years various cyclinacs have been designed by the TERA group
(TErapia con Radiazioni Adroniche). The first scheme is based on a commercial highcurrent proton cyclotron, which, as said before, accelerates protons up to 30 MeV,
followed by a linac of the LIBO type running at 3 GHz which boost them to 230 MeV.
The second design is based on a superconducting cyclotron that accelerates carbon ions
C+6 to 300 MeV/u. In both cases the hadron be a mismaintained focused by a FODO
structure of Permanent Magnet Quadrupoles (PMQs), which are integrated in gaps
located between two successive ‘tanks’, made of 15–16 accelerating cells each. The 300
MeV/u cyclotron, dubbed SCENT (Superconducting Cyclotron for Exotic Nuclei and
Therapy), was designed by Calabretta et al. [35]. It accelerates H2+1 hydrogen molecules
(which are extracted as usual from the cyclotron in the form of single protons by
stripping in a thin foil) and also carbon ions C+6, extracted through the same magnetic
channel by a deflector. The 250 MeV protons are used for proton therapy. The 3600
45
MeV carbon ions penetrate 17 cm of water while the output beam of the linac CABOTO
(Carbon Booster for Therapy in Oncology) has a 5160 MeV (430MeV/u) maximum
energy and reaches a depth of 32cm (Fig. 2.13).
The three-dimensional pencil beam scanning technique can be applied to large deepseated tumours by a fast-cycling accelerator. For these applications the rapid (1–2 ms)
and continuous energy variation of the accelerated beam is obtained by
(i)
switching off the output RF power of a number of klystrons and
(ii)
adjusting the power of the last active klystron.
This is a unique possibility offered by the modularity of the linac but implies a
delicate balance between the lengths of the tanks (i.e. the distances between successive
PMQs forming the focussing FODO structure), the number of tanks powered by a single
klystron and the peak power of the available klystrons [36]. The result of this
optimization is that the proton and carbon ion linacs, providing 200 MV in 18 m and 2 x
(430-300) = 260 MV in 22 m, need 10 and 16 7.5 MW klystrons, respectively. It has to
be remarked that the rapid and continuous energy variation in linacs is technically
simpler than in FFAGs because of the linearity of the particle trajectories and the
modularity of the structure. Higher gradients, and thus shorter structures, are a natural
line of development of the linac approach to hadrontherapy.
Fig. 2.13: Model view of the cyclotron (120 MeV/u) and the linac (120-400 MeV/u) (left). This
CABOTO is made of 54 tanks similar to the one shown in this figure. The lengths are increasing
to keep the 5.71 GHz field in synchronism with the accelerated particles (right).
46
2.5 Future perspective
2.5.1 Rotating SC synchrocyclotron
In 1993, Blosser proposed a facility based on a 200 MeV rotating superconducting
synchrocyclotron. Its modern version is the single-room facility now under development
by Still River Systems Inc. in collaboration with MIT [37]. This machine is a very high
field niobium–tin superconducting synchrocyclotron designed to fit in a single treatment
room and rotate around the patient. The fixed energy output beam will be pulsed at 200
Hz. Of course, as in the case of cyclotrons, movable absorbers are needed to adjust the
proton beam energy to scan the tumour longitudinally.
Fig. 2.14: Representation of the River’s rotating synchrocyclotron idea.
The shielding of the patient from the neutrons produced in the close-by absorbers is a
challenging problem. In 2009, the 15 tons synchrocyclotron has been constructed and in
2010 the company foresees the installation of the first two systems.
Another single-room facility is based on the slow cycling synchrotron by ProTom
International, which is designed to treat the patients with a horizontal proton beam. This
compact synchrotron (5.5 m diameter for 330 MeV proton beams) has been developed
in Russia by the Lebedev Physics Institute. Successful acceleration tests have been
recently performed at the MIT-Bates Linear Accelerator Centre. Two further projects,
which should produce proton beams rotating around the patient, are under study.
47
2.5.2 Dielectric Wall Accelerator
The Dielectric Wall Accelerator (DWA), accelerates protons in a non-conducting
beam tube (the dielectric wall) energized by a pulsed power system. DWA is an
induction accelerator. A classical induction accelerator is made of modules, containing
ferromagnetic cores that, powered in sequence, accelerate large currents with gradients
of the order of 1 MV/m. The high-gradients (100 MV/m) and low currents needed for a
medical DWA can be obtained with a coreless induction accelerator which applies the
voltage on a High Gradient Insulator (HGI) made of alternating layers of conductors
and insulators with periods of about 1 mm. Open problems of this scheme are the
focusing of the accelerated protons and the practical feasibility of a 100 MV/m
gradient, which would allow having the DWA small enough to be mounted on a gantry
directly aimed at the patient and so rotating around the patient in a small single-room
facility.
Fig. 2.15: A schematic representation of the Dielectric Wall Accelerator.
The main DWA characteristics are:
i)
200 MeV proton beams in 2 meters;
ii)
Variable spot energy and intensity pulse to pulse;
iii)
Nano-second pulse lengths;
iv)
200 degrees of rotation at least;
v)
Up to 50 Hz pulse repetition rate;
vi)
Less neutron dose;
vii)
System will provide CT-guided, rotational IMPT.
48
2.5.3 Turning Linac for Proton therapy
A high-frequency proton linac rotating around the patient is a much better
understood solution but it would take more space. To reduce the length of TULIP
(Turning Linac for Proton therapy) a 6 GHz radio frequency has been chosen by
designing CCL with an average electric field of about 40 MV/m. High-gradient linac of
frequencies larger than 3 GHz are pursued by TERA in collaboration with the RF group
of the CERN electron–positron linear collider CLIC. A rotating linac, can produce a
proton beam cycling at hundreds of Hz, which is advantageous in spot scanning since it
can apply the very powerful technique called Distal Edge Tracking (DET) [38].
Moreover, there is no intense neutron flux close to the patient respect to typical flux of
fixed-energy cyclotrons or of the Still River Systems synchrocyclotron.
Fig. 2.16: A schematic representation of Turning Linac for Proton therapy.
2.5.3 Laser-driven accelerators
The approach of using a laser to generate energetic proton beams for proton therapy
can be of interest, because the laser and light transmission components can be installed
in normal rooms, without the need of heavy concrete shielding. Further, one might save
a lot of weight when the easily transportable light beam is coupled on a rotatable gantry,
because magnets are not needed anymore. Also scanning the light beam would in
principle provide opportunities for pencil beam scanning.
49
Fig. 2.17: Representation of a laser-based treatment structure.
Even further in the future, the first proton single-room facility based on the
illumination of a thin target with powerful (1018–1020 W/cm2) and short (30–50 fs) laser
pulses is expected. However, at present the beam properties of laser-accelerated ions are
not at all what is required for therapy (high-intensity, well-defined energy) and many
technical challenges must be addressed.
At the moment most experience has been obtained with the target normal sheet
acceleration (TNSA) method [39]. As shown in Figure 2.18 b, a high-intensity laser
irradiates the front side of a solid target, which may be saturated with hydrogen when
protons are accelerated. At the front surface, plasma is created due to the energy
absorption in the foil. The electrons in this plasma are heated to high energies and
penetrate through the target and emerge from the rear surface. This induces strong
electrostatic fields, which pull ions and the protons out of the target at its rear surface.
The highest proton energies observed in this method are about 20 MeV [40]. This has
been achieved with a laser power intensity of 6 × 1019 W/cm2 and a pulse length of 320
fs.
Fig. 2.18: a) The concept of a treatment facility using protons that are generated by a laser. b)
An intensive laser accelerates electrons from a proton-enriched area (polymer) at the far side of
a titanium foil. This creates a strong electric field that accelerates protons out of the surface.
50
Currently, much work is going on to model the interaction of the laser with the target
and to make predictions for other target geometries and materials. Extrapolation of this
model to calculate the optimum target and laser beam parameters for delivering a 200
MeV beam from different thicknesses of targets indicate that the needed laser power is
as high as 1022 W/cm2. Apart from the request to obtain higher proton energies, the
obtained energy spectrum is also of concern. The obtained energy spectrum (Figure
2.19) shows a broad continuum that is not suitable for proton therapy. Although some
filter and energy compression techniques are proposed, one must be aware of neutron
production when simple filtering techniques are used just before the patient.
The physical systems are highly complex and suffer from instabilities and
uncertainties in this regime of intensity.
Fig. 2.19: The measured and modelled proton intensities as a function of laser power.
J., et al., Nat. Phys. 2, 48–54, 2006.
The obtained proton beam intensities are still too low, for example, 109 protons per
pulse in a broad energy spectrum or 108 protons per pulse with peak energy well below
10 MeV [41]. Even neglecting losses due to energy selection and collimation of the
proton beam, this would require an increase of the repetition rate to 10–100 Hz, which
is currently at the limit of the advertised new generation lasers.
An alternative method uses radiation pressure acceleration (RPA), sometimes
referred to as the laser piston regime. Here the light pressure of a laser pulse incident on
a foil, with thickness less than 100 nm, accelerates the whole foil as a plasma slab.
Simulations predict that the RPA method can provide higher proton energies and less
energy spread than TNSA. However, the RPA method faces even more technological
challenges.
51
2.6 A final remark
As said in the first part of this chapter, in order to deliver a standard dose of
2 Gy/(min ∙ l), the typical beam intensities are between 1.8 x 1011 and 3.6 x 1011
particles per minute. However, the new projects of more compacted accelerators need
higher magnetic fields to keep particles in the correct orbits and therefore higher
intensities provided by radio frequency accelerating systems, to overcome the
focalization problems. Thus, the intensity for a new generation accelerator for
hadrontherapy, is in the order of 1014 particles for minute.
52
Chapter 3
Gas Filled Detectors
3.1 Introduction
When a charged particle crosses a gaseous medium, it interacts primary by ionization
and excitation of gas molecules along the particle track. If the energy released by the
particle is higher than the ionization potential of the gas crossed, charge pairs are
produced and, by the application of an external electric field, they move in opposite
directions. The result is an electric signal that can be measured by an associated
measuring device. This process has been used to construct the ionization, gas filled,
detectors. A typical gas filled detector consists of a gas enclosure and positive and
negative electrodes set at a high potential difference. The creation and movement of
charge pairs due to the ionization induced by the ionizing radiation through the gas,
perturbs the externally applied electric field producing a pulse at the electrodes. The
resulting charge, current, or voltage difference at one of the electrodes gives information
about the energy of the particle beam and its intensity if measured and properly
converted. In order to work efficiently, this system needs that a large number of charge
pairs is
created and
readily collected at the electrodes before the free charges
recombine to form neutral molecules. The choice of gas, the geometry of the detector,
and the applied potential give us controlling power over the production of charge pairs
and their kinematic behaviour in the gas.
Ion chambers in principle are the simplest of all gas-filled detectors. As with other
detectors, ion chambers can be operated in current or pulse mode. In most common
applications, ion chambers are used in current mode as direct current devices; in
contrast, proportional counters or Geiger tubes are almost used in pulse mode.
53
3.2 Production of Electron-Ion Pairs
Whenever radiation or a charged particle interacts with a gas, it may excite the
molecules, ionize them, or do nothing at all. There are different mechanisms through
which these interactions could take place.
At a minimum, the particle must transfer an amount of energy equal to the ionization
energy of the gas molecule to permit the ionization process to occur. The average
energy needed to create an electron-ion pair in a gas is called the W-value. An
interesting point to note here is that the W-value is significantly higher than the first
ionization potential for gases, implying that not all the energy goes into creating
electron-ion pairs.
The charges created by the incident radiation are called primary charges to
distinguish them from the ones that are indirectly produced in the active volume. The
production mechanism of these additional charge pairs are similar to those of primary
charges except that they are produced by ionization caused by primary charge pairs and
not the incident radiation. The W-value represents all such ionizations that occur in the
active volume; this is in principle a function of the species of gas involved, the type of
radiation, and its energy. Empirical observations, however, show that it is not a strong
function of any of these variables and is a remarkably constant parameter for many
gases and different types of radiation and a typical value is 25-35 eV/ion pair.
Therefore, an incident 1 MeV particle, if it fully stops within the gas, creates about
30.000 ion pairs. Assuming that W is constant for a given type of radiation, the
deposited energy will be proportional to the number of ion pairs formed and can be
determined if a corresponding measurement of the number of ion pairs is carried out.
For a particle that deposits energy ΔE inside a detector, the W-value can be used to
determine the total number of electron-ion pairs produced by
𝑁=
∆𝐸
𝑊
(3.1)
If the incident particle deposits all of its energy inside the detector gas, then of course
ΔE would simply be the energy E of the particle. However in case of partial energy loss,
we must use some other means to estimate ΔE.
54
Table 3.1: Ionization potentials Ie, W-values, stopping powers (dE/dx), primary ionization yield
np, and total ionization yield nt of different gases at standard atmospheric conditions for
minimum ionizing particles (ip stands for the number of electron-ion pairs) [42].
In terms of stopping power, the above relation can be written as
𝑁=
1 𝑑𝐸
∆𝑥
𝑊 𝑑𝑋
(3.2)
where Δx is the path covered by the particle. Sometimes it is more convenient, at least
for comparison purposes, to calculate the number of electron-ion pairs produced per unit
length of the particle track
𝑛=
𝑑𝐸
𝑑𝑋
(3.3)
As we saw in chapter 1, due to energy straggling, the stopping power fluctuates
around its mean value. Similarly, the W-values for different gases suffer from
significant uncertainties.
The W-value represents all ionizations that occur inside the active volume of the
detector but sometimes the primary charge pair yields would be known as well.
However, because of almost inevitable secondary ionizations that occur at nominal
applied voltages, it is not always possible to determine this number experimentally.
55
In order to determine the number of total and primary charge pairs in a gas mixture, a
composition law of the equation 3.2 can be used, referring to the values in Tab. 3.1:
𝑛𝑡 = � 𝑥𝑖
𝑖
𝑎𝑛𝑑
(𝑑𝐸/𝑑𝑋)𝑖
𝑊𝑖
𝑛𝑝 = � 𝑥𝑖 𝑛𝑝,𝑖
𝑖
(3.4)
(3.5)
Here the i refers to the ith gas in the mixture and xi is the path covered by the particle i.
3.3 Energy resolution and the Fano factor
In addition to the mean number of ion pairs formed by each incident particle, the
fluctuation in their number for incident particles with identical energy is also of interest.
These fluctuations will set a fundamental limit on the energy resolution that can be
achieved in any detector based on collection of the ions. In the simplest model, the
probability of each ion pair creation follows a Poisson distribution.
The energy resolution of the detector is conventionally defined as the FWHM
divided by the location of the peak centroid Ho. The energy resolution R is thus a
dimensionless fraction conventionally expressed as a percentage.
Several sources of fluctuation in the response of a given detector result in imperfect
energy resolution. These include any drift of the detector operating characteristics
during measurements, sources of random noise within the detector and frontend readout,
and statistical noise arising from the discrete nature of the measured signal itself.
The third source is the most important because it represents a minimum amount of
fluctuation that is always present in the detector signal independently by the detector
construction. In a wide category of detector applications, the statistical noise represents
the dominant source of fluctuation in the signal and thus sets an important limit on
detector performance.
The statistical noise arises from the fact that the charge Q generated within the
detector is not a continuous variable but instead represents a discrete number of charge
56
carriers. For example, in an ion chamber the charge carriers are the ion pairs produced
by the passage of the charged particle through the chamber.
Fig. 3.1: Definition of detector resolution. For peaks whose shape is Gaussian with standard
deviation σ, the FWHM is given by 2.35 σ.
In all cases the number of carriers is discrete and subject to random fluctuation from
event to event even though exactly the same amount of energy is deposited in the
detector.
The amount of fluctuation can be estimated by assuming that the formation of each
charge carrier is a Poisson process. Under this assumption, if a total number N of charge
carriers is on average generated, the standard deviation to characterize the inherent
statistical fluctuation is √𝑁. If this is the only source of fluctuation in the signal, the
response function, as shown in Fig. 3.1, should have a Gaussian shape, because N is
typically a large number.
The response of many detectors is approximately linear, so that the average pulse
amplitude Ho = KN, where K is a proportionality constant. The standard deviation σ of
the peak in the pulse height spectrum is then 𝜎 = 𝐾√𝑁 and its FWHM is 2.35K√𝑁.
We then would calculate a limiting resolution R due only to statistical fluctuations in
the number of charge carriers as
R Poisson =
FWHM
H0
=
2.35K√N
KN
=
2.35
√N
(3.6)
Note that this limiting value of R depends only on the number of charge carriers N, and
the resolution improves (R will decrease) as N is increased.
57
Careful measurements of the energy resolution of some types of radiation detectors
have shown that the achievable values for R can be reduced by a factor as large as 3 or 4
respects to the minimum predicted by the statistical arguments given above. These
results would indicate that the processes that give rise to the formation of each
individual charge carrier are not independent, and therefore the total number of charge
carriers cannot be described by simple Poisson statistics. The Fano factor has been
introduced in an attempt to quantify the departure of the observed statistical fluctuations
in the number of charge carriers from pure Poisson statistics and is defined as
F≡
observed variance in N
Poisson predicted variance
(3.7)
Since the variance is given by σ2, the Eq. (3.6) can be written as the following Eq.
(3.8)
R Statistical limit =
2.35K√N√F
F
= 2.35 �
KN
N
(3.8)
Any other source of fluctuations in the signal chain will combine with the inherent
statistical fluctuations to give the overall energy resolution of the measuring system. It
is sometimes possible to measure the contribution to the overall FWHM due to a single
component. For example, if the detector is replaced by a stable pulse generator, the
measured response will show a fluctuation due primarily to the electronic noise. If there
are several symmetric and independent sources of fluctuation, statistical theory predicts
that the overall response function will always tend toward a Gaussian shape, even if the
individual sources are characterized by distributions of different shape. Then the total
FWHM will be the quadrature sum of the FWHM values for each individual source of
fluctuation:
(FWHM)2 overall = (FWHM)2 statistical + (FWHM)2 noise + (FWHM)2 drift + …
Each term on the right is the square of the FWHM that are observed when all the
other sources of fluctuation are zero.
58
3.4 Diffusion and Drift of Charges in Gases
The neutral atoms or molecules of the gas are in constant thermal motion,
characterized by a mean free path for typical gases under standard conditions of about
10-6-10-8 m. Positive ions or free electrons created within the gas also take part in the
random thermal motion and therefore have some tendency to diffuse away from regions
of high density. This diffusion process is much more pronounced for free electrons than
for ions since their average thermal velocity is much greater. A point-like collection of
free electrons will spread about the original point into a Gaussian spatial distribution
whose width will increase with time.
3.4.1 Diffusion in the Absence of Electric Field
In absence of an externally applied electric field, the electrons and ions having
energy E can be characterized by the Maxwellian energy distribution,
𝐹(𝐸) =
2
√𝜋
(𝑘𝑇)−3/2 √𝐸 𝑒 −𝐸/𝑘𝑇
(3.9)
where k is the Boltzmann’s constant and T is the absolute temperature. The average
energy of charges, as deduced from this distribution, turns out to be
𝐸�⃗ =
3
𝑘𝑇
2
(3.10)
which is equivalent to about 0.04 eV at room temperature. When the externally applied
electric field is null, there is no preferred direction of motion for the charges in a
homogeneous gas and therefore the diffusion is isotropic. In any direction x, the
diffusion can be described by the Gaussian distribution as follow
𝑑𝑁 =
𝑁
√4𝜋𝐷𝑡
𝑒 −𝑥
2 /4𝐷𝑡
𝑑𝑥
(3.11)
59
where N is the total number of charges and D is the diffusion coefficient. The Eq (3.11)
represents the number of charges, dN, expected in an element dx at a distance x from the
centre of the initial charge distribution after a time (t). D is generally reported in cm2/s
and can be used to determine the standard deviation of the linear distribution of charges
as well as of the volume distribution through the following relations
𝜎𝑥 = √2𝐷𝑡
(3.12)
𝑎𝑛𝑑 𝜎𝑣 = √6𝐷𝑡
(3.13)
Electrons, owing to their very small mass, diffuse much faster. This can also be
deduced by comparing the thermal velocities of electrons and ions, which usually differ
by two to three orders of magnitude. The diffusion coefficient for electrons is, therefore,
much different from that of the ions in the same gas. Since the diffusion coefficient has
mass and charge dependences, therefore for different ions it assumes values that may
differ significantly from each other. Further complications arise due to dependences on
the gas in which the ion is moving. Since in radiation detectors we are concerned with
the movement of ions produced by the incident radiation, we restrict ourselves to the
diffusion of ions in their own gas. Addition of admixture gases in the detector can also
modify the diffusion properties and, as consequence, the correct value of the diffusion
coefficient, corresponding to the types and concentrations of the gases introduced,
should be sought. The values of diffusion coefficients for different gases and gas
mixtures have been experimentally determined and reported in Table 3.4.1.
3.4.2 Charge diffusion in the presence of electric field
In the presence of an electric field the diffusion is no longer isotropic and therefore
can’t be described by a scalar diffusion coefficient. The diffusion coefficient in this case
is a tensor with two non-zero components: a longitudinal component DL and a
transverse component DT. For many gases, the longitudinal diffusion coefficient DL is
smaller than the transverse diffusion coefficient DT.
60
3.5 Drift of Charges in Electric Field
In a gaseous detector, the Maxwellian shape of the energy distribution of charges
cannot be guaranteed. The reason is the applied bias voltage that creates electric field
inside the active volume. The electrons, owing to their small mass, experience a strong
electric force and consequently their energy distribution deviates from the pure
Maxwellian shape. On the other hand, the distribution of ions is not significantly
affected if the applied electric field is not high enough to cause discharge in the gas
[43]. The electrons behave quite differently than ions in the presence of electric field
and therefore they are studied separately.
3.5.1 Drift of Ions
In a gaseous detector the pulse shape and its amplitude depend on the motion of both
electrons and ions. The latters are positively charged and much heavier than electrons
and therefore move around quite slowly. In most gaseous detectors, especially
ionization chambers, the output signal can be measured from the positive or from the
negative electrode. In both cases, however, what is measured is actually the electric
field variation inside the active volume. Hence the drift of both electrons and ions
contribute to the overall output pulse. This implies that understanding the drift of
positive ions in a chamber is as important as the drift of electrons.
In the presence of externally applied electric field, ions move toward the negative
electrode with a drift velocity that is much lower than that of electrons. The ions
distribution can be described accurately by the following Gaussian distribution
𝑑𝑁 =
𝑁
√4𝜋𝐷𝑡
2 /4𝐷𝑡
𝑒 −(𝑥−𝑡𝑣𝑑 )
𝑑𝑥
(3.14)
where vd is the drift velocity of ions, which is actually the velocity of the ions cloud of
moving along the electric field lines. This velocity is much lower than the instantaneous
61
velocity of ions. t is the ion drift time. The drift velocity tells us how quickly we should
expect the ions to reach the cathode and get collected. It has been found that as long as
no breakdown occurs in the gas, this velocity remains proportional to the ratio of
electric field and gas pressure.
𝑣𝑑 = 𝜇+
𝐸
𝑃
(3.15)
Here E is the applied electric field, P is the pressure of the gas, and μ+ is the mobility
of ions in the gas. Mobility depends on the mean free path of the ion in the gas, the
energy it loses per impact, and the energy distribution. In a given gas, it therefore
remains constant for a particular ion. Table 3.4.1 gives mobility, diffusion coefficient,
and mean free path of several ions in their own gas under standard conditions of
temperature and pressure.
Table 3.4.1: Mean free path λ, diffusion coefficient D, and mobility μ of ions in their own gas
under standard conditions of temperature and pressure.
A useful relationship between mobility and diffusion coefficient is given by
𝜇+ =
𝑒
𝐷
𝑘𝑇 +
(3.16)
and is known as Nernst-Einstein relation. Here k is the Boltzmann’s constant and T is
the absolute temperature.
For a gas mixture, the effective mobility can be computed from the Blanc’s law
𝑛
𝑐𝑗
1
= � 𝑖𝑗
𝜇+
𝜇
𝑗=1 +
(3.17)
62
where n is the number of gas types in the mixture, μij
+
is the mobility of ion i in gas j
and cj is the volumetric concentration of gas j in the mixture.
As said above, the drift velocity of ions is roughly two to three orders of magnitude
lower than that of electrons. The slow movement of ions causes problems of space
charge accumulation, and the effective electric field experienced by the charges
decreases; also the pulse height at the readout electrode decreases for this reason.
3.5.2 Drift of Electrons
Electrons within a constant electric field applied between two electrodes are rapidly
accelerated. Since they have a small mass, the energy lost by collisions with gas
molecules is low and so an electron gains energy, drifting to the electrode;
consequently, the electrons energy distribution can no longer be described by a
Maxwellian distribution.
Along the electric field lines, the electrons drift with velocity vd which is usually an
order of magnitude smaller than the velocity of thermal motion ve. However the
magnitude of drift velocity depends on the applied electric field. The approximate
dependence of drift velocity on the electric field E is given by:
𝑣𝑑 =
2𝑒𝐸𝑙𝑚𝑡
3𝑚𝑒 𝑣𝑒
(3.18)
where lmt is the mean momentum transfer path of electrons [43].
Fig. 3.2 shows the variation of electron drift velocity in methane, ethane, and
ethylene with respect to the applied electric field. It is apparent that only in the low field
region, the drift velocity increases with the energy. Beyond a certain value of the
electric field that depends on the type of gas, the velocity either decreases or stays
constant.
63
Figure 3.2: Variation of drift velocity of electrons in methane, ethane, and ethylene [44].
As evident from the figure 3.3, this behaviour is typical of gases that are commonly
used in radiation detectors. An important consequence of Fig.3.3 results is the nonnegligible dependence of electron drift velocity on the pressure of the gas. This effect is
due to the fact that as the pressure of the gas increases, the density of the target atoms
also increases, thus forcing an electron to make more collisions along its track.
Due to this dependence, many authors prefer to tabulate or plot the electron drift
velocities with respect to the ratio of electric field intensity and pressure, that is, E/P.
Such a curve is shown in Fig. 3.3.
Figure 3.3: Variation of drift velocity of electrons in a mixture of argon, propane, and isobutane
with respect to electric field strength [45].
64
3.6 Effects of Impurities on Charge Transport
Usually gaseous detectors are filled with a mixture of gases instead of a single gas.
The ratio of the gases in the mixture depends on the type of detector and the application.
In addition to these, the detector also has pollutants or impurities, which degrade its
performance. Most of these pollutants are polyatomic gases, such as oxygen and air.
Since they have several vibrational energy levels therefore they are able to absorb
electrons in a wide energy range. Such agents are called electronegative and their
electron attachment coefficients are generally high enough to be of interest. The main
effect of these impurities is that they absorb electrons and result in degradation of the
signal.
There are two methods by which electron capture occurs in gaseous detectors:
resonance capture and dissociative capture. Resonance capture can be written as
𝑒 + 𝑋 → 𝑋 −∗
(3.19)
where X represents the electronegative molecule in the gas and ∗ denotes its excited
state. To de-excite, the molecule can either transfer the energy to another molecule
𝑋 −∗ + 𝑆 → 𝑋 − + 𝑆 ∗ ,
(3.20)
𝑋 −∗ → 𝑋 + 𝑒.
(3.21)
or emit an electron
Here S can be any gas molecule in the gas but is generally an added impurity called
quench gas.
The process of electron emission is favourable for radiation detectors because the
only effect is the introduction of a very small time delay between capture and reemission of the electron. It does not have any deteriorating effect on the overall signal
height.
65
Figure 3.4: Variation of drift velocity of electrons in a mixture of xenon and C2H6 with respect
to electric field strength. The curves have been drawn for different values of externally applied
magnetic fields. The variation of drift velocity with magnetic field is very small and therefore
except for very high field strengths it can be neglected for most practical purposes [46].
If a constant electric field is applied between two electrodes, the number of electrons
surviving the capture by electronegative impurities after traveling a distance x is given
by
𝑁 = 𝑁0 𝑒 −𝜇𝑐𝑥
(3.22)
where N0 is the number of electrons at x = 0 and μc is the electron capture coefficient,
which represents the probability of capture of an electron. It is related to electron’s
capture mean free path λc by
𝜇𝑐 =
1
𝜆𝑐
(3.23)
Using this, we can define λc as the distance travelled by electrons such that about
63% of them get captured. The capture mean free path depends on the electron
attachment coefficient η, which characterizes the probability of electron capture in each
single scattering event. If σ is the total electron scattering cross section of the
electronegative gas, then ησ will represent the attachment cross section. If Nm is the
density of molecules of the gas (number of molecules per unit volume) and f is the
fraction of its electronegative component, then the capture coefficient and the capture
mean free path can be written as
𝜇𝑐 = 𝑓𝑁𝑚 𝜂𝜎
(3.24)
66
𝜆𝑐 =
1
𝑓𝑁𝑚 𝜂𝜎
(3.25)
Now since λc is the capture mean free path, we can simply divide it by the average
electron velocity v to get its capture mean lifetime τc
The previous exponential relation can also be written as
𝑁 = 𝑁0 𝑒 −𝑡/𝑡𝑐
(3.26)
where N0 is the initial electron intensity and N is the intensity at time t.
The factors h, σ, and v in the above relations depend on the electron energy while Nm
depends on temperature and pressure. Therefore it is not possible to find in literature the
values of these parameters for all possible energy and working conditions. Further
complications arise when there are more than one electronegative elements in the gas.
This is because the charge exchange reactions between these elements can amount to
significantly higher electron attachment coefficients as compared to the ones obtained
by simple weighted mean. In such cases, one should resort to the experimentally
determined values of λc or τc, which are available for some of the most commonly used
gas mixtures.
3.7 Regions of Operation for Gas Filled Detectors
Fig. 3.5 shows different regions of operation for a gas filled detector. Based on the
applied bias voltage, a detector can operate in several modes, which differ from one
another by the amount of charges produced and their movement inside the detector
volume. The choice depends on the application and generally detectors are optimized to
work in a well defined range of the applied voltage that is characteristic of a single
mode of operation. These operation regions are briefly discussed below.
67
Figure 3.5: Variation of pulse height produced by different types of detectors with respect to
applied voltage. The two curves correspond to two different energies of incident radiation.
3.7.1 Recombination Region
In the absence of an electric field the charges produced by the passage of radiation
quickly recombine to form neutral molecules. When the bias voltage is applied, some of
the charges begin to drift towards the opposite electrodes. As this voltage is raised the
recombination rate decreases and the current flowing through the detector increases.
The recombination region showed in Fig. 3.5 refers to the range of applied voltage up to
the value for which the recombination is negligibly small. Because of appreciable
recombination in this region, the current measured by the detector does not correspond
to the totalenergy deposited by the incoming radiation.
3.7.2 Ion Chamber Region
The collection efficiency of electron-ion pairs in the recombination region increases
with applied voltage until all the charges that are being produced get collected. In the
ion chamber region further increasing of the high voltage does not affect the measured
68
current since all the charges being produced are collected efficiently by the electrodes.
In this region, the current measured by the detector frontend electronics is called
saturation current and is proportional to the energy deposited by the incident radiation.
The detectors designed to work in this region are called ionization chambers.
It is almost impossible to completely eliminate the possibility of charge pair
recombination in the ion-chamber region. However, with proper design, ionization
chambers having plateaus of negligibly small slopes can be built.
3.7.3 Proportional Region
If the charges produced during primary ionization have enough energy they
themselves can produce additional electron-ion pairs, a process called secondary
ionization. Further ionization from these charges is also possible if they have enough
energy. This process occurs only if the electric potential between the electrodes is so
high that the charges could attain very high velocities. Although the energy gained by
the ions also increases as the bias voltage is increased, the electrons, owing to their very
small mass, are the ones that cause most of the subsequent ionizations.
This multiplication of charges at high fields is exploited in the proportional detectors
to increase the height of the output signal. In such a detector the multiplication of
charges occurs in such a way that the output pulse remains proportional to the deposited
energy.
These devices are so called proportional counters because the total number of
charges produced after multiplication is proportional to the initial number of charges.
3.7.4 Region of Limited Proportionality
When the bias voltage increases more and more charges are created inside the active
volume of the detector. Now since heavy positive charges move much slower than the
electrons, they tend to form a cloud of positive charges between the electrodes. This
cloud acts as a shield to the electric field and reduces the effective field seen by the
charges. Consequently, the proportionality of the total number of charges produced with
the initial number of charges is not guaranteed.
69
3.7.5 Geiger-Mueller Region
Increasing the voltage further may increase the local electric field to such high values
that an extremely severe avalanche occurs in the gas, producing very large number of
charge pairs. Consequently, a very large pulse of several volts is detected by the readout
electronics. This is the onset of the so called Geiger-Mueller region. In this region, it is
possible to count individual incident particles since each particle causes a breakdown
and a large pulse. Since the output pulse is neither proportional to the deposited energy
nor dependent on the type of radiation, the detectors operated in this region are not
appropriate for example for spectroscopy.
There is also a significant dead time associated with such detectors. If there is a large
accumulation of positive charges, it can reduce the internal electric field to a value that
it can no longer favour avalanche multiplication. If radiation produces charge pairs
during this time, the charges are not multiplied and no pulse is generated. The detector
starts working again as soon as most of the positive charges have been collected by the
respective electrodes. The multiplication of charges in a GM detector is so intense that
sometimes it is termed as breakdown of the gas.
3.7.6 Continuous Discharge
The breakdown process can further advance to the process of continuous discharge if
the high voltage is raised to very high values. This continuous discharge starts as soon
as a single ionization takes place and cannot be controlled unless the voltage is lowered.
In this region, electric arcs can be produced between the electrodes, which may
eventually damage the detector. It is so obvious thatsuchhigh voltages must be avoided.
3.8 Ionization Chambers
Ionization chambers are one of the earliest constructed radiation detectors. Because
of their design simplicity and well understood physical processes they are still one of
the most widely used detectors.
70
3.8.1 Current Voltage Characteristics
Fig.3.6 shows the current-voltage characteristics of an ionization chamber at
different incident radiation intensities. Normally the chambers operate in the middle of
the plateau region to avoid any large variation of current with small variations in the
power supply voltage.
As we said previously, the plateau of any chamber always has some slope but
normally it is so small that it does not affect the signal to noise ratio in any significant
way. As shown in Fig.3.6, the form of the characteristic current-voltage curve of an ion
chamber does not depend on the intensity of the incident radiation and two differences
arise: one is the onset of the plateau region and the second is the output current
amplitude. The underlying reason for both of these differences is the availability of
larger number of electron-ion pairs at higher intensities. If the rate of production of
charge pair increases, then a higher electric field intensity will be needed to eliminate
(or more realistically to minimize) their recombination. Hence, the plateau in such a
case will start at a higher voltage. In addition, as we will see later, the output current is
proportional to the number of charge pairs in the plateau region and therefore at higher
intensities the plateau current is higher.
Fig. 3.6: Current-voltage characteristic curves of an ionization chamber at different incident
radiation intensities. The output signal as well as the onset of the plateau (indicated on the plot
with 1, 2, and 3) increase with increasing intensity or flux of radiation.
71
3.8.2 The ionization current
In the presence of an electric field, the drift of the positive and negative charges
represented by the ions and electrons generates an electric current. If a given volume of
gas is undergoing steady-state irradiation, the rate of ion pairs creation is constant.
When recombination is negligible and all the charges are efficiently collected, the
steady-state current produced is an accurate measure of the rate at which ion pairs are
formed within the volume. Measurement of this ionization current is the basic principle
of the ion chamber.
The current-voltage characteristics of such a chamber are also sketched in Fig. 3.7.
Neglecting some subtle effects related to differences in diffusion characteristics between
ions and electrons, no current should flow in the absence of an applied voltage because
no electric field will then exist within the gas.
As the voltage increases, the resulting electric field begins to separate the ion pairs
more rapidly, and columnar recombination diminishes (as explained in the following
sections). The positive and negative charges move toward the respective electrodes with
increasing drift velocity, reducing the equilibrium concentration of ions within the gas
and therefore further suppressing volume recombination between the point of origin and
the collecting electrodes.
Figure 3.7: The basic components of an ion chamber and the corresponding current-voltage
characteristics.
72
The measured current thus increases with applied voltage as these effects reduce the
amount of the original charge that is lost. At a sufficiently high voltage, the electric field
is large enough to effectively suppress recombination to a negligible level, and all the
original charges created through the ionization process contribute to the ion current.
Increasing the voltage further cannot increase the current because all charges are already
collected and the rate of formation is constant. This is the ion saturation region where
ion chambers conventionally operate because the current measured in the external
circuit An accurate measurement of the rate of all charges creation due to ionization
within the active volume of the chamber.
3.8.3 Mechanical Design: parallel plate geometry
The mechanical design of an ion chamber consists of three main components: an
anode, a cathode, and a gas enclosure. The geometry of these parts are application
dependent. Fig.3.8 shows the most common ion chamber geometry and the electric field
inside the active volume. Although, as we saw above, the curvature in the lines of
electric field at the edges of such a detector can potentially cause nonlinearity in the
response, but a proper design overcomes this problem.
Figure 3.8: Parallel plate ion chamber and a two dimensional view of electric field inside its
active volume.
It can be noted that the voltage pulse is actually the result of the perturbation in the
electric potential caused by the movement of charge pairs towards opposite electrodes.
73
This is because the electrons and ions generated inside the chamber decrease the
effective electric field. The strength of this effective field varies as the charges move
toward opposite electrodes, generating a voltage pulse at the output. The effective
voltage at any time t inside the chamber can be written as
𝑉𝑒𝑓𝑓 (𝑡) = 𝑉0 − 𝑉𝑛𝑝 (𝑡)
(3.27)
where V0 is the static applied potential and Vnp(t) is the potential difference at time t
caused by the electrons and ions inside the chamber.
If we have N0 ion pairs at any instant t, then the electrons kinetic energy with an
averaged velocity vn is given by
𝑇𝑛 (𝑡) = 𝑁0 𝑒𝐸𝑣𝑛 𝑡 =
𝑣0
𝑁 𝑒𝑣 𝑡
𝑑 0 𝑛
(3.28)
where we have assumed that the electric field intensity E, under whose influence the
electrons move, is homogeneous within the active volume and can be written as E =
V0/d, being d the distance between the electrodes.
Similarly, the kinetic energy of ions having average velocity vp can be written as
𝑇𝑝 (𝑡) = 𝑁0 𝑒𝐸𝑣𝑝 𝑡 =
𝑣0
𝑁 𝑒𝑣 𝑡
𝑑 0 𝑝
(3.29)
Fig. 3.9: Simple parallel plate ionization chamber. In this geometry the output voltage Veff
depends on the point where charge particles are generated. Electrons owing to their small mass
move faster than ions and therefore the electrons distribution is shown to have crossed a larger
distance as compared to that of ions.
74
The potential energy contained in the chamber volume having capacitance C is
defined as
𝑈𝑐ℎ =
1 2
𝐶𝑉
2 𝑛𝑝
(3.30)
while the total energy delivered by the applied potential V0 is
𝑈𝑡𝑜𝑡𝑎𝑙 =
1 2
𝐶𝑉
2 0
(3.31)
In the short circuit condition, this total energy should be equal to the total of kinetic
and potential energy inside the chamber volume, that is
𝑈𝑡𝑜𝑡𝑎𝑙 = 𝑈𝑐ℎ + 𝑇𝑝 + 𝑇𝑛
1 2
1
+ 𝑁0 𝑒𝐸𝑣𝑛 𝑡 + 𝑁0 𝑒𝐸𝑣𝑝 𝑡
→ 𝐶𝑉02 = 𝐶𝑉𝑛𝑝
2
2
(3.32)
The above equation can be rearranged to give an expression for the effective
potential Veff = V0-Vnp as follow
�𝑉0 − 𝑉𝑛𝑝 ��𝑉0 + 𝑉𝑛𝑝 � =
→ 𝑉𝑒𝑓𝑓 ≅
2𝑁𝑜 𝑉0 𝑒
�𝑣𝑝 + 𝑣𝑛 �𝑡
𝐶𝑑
𝑁𝑜 𝑒
�𝑣 + 𝑣𝑛 �𝑡
𝐶𝑑 𝑝
(3.33)
Where the following approximation has been used
𝑉0 + 𝑉𝑛𝑝 ≈ 2𝑉0
(3.34)
Since the electrons move much faster than ions (vn >> vp), therefore initial pulse
shape is almost exclusively due to electron motion. If we assume that the charge pairs
are produced at a distance x from the anode (see Fig.3.9), then the electrons will take a
time
tn = x/vn to reach the anode. This will inhibit a sharp increase in pulse height
with the maximum value attained when all the electrons have been collected by the
anode. The ions will keep on moving slowly toward cathode until time tp = (d−x)/vp,
increasing the pulse height further, however at a much lower rate.
75
The maximum voltage is reached when all the charges have been collected. Based on
these arguments, we can rewrite the expression for the output pulse time profile for
three distinct time periods as follows.
𝑁𝑜𝑒
�𝑣 + 𝑣𝑛 �𝑡 ∶ 0 ≤ 𝑡 ≤ 𝑡𝑛
𝐶𝑑 𝑝
𝑁𝑜𝑒
�𝑣 + 𝑥�𝑡 ∶ 𝑡𝑛 ≤ 𝑡 ≤ 𝑡𝑝
𝐶𝑑 𝑝
𝑁𝑜𝑒
∶ 𝑡 ≥ 𝑡𝑝
𝐶𝑑
(3.35)
(3.36)
(3.37)
However, a reall pulse measured through some associated readout electronics differs
from the curve shown here due to the following reasons:
•
a real voltage readout circuit has a finite time constant;
•
the charge pairs are not produced in highly localized areas.
In the above derivation leading to the pulse profile of Fig.3.10 we have not
considered the effect of the inherent time constant of the detector and associated
electronics on the pulse shape. Time constant is the product of resistance and
capacitance of the circuit (τ = RC). Every detector has some intrinsic capacitance as
well as the cable capacitance. These capacitances together with the eventual installed
capacitor and load resistance of the output make up the effective time constant of the
circuit. The difference between this time constant and the charge collection time
characterizes the shape of the output pulse (see Fig. 3.11).
Fig. 3.10: Pulse shape of an ideal parallel plate ion chamber. Vn and Vp are the voltage profiles
due mainly to collection of electrons and ions respectively.
76
Fig. 3.11: Realistic pulse shapes of an ion chamber with different time constants. The difference
between the effective time constant of the detector and its charge collection time determines the
shape of the pulse.
Therefore, the quicker the pulse falls down, the easier it will be to distinguish it from
the subsequent pulse. On the other hand, very small time constant may amount to loss of
information and even non-linearity. Therefore considerable effort is warranted to tune
the effective time constant according to the requirements.
3.8.4 Choice of Gas
Since the average energy needed to produce an ion pair in a gas (W-value) depends
weakly on the type of gas, therefore, in principle, any gas can be used in an ionization
chamber. Air filled ion chambers are rather common. However to build accurate
detectors, the W-value is not the only factor that has to be considered since the precision
of a detector mainly depends on the charge collection efficiency. Moreover, the charge
collection efficiency depends not only on detector geometry and bias voltage but also on
the drift and diffusion properties of the electrons and ions in the gas. The choice of gas
is strictly application dependent.
3.8.5 Advantages and Disadvantages of Ion Chambers
Talking about advantages and disadvantages of detectors is somewhat relative,
because it depends to the manner of use of these devices. Still, due to the versatility of
ionization chambers it is possible to get a general look at their advantages and
disadvantages. Let us first discuss some of their advantages.
77
•
Insensitivity to applied voltage: Since the ionization current is essentially
independent of the applied voltage in the ion chamber region, therefore small
inevitable fluctuations and drifts in high voltage power supplies do not
deteriorate the system resolution. This also implies that less expensive power
supplies can be safely used to bias the detector.
•
Proportionality: The saturation current is directly proportional to the energy
deposited by the incident radiation.
•
Less Vulnerability to Gas Deterioration: There is no gas multiplication in
ionization chambers and therefore small changes in the gas quality, such as
increase in the concentration of electronegative contaminants, does not severely
affect their performance. This is true for at least the low resolution systems
working in moderate to high radiation fields.
Even though the ionization chambers are perhaps the most widely used detectors,
still they have their own limitations, the most important of which are listed below.
•
Low current: The current flowing through the ionization chamber is usually very
small for typical radiation environments. For low radiation fields the current
could not be measurable at all. This, of course, translates into low sensitivity of
the system and makes it unsuitable for low radiation environments. The small
ionization current also warrants the use of low noise electronics circuitry to
obtain good signal to noise ratio.
•
Vulnerability to atmospheric conditions: The response of ionization chambers
may change with change in atmospheric conditions, such as temperature and
pressure. However the effect is usually small and is only of concern for high
resolution systems.
78
3.9 Sources of Error in Gaseous Detectors
Ideally the measured ionization current in an ionization chamber should consist of all
the electron-ion pairs generated in the active volume. However, due to different losses,
the electrons and ions are not fully collected. For precision measurements, these losses
must be taken into account.
3.9.1 Effects of contaminants
The gases used in radiation detectors are generally not free from contaminants. The
most problematic of these contaminants are the electronegative molecules, which
parasitically absorb electrons and form stable or metastable negative ions. Some of
these impurity atoms are listed in Table 4.1.The most commonly found contaminants in
gaseous detectors are oxygen and water vapours. It is almost impossible to purify a
filling gas completely of oxygen. In fact, generally a few parts per million of oxygen is
present at the filling of any gaseous detector. This concentration increases with time due
to degassing of the chamber and, if the detector windows are very thin, by diffusion
from outside.
The capture of electrons by these contaminants is not only a problem for proportional
counters but also for high precision ionization chambers. On the other hand, for general
purpose ionization chambers, capture of a few electrons by the contaminants is of not
much concern as the nonlinearity caused by this generally falls within the tolerable
uncertainty in detector response.
Table 3.1: Electro affinities of different molecules and ions
79
The probability of electron attachment for a gas, is defined with the help of two
factors that have been measured for different gases: the mean lifetime τe for the
electrons and their collision frequency νe. In terms of τe and νe the probability of capture
in a single collision can be written as
𝑝=
1
𝜏𝑒 𝜈𝑒
(3.38)
The values of these parameters for some common gases are shown in Table 3.2. It is
apparent that the extremely small capture lifetimes of these gases can be a serious
problem for at least high precision systems. Even small quantities of contaminants such
as oxygen and water can produce undesirable non-linearity in detector response.
Table 3.2: Mean capture time τe, collision frequency νe, and probability of electron capture in
a single collision p for some common contaminants and filling gases for radiation detectors
[47]. All the values correspond to electrons at thermal energies and gases under standard
atmospheric conditions.
There are different mechanisms by which the contaminants capture electrons.
Radiative Capture
In this kind of capture, the capture of electron leaves the molecule in such an excited
state that leads to the emission of a photon:
𝑒 + 𝑋 → 𝑋 −∗
𝑋− → 𝑋− + 𝛾
where ∗ represents the excited state of molecule X. The radiative capture occurs in
molecules that have positive electron affinity. Fortunately enough, for the contaminants
80
generally found in filling gases of radiation detectors the cross section for this reaction
is not significant [48].
Dissociative Capture
In this process the molecule that has captured an electron, dissociates into simpler
molecules. The dissociation can simply be the emission of an electron with smaller
energy than the energy of the original electron
𝑒 + (𝑋𝑌. . 𝑉𝑍) → (𝑋𝑌. . 𝑉𝑍)−∗
(𝑋𝑌. . 𝑉𝑍)−∗ → (𝑋𝑌. . 𝑉𝑍)∗ + 𝑒 ′ 𝑤𝑖𝑡ℎ 𝐸𝑒 ′ < 𝐸𝑒
Here (XY..V Z) represents a polyatomic molecule. In a proportional counter, the
energy and the point of generation of the second electron may or may not be suitable to
cause an avalanche. This uncertainty can therefore become a significant source of
nonlinearity in the detector’s response if the concentration of such molecular
contaminants in the filling gas is not insignificant.
Not all polyatomic molecules emit secondary electrons during the process of deexcitation. Some molecules dissociate into smaller molecules such that each of the
fragments is stable.
𝑒 + (𝑋𝑌. . 𝑉𝑍) → (𝑋𝑌. . 𝑉𝑍)−∗
(𝑋𝑌. . 𝑉𝑍)−∗ → (𝑋𝑌)∗ + (𝑉𝑍)− (𝑠𝑡𝑎𝑏𝑙𝑒) 𝑜𝑟
(𝑋𝑌. . 𝑉𝑍)−∗ →
(𝑋𝑌. . 𝑉)∗ + 𝑍 − (𝑠𝑡𝑎𝑏𝑙𝑒).
It is also possible for a fragmented part of the molecule to go in a metastable state
and then decay to ground state by emitting an electron or by further dissociating
according to
𝑒 + (𝑋𝑌. . 𝑉𝑍) → (𝑋𝑌. . 𝑉𝑍)−∗
(𝑋𝑌. . 𝑉𝑍)−∗ → (𝑋𝑌)∗ + (𝑉𝑍)−∗
(𝑋𝑌)∗ + (𝑉𝑍)−∗ → (𝑋𝑌)∗ + (𝑉𝑍)∗ + 𝑒 𝑜𝑟
(𝑋𝑌)∗ + (𝑉𝑍)−∗ → (𝑋𝑌)∗ + 𝑉 ∗ + 𝑍 − .
81
Capture without Dissociation
In this process the polyatomic molecule captures an electron and instead of
dissociating into simpler molecules, it transfers its excess energy to another molecule.
This reaction can be written as:
𝑒 + (𝑋𝑌) → (𝑋𝑌)−∗
(𝑋𝑌)−∗ + 𝑍 → (𝑋𝑌)− + 𝑍 ∗
𝑍 ∗ → 𝑍 + 𝛾.
3.9.2 Recombination Losses
The recombination of electrons and ions is one of the major sources of uncertainty in
measurements especially at high fluxes of incident photons. Intuitively one can think
that the recombination rate should depend directly on the concentration of charges. This
suggests that the rate of change in the number of positive and negative charges should
be proportional to the number of charges themselves, that is
𝑑𝑛+
= 𝑆−∝ 𝑛+ 𝑛−
𝑑𝑡
𝑑𝑛−
= 𝑆−∝ 𝑛+ 𝑛− .
𝑑𝑡
(3.39)
(3.40)
Here α is called the recombination coefficient and S represents the source of charges.
The above two equations can be combined to give
𝑑(𝑛− − 𝑛+ )
= 0 (𝑎)
𝑑𝑡
→ 𝑛− = 𝑛+ +𝐶1 (𝑏)
(3.41)
where C1 is the constant of integration and depends on the initial difference between the
number of positive and negative charges. Substituting equation a into equation
b(equazioni da numerare dall’inizio) gives
82
𝑑𝑛−
= 𝑆−∝ (𝑛− )2 + ∝ 𝐶1 𝑛− . (𝑐)
𝑑𝑡
(3.42)
This is a first order linear differential equation with a solution of
𝑛− =
𝑟𝑆
𝑟1 − 𝑟2 𝐶2 𝑒𝑥𝑝 ��𝐶12 + ∝ 𝑡�
1−
𝐶2 𝑒𝑥𝑝 ��𝐶12
𝑟𝑆
+ ∝ 𝑡�
.
(3.43)
Here r1 and r2 are the roots of the quadratic equation on the right side of the quation c
given by
1
4𝑆
𝑟1 , 𝑟2 = �𝐶1 ± �𝐶12 + � .
2
∝
(3.44)
Similarly the solution for positive charges can be obtained. The roots in this case are
given by
𝑟1 , 𝑟2 =
1
4𝑆
�−𝐶1 ± �𝐶12 + �
2
∝
(3.45)
The constants C1 and C2 can be determined by using the boundary conditions: n = n0
at t = 0 and n = n at t = t. Instead of solving this equation for a particular case, we note
that these solutions represent complex transcendental behaviour, which eventually reach
the steady state value of r2, that is
𝑛∞ → 𝑟2 𝑎𝑠 𝑡 → ∞
(3.46)
For a special case when the initial concentrations of positive and negative charges are
equal, the constant C1 assumes the value zero and consequently the steady state charge
concentration becomes
83
𝑆
𝑛∞ = �
∝
(3.47)
This shows that the equilibrium or steady state charge concentration is completely
determined by the source producing electron-ion pairs and the recombination
coefficient. Application of electric field forces the charges to move toward respective
electrodes thus reducing the recombination probability.
84
Chapter 4
Collection efficiency: the ions recombination
correction factor
4.1 Introduction
In most radiotherapy clinics the dose released in a given point in a medium is
determined by measuring the amount of charge Q produced in a small cavity located at
that point. The cavity is usually an ionization chamber filled with gas at room
temperature and pressure. As explained in the previous chapters, when charged particles
cross a gaseous medium, positive ions and free electrons are created in the cavity by the
gas ionization.
The charge Q(V) measured at a given chamber potential V is generally smaller than
the saturation charge Qsat ; the loss charge is principally due to recombination of
positive and negative ions within the cavity. The ratio Q(V)/Qsat for a given chamber
potential V is defined as the charge collection efficiency or ion collection efficiency
f(V):
𝑓=
𝑄
𝑄𝑠𝑎𝑡
(4.1)
The ion collection efficiency of the chamber increases by raising the electric
potential between the polarizing and collecting electrodes. When all the other conditions
remain constant, as the polarizing potential increases from zero to some large value, the
quantity of charge collected increases rapidly and almost linearly, while at higher
voltages the increase in collected charge is more gradual and asymptotically approaches
the saturation charge Qsat. A plot of the collected charge Q versus the polarizing voltage
V results in the saturation curve. Fig. 4.1 shows a typical saturation curve. The ion
chamber collection efficiency is given by the saturation curve divided by the saturation
charge Qsat.
85
Figure 4.1 shows that charge loss in an ionization chamber decreases with increasing
polarizing potential V. However, there is an upper limit to the voltage to apply across
the plates of the chamber because of the onset of either electric breakdown of the
insulators constituting the chamber or charge multiplication in the chamber sensitive
gas.
Fig. 4.1: Typical plot of measured charge Q as a function of the chamber polarizing potential V.
The measured charge increases almost linearly for low voltages and approaches asymptotically
the saturation charge Qsat at higher voltages.
Determination of the collection efficiency can be accomplished easily in practice
assuming that no pockets of low field-strength exist in the chamber volume because of
poor chamber geometry where ion recombination may persist. If the collection
efficiency of a chamber is known for a given electrode separation and polarizing
potential, Qsat can be determined through a measurement of Q( V) using Eq. (4.1).
The appropriate Qsat for dose determination in radiation dosimetry is calculated from
the measured charge Q following suitable models for charge loss from ion
recombination. There are two types of recombination processes, namely initial
recombination and general recombination; the latter separates two categories of
ionizing radiations: continuous and pulsed.
Initial recombination represents the recombination that occurs between ions
produced within the track of a single ionizing particle and is thus independent of dose
rate. For initial recombination, 1/Q varies linearly with 1/V. General recombination, in
contrast to initial recombination, depends on dose rate and applies to ions produced in
different ion tracks that meet and recombine. For general recombination, l/Q in the near
saturation region (f ≥ 0.7) was found to vary linearly with l/ V2 in continuous beams
86
and linearly with 1/ V in pulsed beams; in electronegative gases it was shown that in the
near saturation region, initia1 recombination is negligible, in comparison with general
recombination [49].
4.2 Theoretical background
4.2.1. Recombination rate
The probability that an ion pair recombines in the chamber volume depends on the
concentration of positive and negative ions at a given location in the chamber and on the
ion interaction time. The number of ions per unit volume dN/dV lost for recombination
per unit time, di, is the so-called recombination rate and can be found from the
following relationship:
𝑑 𝑑𝑁
� � = 𝛼𝐶 + 𝐶 −
𝑑𝑉 𝑑𝑡
(4.2)
where α is a constant of proportionality called recombination coefficient, and C+ and
C - are the positive and negative ion concentrations, respectively.
Equation (4.2) can be written in terms of the amount of charge lost for recombination
q = eN and as a function of the positive and negative charge densities
ρ+ = eC+ and ρ-
= eC-, respectively, where e is the electron charge. The rate at which charge is lost for
recombination is the following:
𝑑 𝑑𝑞
𝑑𝜌 𝛼 + −
� �=
= 𝜌 𝜌
𝑑𝑉 𝑑𝑡
𝑑𝑡 𝑒
(4.3)
Both the exact ions concentration at a given point in the sensitive volume and the
interaction time are directly related to the polarizing potential V, to the electrode
separation d, and to the positive and negative ions mobility in the chamber gas, k+ and krespectively. Inside a polarized ionization chamber, positive ions drift toward the
cathode while negative ions drift towards the anode. The ions have drift velocities that
are proportional to the electric field E in the chamber; positive ions drift toward the
87
cathode with a velocity of 𝑣 + = 𝑘 + ∙ 𝐸 and negative ions toward the anode with a
velocity of 𝑣 − = 𝑘 − ∙ 𝐸.
In air and in other electronegative gases with high electron affinities, free electrons
produced by ionizing radiation quickly attach themselves to a gas molecule, resulting in
a heavy negative ion, thus k-≈ k+. In inert gases, electrons do not combine with gas
molecules, thus the negative charge carriers are free electrons with mobility k- about 3
orders of magnitude greater than k+. The ion mobility, greatly influences the
recombination rate in the chamber. The ions with high mobility have less time to
interacts, consequently, the probability of recombination is reduced.
4.2.2 Collection efficiency for general recombination in continuous
radiation beams
Boag and Wilson [49], expanding the work of Mie [50], developed a straightforward
theory for general recombination in a continuous beam of radiation.
In a parallel plate ionization chamber exposed to a field of ionizing radiation, which
produces a uniform charge per unit volume of gas and per unit time, if recombination of
ions in the chamber volume does not occur, the ion current I at the collecting electrode
is:
𝐼 = 𝜌𝑐̇ 𝐴𝑑
(4.4)
where ρc is the rate of ion production per unit volume by a continuous source of
radiation, A is the area of the collecting electrode, and d is the electrode separation.
Under the influence of the electric field, positive ions produced in the cavity volume
will migrate towards the negative electrode N with a velocity of k+V/d and negative ions
will migrate towards the positive electrode P with velocity k-V/d. The steady flow of
ions will create a charge gradient between the electrodes N and P. Under steady-state
conditions, the positive charge density 𝜌𝑐+ will increase linearly from zero at P until a
maximum value reached at N. Let 𝜌𝑐+ (𝑥) be the positive charge density at a distance x
from the positive electrode P. The current I(x) corresponds to the quantity of charge per
second crossing a plane located at x and parallel to the electrode plates.
88
Thus on the electrode N the expected current is:
𝐼(𝑑) = 𝜌𝑐+ (𝑑) 𝐴
𝑘+𝑉
𝑑
(4.5)
and the positive charge density can be calculated as follow :
𝜌𝑐+
𝜌𝑐̇ 𝑑2
(𝑑) = +
𝑘 𝑉
(4.6)
considering the equations (4.4) and (4.5).
By a linear interpolation between positive charge density at zero and results of Eq.
(4.6), the positive charge density at any distance x from P is available as follow:
𝜌𝑐+ (𝑥) =
𝜌𝑐̇ 𝑑
𝑥
𝑘+𝑉
(4.7)
With the same procedure the negative charge density at a distance x from P is
available with the following equation :
𝜌𝑐− (𝑥) =
𝜌𝑐̇ 𝑑
(𝑑 − 𝑥)
𝑘+𝑉
(4.8)
A schematic diagram of the steady-state positive and negative ion density developed
between the polarizing and collecting electrodes of a parallel-plate ionization chamber
is show in Fig. 4.2.
Fig. 4.2: Schematic diagram of a parallel-plate chamber in which charges are continuously
produced uniformly throughout the chamber volume. The densities of the positive and negative
charge carriers are show as a function of the distance x from the positive electrode P.
89
If equations (4.7) and (4.8) are used, in Eq. (4.3), the loss charge for recombination per
second (dq/dt) in a volume of area A and infinitesimal thickness dx is described by the
following equation:
𝑑𝑞
∝ 𝜌𝑐2̇ 𝑑 2
= � � + − 2 𝑥 (𝑑 − 𝑥)𝐴𝑑𝑥.
𝑑𝑡
𝑒 𝑘 𝑘 𝑉
(4.9)
To obtain the total loss charge for recombination per second within the entire
chamber volume, the eq. 4.9 must be integrated from x = 0 to x = d as follow:
𝑥=𝑑
∝ 𝜌𝑐2̇ 𝑑2
∝ 𝜌𝑐2̇ 𝑑 5
𝐴� � + − 2�
𝑥 (𝑑 − 𝑥)𝑑𝑥 = 𝐴 � � + − 2
𝑒 𝑘 𝑘 𝑉 𝑥=0
𝑒 𝑘 𝑘 𝑉
(4.10)
Dividing Eq. (4.10) by the ideal ion current I [Eq. (4.4)], we obtain the fraction 𝑓𝑟′ of
charge recombined in the chamber cavity:
where
∝ 𝜌𝑐̇ 𝑑 4
1
𝑓𝑟′ = � � + − 2 = 2
𝑒 𝑘 𝑘 𝑉
𝜁
∝ 𝑘+𝑘− 2
𝜁 = 6� �
𝑉
𝑒 𝜌𝑐̇ 𝑑 4
2
(4.11)
(4.12)
If the ion recombination in the chamber is not negligible, then Eq. (4.11)
overestimates the fraction of ions lost for recombination since the charge density is
assumed maximal at all points along the integration. We can attempt to improve the
solution found in Eq. (4.11) by postulating that the charge densities at each electrode are
only a fraction f of the total current, i.e., 𝜌𝑐+ (𝑑) = 𝑓𝜌𝑐 𝑑 2̇/𝑘 + 𝑉 and 𝜌𝑐− (𝑑) =
𝑓𝜌𝑐 𝑑2̇/𝑘 − 𝑉 instead of the values given in Eqs. (4.7) and (4.8). Repeating the
calculations leading up to Eq. (4.11) with this reduced charge density values the fraction
of charge 𝑓 ′′ lost for recombination in the chamber is :
𝑓𝑟′′ =
𝑓2
𝜁2
(4.13)
90
The above expression, however, underestimates the fraction of the charge
recombined because a minimum charge distribution is assumed at all points along the
integration. The actual charge distributions do not remain linear with distance from the
electrodes; in fact, they are slightly sigmoidal in shape due to the influence of space
charge on the electric field. A more detailed analysis of the charge distribution was
presented by Mie [50] and simplified by Greening [51] for ionization in air. This work
leads to an estimation of the actual fraction of charge fr lost by recombination in the
chamber which is the geometric mean of Eqs. (4.11) and (4.12), giving
𝑓2
𝑓𝑟 = 2
𝜁
(4.14)
One can express the fraction of the ionization which is measured at the collecting
electrode as f = ( 1 - fr ) . Rearranging Eq. (4.13) and solving for f gives
𝑓=
1
1+
1
𝜁2
(4.15)
Thus, the charge collection efficiency 𝑓𝑔𝑐 (𝑉) for general recombination as a function
of applied potential V in an ionization chamber filled with electronegative gas and
irradiated by a continuous particle flow, with a constant dose rate is given by the
following relations:
𝑓𝑔𝑐 (𝑉) =
𝑄(𝑉)
𝑄𝑠𝑎𝑡
=
1
Λ𝑐
𝑔
1+ 2
𝑉
(4.16)
in which the constant Λ𝑐𝑔 is expressed as
∝ 𝜌𝑐̇ 𝑑 4
Λ𝑐𝑔 = � � + − 2
𝑒 𝑘 𝑘 𝑉
(4.17)
where the superscript c denotes continuous radiation and the subscript g denotes
general recombination. The relationship was found to be valid in the near saturation
region (𝑓𝑔𝑐 ≥ 0.7) and may also be written in the following form:
91
𝜆𝑔𝑐
1
1
=
+
𝑄 𝑄𝑠𝑎𝑡 𝑉 2
(4.18)
where constants Λ𝑐𝑔 and 𝜆𝑔𝑐 contain chamber and gas parameters and are related by
𝜆𝑔𝑐 = Λ𝑐𝑔 /𝑄𝑠𝑎𝑡 .
From the Eq. (4.18), it can be seen that, as expected, whenever 𝑉 → ∞, 𝑄 → 𝑄𝑠𝑎𝑡
(see Fig. 4.3).
A method used to correct for general recombination in case of continuous radiation,
is the so called two-voltage method, in which the collected charge is measured at two
voltages, VH and VL, assuming that Eq. (4.16) is valid in the region spanned by the two
voltage points. [52].
If QH and QL are measured charges at VH and VL, respectively, then 𝑓𝑔𝑐 (𝑉𝐻 ) can be
written as follow:
𝑓𝑔𝑐 (𝑉𝐻 ) =
𝑄𝐻
=
𝑄𝑠𝑎𝑡
𝑄𝐻
𝑉
�𝑄 − � 𝐻�𝑉 �
𝐿
𝐿
1−�
𝑉𝐻
�𝑉 �
𝐿
2
2
.
(4.19)
Fig. 4.3: Jaffe diagrams: for the determination of Qsat through a linear extrapolation of (a) l/Q vs
1/V2 for general recombination with continuous radiation for which the collection efficiency has
1
1
the form 𝑓 = Λ𝑐𝑔 and (b) 1/Q vs l/V for collection efficiencies having the form 𝑓 = Λ𝑝
1+ 2
𝑉
1+
𝑔
𝑉
92
4.2.3 Collection efficiency for general recombination in pulsed
radiation beams
For an ionization chamber filled with electronegative gas irradiated with a pulsed
radiation at constant dose rate and where the pulse duration is short compared to the
mean ion transit time in the cavity, the chamber collection efficiency does not follow
the theory described in the previous section.
For pulsed radiation beams no steady-state ion density is assumed in the chamber
volume and the ionization produced during each pulse must be considered separately.
The total charge density per pulse ρp, is considered instantaneous. [53]
Between pulses, the ions drift to the oppositely charged electrodes and creating three
distinct regions in the chamber sensitive volume: (1) a positive ion region near the
cathode N, (2) a negative ion region near the anode P, and (3) a recombination region in
which positive and negative charges coexist. These regions are shown schematically in
Fig. 4.4. The width ω of the envelope of the recombination region can be expressed by
the following equation:
𝜔(𝑡) = 𝑑 − 𝑡(𝑘 + + 𝑘 − )
𝑉
𝑑
(4.20)
Thus at time t = 0 the width 𝜔(0) of the region in which positive and negative
charges can interact to recombine is equal to the electrode separation d. At a time T, the
width of the recombination region will be zero and recombination is no longer possible.
The period of recombination T is solved for by setting the width 𝜔(𝑇) = 0 and solving
for T as follow:
𝑇=
𝑑2
(𝑘 + 𝑘 − )𝑉
(4.21)
When gas ionization occurs by radiation, an equal number of positive and negative
ions is produced. Since a negative ion necessarily recombines with a positive ion, the
positive and negative charge densities are always equal, and one can assume ρ = ρ+ = ρinto Eq. (4.3) to get
93
𝑑𝜌 𝛼 2
= 𝜌
𝑑𝑡 𝑒
(4.22)
Integrating this equation and solving for the charge density ρ at a given time t yields
𝜌(𝑡) =
𝜌𝑝
.
𝛼
1 + � 𝑒 � 𝜌𝑝 𝑡
(4.23)
where ρp, is the instantaneous charge density produced during each pulse.
Fig.4.4: Schematic diagram of a parallel-plate chamber in which a pulsed radiation beam has
produced a uniform distribution of positive and negative charges. Positive charges drift toward
the negative electrode N with velocity V+, while negative charges drift toward the positive
electrode P with velocity V-. Charge recombination is possible only in the overlap region having
a width 𝜔 chat decreases with time.
There is a finite probability for ion recombination as long as there exists some
overlap of the positive and negative ions in the chamber volume. The fraction of ions
which recombine in the chamber volume in a pulsed radiation field is a function of the
positive and negative electron densities, of the ion overlap region dimension and of the
electric polarizing potential.
The recombination fraction fr may be expressed as:
fr =
T
α
� � � ρ2 (t)ω(t)dt,
�ρp Ad� 0 e
A
(4.24)
94
where A is the electrode area, ρ(t) is given by Eq. (4.23), and ω(t) is given by
Eq. (4.20).
The integral can be divided into two parts and solved to give
1
fr = �1 − ln(1 + u)� ,
u
where
∝ ρċ d2
u=� � + −
e k k V
(4.25)
(4.26)
Hence, the collection efficiency 𝑓 = 1 − 𝑓𝑟 , is given by the following relationship:
1
f = ln(1 + u) .
u
(4.27)
The approximation to the collection efficiency f for V → ∞, i.e., for u → 0 is found
by expanding In ( 1 + u) for, u → 0,
u2 u3
u− 2 + 3
u
1
f=
≈ 1− ≈
.
u
2 1+u
2
(4.28)
In the near saturation region, a modified expression for the charge collection
efficiency in a pulsed radiation beam can be written as:
p
fg (V) =
Q(V)
=
Qsat
p
1
p
λg
1+ V
(4.29)
where Λ g = αρp d2 /2(k + + k − )eV. Equation (5.27) may also be written as
p
p
λg
1
1
=
+
,
Q Qsat V
p
(4.30)
p
with the constant λg defined as λg = Λ g /Qsat . As seen in the case of continuous
radiation, from Eq. (4.30), for 𝑉 → ∞, 𝑄 → 𝑄𝑠𝑎𝑡 .
95
A two-voltage technique from Eq. (4.29) allows determining Qsat. If QH and QL are
p
charges measured at VH and VL, respectively, then fg (VH ) can be written as:
p
fg (VH ) =
QH
=
Qsat
V
QH
�Q − � H�V �
L
L
V
1 − � H�V �
L
.
(4.31)
96
4.3 The multiple gap ionization chamber
As explained in chapter 2, the development of accelerators for hadrontherapy is
towards compact machines that produce high-intensity, pulsed beam. These new beam
characteristics require an optimized version of the current detectors which allows a high
precision of the measurements in conditions of charge collection inefficiencies
described earlier in this chapter.
The University of Torino and INFN are developing, with this aim, an innovative
multiple gap ionization chamber. The purpose of this integral chamber is to measure
high-intensity charged particle beams and simultaneously determine the collection
efficiency. This device includes three parallel plates ionization chambers with
independent anodes and cathodes separated by a gap, filled with nitrogen gas (Fig. 4.5).
The gaps are designed to be of different width in order to have different charge
recombination effects. The chamber layer-structure is represented in Fig. 4.6, with its
construction specifications. Since the chambers have different collection efficiencies, a
procedure based on the data collected in a pair of chambers was developed which allows
to correct the recombination and to determine the total ionization charge.
a
b
c
d
Fig 4.5: Photos of: a) chatode, made in aluminium deposited over a thin layer of mylar; b)
anode, made in aluminium deposited over a layer of kapton; c) empty chamber’s box; d) the
assembled triple gap ionization chamber.
97
Fig. 4.6: Representation of the chamber layer-structure with its construction specifications.
This chapter will describe in detail the principle of operation of the multi gap chamber.
The front-end readout electronics will be described in the next chapter.
4.3.2 Method for the determination of the collection efficiency
When high intensity pulsed beams with intensities of 1012 ions/s are considered, and
the gaps of the chamber are in the order of few millimetres, the detector will work in the
recombination region (Fig. 3.5, Chapter 3); in order to prevent the discharges, the bias
voltage is limited and the released charges cannot be totally collected. Therefore,
working in this unsaturated zone, the recombination of the charges becomes nonnegligible and it is necessary to correct for it.
In order to simplify the notation, from this point on, Q stands for the charge released
into the chamber gas (previously named Qsat) and Q’ is used for the charge collected by
the electrodes. The collection efficiency is expressed as:
𝑓=
𝑄′
𝑄
(4.32)
98
Let us consider two gaps with different thickness and different applied voltage, both
filled with nitrogen. Let us also assume that the electrodes are thin and the two gaps are
close enough such that the beam crossing the perturbation of the beam is negligible.
Therefore
𝑄1′
𝑄2′
𝑓1 =
;𝑓 =
𝑄1 2 𝑄2
(4.33)
The collected charges Q’ are measured with the electronic read-out of each chamber.
The ratio between the collected charges is equal to:
𝑄1′ 𝑓1 𝑄1
=
𝑄2′ 𝑓2 𝑄2
(4.34)
Since the released charges 𝑄1 and 𝑄2 are proportional the distance d between the
electrodes,
1
𝑓1 𝑄1
𝑓1 𝑑1 𝑑1 𝑢1 ln(1 + 𝑢1 )
=
=
𝑓2 𝑄2
𝑓2 𝑑2 𝑑 1 ln(1 + 𝑢 )
2𝑢
2
2
𝑢1 =
𝑢2 =
2
𝛼⁄
𝑑12
𝑒 𝜌1 𝑑1
= 𝜌1 𝜇1
𝑘− + 𝑘+ 𝑉1
𝑉1
2
𝛼⁄
𝑑22
𝑒 𝜌2 𝑑2
= 𝜌2 𝜇2
𝑘− + 𝑘+ 𝑉2
𝑉2
(4.35)
(4.36)
(4.37)
Where 𝜇1 and 𝜇2 are constant values.
99
Fig. 4.7: A schematic representation for the series of two parallel plates ionization chambers.
If the same beam passes through both chambers, 𝜇1 𝜌1 = 𝜇2 𝜌2 and 𝑢2 can be
expressed in terms of 𝑢1 as:
V1 d22
u2 = u1
V2 d12
Q′1 f1 Q1 f1 d1 d1
=
=
=
Q′2 f2 Q2 f2 d2 d2
Let’s rename the ratios as
𝑉2 𝑑22
ln(1 + u1 ) u1
∙
.
𝑉1 𝑑12
V1 d22
ln �1 + u1 V 2 � u1
2 d1
V1
d1
= a;
=b
V2
d2
(4.38)
(4.39)
(4.40)
the formula (4.39) can be rewritten as
Q′1 a ln(1 + u1 )
=
Q′2 b ln �1 + u a �
1 2
b
(4.41)
Q′1
a
a Q′
�1 + u1 2 � 2 = (1 + u1 )b
b
(4.42)
100
or
𝑄1′ 𝑏
𝑎 𝑄′ 𝑎
𝑢1 = �1 + 𝑢1 2 � 2 − 1.
𝑏
(4.43)
This is a transcendental equation in the form
𝑢 = 𝑓(𝑢)
and it can be solved for 𝑢 using an iterative method as the Newton-Raphson method
[54]. This method is a powerful technique for solving equations numerically and it is
based on the simple idea of a linear approximation.
Let u0 be an estimate of 𝑢1 and let 𝑢1 = 𝑢0 + ℎ. Since the true root of the equation is
𝑢1 , and ℎ = 𝑢1 − 𝑢0 , the number ℎ measures how far the estimate 𝑢0 is from the truth.
Since ℎ is small enough, we can use the linear approximation and write:
0 = 𝑓(𝑢1 ) = 𝑓(𝑢0 + ℎ) ≈ 𝑓(𝑢0 ) + ℎ𝑓 ′ (𝑢0 ),
(4.44)
and therefore, unless 𝑓 ′ (𝑢0 ) is close to 0,
ℎ≈−
𝑓(𝑢0 )
.
𝑓 ′ (𝑢0 )
(4.45)
It follows that
𝑢1 = 𝑢0 + ℎ ≈ 𝑢0 −
𝑓(𝑢0 )
.
𝑓 ′ (𝑢0 )
(4.46)
The new value estimated for 𝑢1 is therefore given by
𝑢1 = 𝑢0 −
𝑓(𝑢0 )
𝑓 ′ (𝑢0 )
(4.47)
Continue in this way. If 𝑢𝑛 is the current estimate, then the next estimate 𝑢𝑛+1 is given
by
101
𝑢𝑛+1 = 𝑢𝑛 −
𝑓(𝑢)
𝑓′(𝑢)
(4.48)
Here un and un+1 are the estimated values of u for the step n and n+1 of the iterative
method and f’ stands for the first derivative of u as the function reported in Eq. (4.43).
Once obtained the value for 𝑢 it is possible to calculate the collection efficiency 𝑓.
For the first gap:
𝑓1 =
1
ln(1 + 𝑢1 ) .
𝑢1
(4.49)
The same procedure can be applied to obtain 𝑓2 using the formulae described in the
following:
𝑢1 = 𝑢2
𝑢2 = �1 + 𝑢2
𝑓2 =
𝑉2 𝑑12
𝑉1 𝑑22
𝑄2′ 𝑎
2 𝑄′ 𝑏
𝑏
1
𝑎
�
(4.50)
−1
1
ln(1 + 𝑢2 ) .
𝑢2
(4.51)
(4.52)
Once the collection efficiency 𝑓 is determined for both the chambers it is possible to
determine the charge 𝑄 released into the chamber by using the equations (4.33).
This method just described cannot be used online for reasons of computational
speed; therefore, with the aim to estimate the value of 𝑓1 and 𝑓2 , we plan to use the
graphical method explained in the following.
Using the Eq. (4.34) and Eq. (4.35), the ratio f2/f1 can be expressed as,
𝑓2 𝑄2 𝑓2 𝑑2
𝑄2 𝑑2
=
→
=
𝑓1 𝑄1 𝑓1 𝑑1
𝑄1 𝑑1
(4.53)
102
and
𝑓2 𝑄′2 𝑄1 𝑄′2 𝑑1
=
=
𝑓1 𝑄′1 𝑄2 𝑄′1 𝑑2
(4.54)
In so doing, since we know the distances d for the two gaps, we can measure the
collected charges 𝑄′1 and 𝑄′2 . Then, with these values, changing the initial ion density
n0 (i.e. changing the beam intensity), it is possible to tabulate analytically a series of
values of f2/f1. The plot of f2/f1 vs n0 is a monotonic function and for each value of f2/f1,
f1 and f2 are uniquely determined, for a specific n0, as represented in Fig. 4.8.
Fig. 4.8: Example of the graph used for the estimation of the collection efficiencies f1 and f2.
Let’s see what we would expect to find, using the method just presented.
4.3.3 Expected results
In this paragraph I will consider the expected beam parameters, for example the
energy and the intensity, together with the density of the medium crossed by the
particles and the geometry of the detector in order to simulate the effects of charge
recombination and then the collection efficiency differences for each gap of the
chamber. In the calculations, a proton beam will be assumed.
103
When a pulsed-beam crosses a gaseous medium, the charge released by ionization
can be estimated by the formula:
𝑑𝐸� ∙ 𝜌 𝑑 𝐼
𝑑𝑥 𝑔𝑎𝑠 𝑏𝑒𝑎𝑚 ∆𝑡 𝑒
𝑄(𝐸) =
𝑊
(4.55)
Where 𝑑𝐸�𝑑𝑥 [MeVcm2/g] is the stopping power, 𝜌𝑔𝑎𝑠 [g/cm3] is the density of the
gas crossed, 𝑑 [cm] is the length of the path; 𝐼𝑏𝑒𝑎𝑚 is the mean beam intensity [ions/sec]
for a pulse of duration ∆𝑡 [s]; 𝑒 [C] is the charge of the electron and 𝑊 [MeV/pairs] is
the average energy required to create an ion pair for a specific gas.
Let's now consider two different chambers with different gap distances d1, d2; if all
the parameters are known, the released charges Q1 and Q2 are simply calculated. Since
the chambers are in series, the beam characteristics are in good approximation the same.
As mentioned before, the initial recombination effects can be assumed as negligible, so,
for a pulsed beam, the collection efficiency is expressed as:
𝑓=
2
𝛼⁄
1
𝑒 𝜌𝑑
ln(1 + 𝑢) 𝑤𝑖𝑡ℎ 𝑢 =
𝑢
𝑘− + 𝑘+ 𝑉
(4.56)
where α is the recombination coefficient, k- and k+ are the ion mobilities for negative
and positive ions, all depending on the gas, the initial charge density is ρ = n0 ∙ e ,
where n0 is the initial density of ions in the gas created when the beam crosses the
gaseous medium. n0 depends linearly on the beam intensity.
dE� ∙ ρ d I
Q(E)
dx gas beam ∆t
ions
n0 �
=
�cm3 � =
Volume
Wπdr 2
(4.57)
According to the approximation used in this calculation, the ionizing volume of the
beam is considered to be a cylinder with a radius r. In order to fix r value, we referred to
the CNAO synchrotron beam, where the beam sizes have a width at half height at the
isocentre (FWHM)iso comprised between 4 and 10 mm [55]. In our calculation, we
decided to take (FWHM)iso = 10 mm
104
r=
(FWHM)iso
1 cm
=σ=
= 0.43 cm.
2.355
2.355
(4.58)
The Gaussian radius σ is used as the radius r for the cylindrical volume formula.
Once obtained the value of the n0 parameter, u, f and the collected charge Q′ can be
estimated.
Q′ = fQ.
(4.59)
In table 4.1, the values used for the simulations are reported. The gap between the
chamber plates is supposed to be filled with nitrogen N2.
Tab. 4.1: Constant values used for the simulations. 𝑆 [MeVcm2/g] is the stopping power for a
particle beam energy of 150 MeV, 𝐼𝑏𝑒𝑎𝑚 is the mean beam intensity for a pulse of duration 𝑑𝑡.
Qc is the quantum charge, the sensibility of the detecting system [56], n0 is the initial ions
density, V1 is the fixed bias voltage of the chamber 1 whereas V2, the bias voltage of chamber 2,
has three different values. On the right, the parameters related to the nitrogen gas that fills the
gaps. 𝜌𝑔𝑎𝑠 is the density of the nitrogen contained between the electrodes, 𝑊 is the average
energy required to create a pair for the nitrogen. α is the recombination coefficient, k- , k+ are the
ion mobility for negative and positive ions in the considered gas.
The collection efficiency is obviously strongly dependent on n0 because the higher is
the number of the charge density and the higher will be the probability that they
recombine.
Equation 4.57 shows that the initial charge density n0 is linearly dependent on the
beam intensity. Starting from the values in Tab. 4.1, if we try to change the n0 value,
105
(i.e. the beam intensity per pulse), reducing it by a couple of order of magnitude, the
recombination effects fall sharply and the number of the collected charges increases.
The plot below shows the normalized charge saturation as a function of the applied
voltage for three values of beam intensity.
Fig. 4.9: Saturation curves for 𝑛0 = 2,87 ∙ 109 , 𝑛0 = 2,87 ∙ 108 and 𝑛0 = 2,87 ∙ 107 . The
reference ionization chamber has d=0,5 cm and it is filled by nitrogen.
Another question of interest is the determination of the uncertainty in the collection
efficiency estimation. Among the different sources of uncertainties, the charge quantum
Qc, representing the uncertainty in the measurement of the collected charge, is expected
to be dominant. In the following, a Qc of 200fC is assumed which corresponds to the
value in use in the monitor chambers at CNAO. As mentioned before, with the Eq.
(4.55) and Eq. (4.56), we can estimate the charge released and the collection efficiency,
and therefore the collected charge Q’ that has Qc as uncertainty. The uncertainty will be
propagated to the collection efficiency, for different settings of bias voltage and initial
ion density n0.
Let's consider chamber 1 as the reference one. The voltage between the electrodes of
this chamber is kept constant. Varying the value of 𝑛0 (i.e. considering different values
of ion beam intensity), it is possible to observe the trend of f1, f2 and f2/f1 for some
typical values of V2, as reported in Fig. 4.10. Observing these plots it is possible to
estimate the collection efficiency variations for different configurations of the chamber
106
and it is precisely from the relative collection efficiency f2/f1 that we can derive the
efficiency of the two chambers separately correct for it.
Fig. 4.10: Collection efficiencies in function of 𝑛0 for V1 = 600V fixed, and V2 = 200, 300 and
400 V.
107
Assuming that only the Q’ have not negligible errors, the f2/f1, uncertainty can be
obtained from the error propagation:
𝑄2′
𝑄1′
=
𝑓2 𝑄2
𝑓1 𝑄1
, Q1 and Q2 differ only for the distance between the electrodes so
𝑓2 𝑄2′ 𝑑1
=
𝑓1 𝑄1′ 𝑑2
(4.60)
therefore
�
2
2
⃓
⃓
′
′
⃓
𝑄
𝑄
⃓
𝛿 � 2�𝑄 ′ �
𝛿 � 2�𝑄 ′ �
⃓
⎛
⎞
⎛
⎞
1
1
𝑓2
𝑑1 ⃓
⃓
⎜
⎟
⎜
⎟
𝜎� � = ⃓
𝜎(𝑄2′ )⎟ + ⎜
𝜎(𝑄1′ )⎟
⎜
𝛿𝑄2′
𝛿𝑄1′
𝑓1
𝑑2 ⃓
⃓
⎜
⎟
⎜
⎟
⃓
⃓
⃓
⎷⎝
⎠
⎝
⎠
(4.61)
With the aim to obtain the standard deviation for u values, we linearize the f2/f1
curves in Fig.4.11 and extract an angular coefficient m for each value of u
𝑓
𝜕 � 2�
𝑓1
m=
𝜕𝑢
𝑓
𝜎 � 2 ��
𝑓2
𝑓1
𝜎 � � = 𝜎(𝑢) ∙ 𝑚 → 𝜎(𝑢) =
𝑚.
𝑓1
(4.62)
(4.63)
At this point, with the error propagation, the σ(f) is obtained:
𝑓=
1
ln(1 + 𝑢)
𝑢
2
��𝑢�1 + 𝑢� − ln(1 + 𝑢)�
𝜕𝑓
�
𝜎(𝑓) = � 𝜎(𝑢)� =
∙ 𝜎(𝑢).
𝜕𝑢
𝑢2
(4.64)
(4.65)
108
A representation of σ(f) as a function of 𝑛0 , is not effective because, we cannot
understand which value of efficiency, the standard deviation is referred to. For this
reason, we decided to use the relative per cent uncertainty
𝜎(𝑓)
�𝑓.
Fig. 4.11: The relative efficiency error for the chamber 1, as a function of n0 and the related
value of 𝑓1 .
From the Fig.4.11, It seems that it can be possible to obtain a good resolution with
errors ≤ 1% for an extended region of 𝑛0 values, where the V2 values do not affect much. In
particular, we can see that there is a minimum for 𝜎𝑟𝑒𝑙 (𝑓1 )% at about n0 = 1E+09 where
the efficiency 𝑓1 is about 0.9 and this minimum is practically the same for the three
values of V2. It seems also that, for n0 > 1E+10, is better to use the higher value of the
bias voltage whereas, for n0 < 1E+08, the best choice would seem to do not use this
method, since the error is increasing in a region where the collection efficiency is closed
to 1.
In Fig. 4.12, there are different series of 𝜎(𝑓1 ) vs V2 for different values of n0 . For
n0 in the order of E+09, the values of the standard deviation are almost constant, as
expected from the previous graph.
109
Fig.4.12: The efficiency error for chamber 1, in function of V2. The different series are related
to different values of n0 .
Though the study is focused on the estimation of the collection efficiency 𝑓1 , the
same procedure is repeated for 𝑓2 . The f vs u2; plots and error propagations are reported
below.
𝑓2
𝜎(u2) = 𝜎 � � ∙ 𝑚
𝑓1
𝜎(𝑓) =
��𝑢�1 + 𝑢� − ln(1 + 𝑢)�
𝑢2
(4.66)
∙ 𝜎(𝑢)
(4.67)
Fig. 4.13: The relative efficiency error for chamber 2, in function of different values of n0 .
110
In Fig. 4.13, similarly to the previous situation, 𝜎𝑟𝑒𝑙 (𝑓2 )% has the same minimum
value for the three different V2 at about n0 = 5E+09, and this minimum is lower than
0.5%.
In Fig. 4.14 the 𝑓2 standard deviations for three values of V2 are represented.
Fig.4.14: The efficiency error for chamber 2, in function of V2. The different series are related
to different values of n0 .
Observing the figure above, we can say that, increasing V2, 𝜎(𝑓2 ) increases. This
behaviour depends on our method of study because, as we can see, the more the gap
characteristics are similar and the higher is the uncertainty in 𝑓2 estimation.
Furthermore, the lowest values of 𝜎(𝑓2 ) correspond to n0 ~5E+09.
111
Chapter 5
The read-out front-end chip characterization
The Multi gap chamber has to be connected to electronic circuits allowing
determining the charge collected at the anodes. The charge is digitized into counts, each
count corresponding to a constant quantum. For this purpose, the INFN in collaboration
with the University of Torino developed a family of chips in the last years, with the aim
of managing currents entering up to 64 channels and measuring the corresponding
charge by converting it into counts. The TERA08 chip is the last version of these ASICs
(application-specific integrated circuit). This chip is purpose-built in order to read the
data from the ionization chambers used for beam monitoring in hadron therapy (Fig.
5.1).
To achieve a large dynamic range, the ASIC architecture is based for each channel
on a current-to-frequency converter, followed by a 32 bit digital counter. Using this
architecture, the charge can be measured by counting the number of pulses coming out
from the converter in a given time [57].
𝜈=
𝐼𝑖𝑛
𝑄𝐶
(5.1)
where ν is the frequency of counts, Iin is the input current and Qc is the charge
quantum. Therefore, the number of pulses generated in the measurement time,
multiplied by the charge quantum, gives the total charge read-out from the channel.
To acquire data from the TERA chip, an acquisition system was developed. It is
based on a National Instrument FlexRIO FPGA module for a PXI platform and Lab
View software. Data acquisition system (DAQ) is performed with a PC using a program
explicitly developed for this purpose. This software reads out the data form the frontend TERA chip and provides several histograms and informations, in particular:
•
the number of counts for a selected channel and the corresponding standard
deviation;
112
•
the total number of counts, i.e. the sum of the count over all the channels, and
the corresponding standard deviation.
Fig. 5.1: A schematic representation of the signal treatment: form the detector to the digitalized
format.
5.1 The TERA08 chip: Circuit architecture and operation
mode
The front-end electronics of the chamber is based on the TERA08 chip. This ASIC,
designed in CMOS 0.35 μm technology, has 64 channels and consists of a current-tofrequency converter followed by a counter; the maximum frequency of the converter is
20 MHz.
The chip design goals were as follows: uniform relative channel-to-channel gain,
linearity over a large dynamic range and negligible background currents. These
requirements demand the use of a large scale integration technology, which
consequently allows installing the chips close to the detector (the size of the chip is 4.55.4 mm2).
The TERA08 can work with inputs of both polarities, having 32 bits synchronous
counters with up/down counting capability. In this way the charge can be measured by
counting the pulses coming out from the converter in a given time interval. The output
of the circuit is therefore already in a digital format, thus making the successive data
handling easier. The schematic representation of a channel is shown in Fig. 5.2.
The chip works with a clock frequency of 100MHz and a maximum conversion
frequency of 20 MHz. The bipolar input conversion allows the extension of the
113
applications to the entire field of detectors, and a better precision in the measurement of
the low current regime (pA) can be obtained.
Fig 5.2: Schematic of a TERA08 channel.
The input current is integrated over a 600 fF capacitor Cint via an operational
transconductance amplifier (OTA). The output voltage of the integrator increases when
the input current is negative (i.e., exits from the chip) and decreases in the opposite
case. This voltage is compared to two fixed thresholds by two synchronous
comparators, CMP-1 and CMP-2. The threshold voltage of the two comparators is fixed
externally: Vth-high is the threshold voltage of the CMP_1 comparator working for
negative input currents, while Vth-low refers to CMP_2, active for positive input currents.
The value of the threshold has no particular influence on the behaviour of the circuit as
long as the voltage variation remains in the output range of the OTA that is explained as
𝑉𝑜𝑢𝑡 = 𝐺 (𝑉𝑖𝑛 − 𝑉𝑂𝑇𝐴𝑟𝑒𝑓 ), whith G, the amplifier gain .
Whenever the comparator input voltage crosses the threshold, the related comparator
sets a level at the input of the pulse generator (PG). As far as an input level is set, PG
sends to the capacitor Csub a positive pulse 20 ns wide (see Fig. 5.3).
114
The voltage amplitude pulse (ΔVpulse) is defined as the difference between two
reference voltages (Vpulse+ and Vpulse_), which are set externally in the range between 0.5
and 3.3 V.
Three parallel capacitors, of 50, 100, and 200 fF respectively, can be independently
added to obtain the total capacitance Csub, for which any value between 50 and 350 fF in
steps of 50 fF can be selected. The output responses of Csub to a voltage pulse are two
opposite sign current signals, δ+ and δ- with an associated charge Q+ and Q_
𝑄+ = 𝐶𝑠𝑢𝑏
𝑄 − = 𝐶𝑠𝑢𝑏
∗
∗
𝛥𝑉𝑝𝑢𝑙𝑠𝑒
(−𝛥𝑉𝑝𝑢𝑙𝑠𝑒)
(5.2)
The timing of the first signal, δ+, is determined by the leading edge of the pulse,
while δ- corresponds to the trailing edge. A schematic of the waveforms is shown in
Fig. 5.3.
Fig. 5.3: Charge subtraction waveforms for a negative current input
Acting on the timing of the commands on the switches sw1 and sw2, Q+ or Q_ can be
routed either to the OTA input or to the OTA-ref. reference voltage, thus adding or
subtracting a fixed amount of charge at each pulse generated by PG. The decision on
which charge signal has to be routed to the OTA depends on the output of the
115
comparators, in order to remove a fixed amount of charge from Cint. This results in a
change in the voltage across Cint, given by Q/Cint.
If, after the above action, the input comparator voltage remains above (below) the
threshold, PG will continue to issue pulses and it will stop when the voltage returns
below (above) the threshold.
In parallel, PG sends a pulse to be counted to the up/down counter. Again, PG,
depending on which comparator level is acting at its input, can decide to count up or
down via Cnt_Down or Cnt_Up.
All operations are synchronized to an external master clock and supervised via a
digital finite state machine (FSM) implemented in the block PG. At a given clock,
whenever PG detects CMP_1 (or CMP_2) active, the next three clock cycles will be
taken by the charge subtraction and switch control pulses. Two extra clock cycles are
required before re-triggering the FSM in order to give time to the OTA to decrease the
output voltage. Thus, to generate a count it requires five master clock pulses (as said
before, the chip works with a clock frequency of 100MHz and the maximum frequency
of the counters is one fifth of the clock frequency corresponding to 20 MHz).
The relationship between output frequency, 𝜈, and input current, Iin, is
𝜈=
𝐼𝑖𝑛
𝑄𝑐
(5.3)
where Qc (charge quantum) is given by
𝑄𝑐 = 𝐶𝑠𝑢𝑏 𝛥𝑉𝑝𝑢𝑙𝑠𝑒 .
(5.4)
The total charge read-out from the detector is given by the number of pulses
generated during the measurement time multiplied by the value of the charge quantum
Qc.
116
Fig. 5.4: The overall schematic of the TERA08 chip
The integration capacitor of all channels can be discharged via a common digital
input, resetA. Similarly, all counters can be zeroed via a common asynchronous digital
input, resetD. The read-out of the counters can be done independently with respect to
any other operation. Asserting the latch, the actual bit configuration of each 32-bit
counter is stored in a 32-bit register. This operation is done in parallel for all the 64
channels. Any given channel can be acquired by addressing it via the six digital inputs
(Channel select
lines). The appropriate register is multiplexed to the 32-bit output bus signal through
MUX.
It is worth to mention the following:
•
the latch operation is done at the same time for all the channels: the
counters are copied to the registers when the counting transitions are
completed;
•
though the acquisition has to be done channel by channel, the counters are
latched to the registers at the same time, thus data refer to the same time;
•
the acquisition being independent from the pulse counting, the data
acquisition does not stop the counter activity, thus there is no dead time
due to read-out.
117
5.2 Chip characterization
Let’s remember that our detector has been designed and will be used with highintensity beam. up to intensities of 1012 ions/second. Using the Eq. (4.53), the expected
current at the electrodes is larger than 10𝜇𝐴, for typical ionization chamber parameters
(see Tab. 4.1).
Using a quantum charge Qc=200fC and considering the maximum acquisition
frequency νmax=20MHz, a single channel of TERA08 saturates at 𝐼 𝑠𝑎𝑡 = 𝑄𝑐 × 𝑣𝑚𝑎𝑥 =
±4 𝜇𝐴. For this reason, it was proposed to connect the input channels in parallel and use
one single chip for the readout of each gap where the current is obtained by adding the
counts of each of the channels. With this configuration, it is expected that the maximum
input current would increase up to 64-times, compared to a single channel, before
saturation occurs.
Fig. 5.5: Representation of the parallel connection of the channels. Rp= 10 MΩ were used for the
chip characterization.
118
As it can be seen in Fig. 5.5, each channel is connected in parallel to the others, using
an input resistance Rp, and this functional choice is made in order to overcome an
electronic characteristic of the chip, as explained in the following.
Whenever there is just a small offset between the two channels, one operational
amplifier (OTA) tries to drive the virtual ground to its value; in this situation, this OA
integrates the current whereas the other one does not work.
Fig. 5.6: A zoom of the parallel connection representation.
It has been observed in out tests that, if resistances are used in series to each channel,
all the operational amplifier start to integrate, but the integrations have different gains. It
was found that these resistances had to be increased up to 10 MΩ for the offset currents
to become negligible, compared to the input current.
𝐼𝑜𝑓𝑓𝑠𝑒𝑡 =
∆𝑉𝑜𝑓𝑓𝑠𝑒𝑡
𝑅𝑃
(5.5)
119
The use of bigger operational amplifiers would be the method to eliminate the offset
current, but this would imply lower integration speed, that means worst performances.
5.2.1 The experimental setup
The experimental setup that has been used to characterize the chips is based on a
National Instrument PCI DAC card and LabView software.
Fig. 5.7: A block diagram representation of the experimental chain: from the ionization chamber
to the PC monitor.
The chips are encapsulated in an MQFP 160 package and mounted on a socket that is
housed on a test board (Fig. 5.8). The board achieves two main functions:
•
interface the input-output lines from the socket to the FlexRIO FPGA module;
•
provide the 100 MHz clock signal to the chips
•
adapt the voltage levels from the chip to the FlexRIO FPGA module.
For most of the tests we need to inject a precise constant current into a given channel.
This was obtained by using a Keithley 2400 in current generator configuration. The
Keithley 2400 provides a precise voltage source in the range between 1 mV and 211 V.
The current generator in connected with a coaxial cable, to an upper board mounted
above the test board. This upper board allows the manual parallel connection of the chip
channels (Fig. 5.8).
120
Fig. 5.8: Pictures of the data acquisition setup. On the left, the voltage power supply for the
chip, the Keithley, the PXI with the NI-FlexRIO module, the PC with the LabVIEW software.
On the right, the test board with the chips (two chips are mounted on a board) and the upper
board for the parallel channels connection.
5.2.2 The linearity test
With such an arrangement, we first tested the linearity in the current-to-frequency
(frequency of counts) conversion by adding in parallel from 2 up to 64 channels and by
adding the corresponding number of counts.
During the entire chip characterization, some parameters were kept constant:
•
Vota = 1.64V, the operational amplifier voltage reference;
•
ΔV = Vp+ - Vp- = 1,02V , where Vp+ and Vp- are the voltages used for the
charge subtraction;
•
Δt = 100ms, the data acquisition time;
•
Qc = 200fC, the charge quantum.
With these parameters and recalling that 20MHz is the maximum frequency, the
expected saturation current for a single channel is:
𝐼𝑚𝑎𝑥 = 𝑄𝑐 𝜈𝑚𝑎𝑥 = 2 ∙ 10−13 𝐶 ∗ 2 ∙ 106 𝑠 = ±4 𝜇𝐴.
(5.6)
When we started to test the linearity we found that indeed the saturation current was
increasing proportionally to the number of channels connected in parallel. However, the
slope of the graph changed symmetrically, for positive and negative input currents, from
up to about ±5μA.
The results for 1,2 and 4 channels, are shown in figure 5.9.
121
Fig. 5.9: Linearity test for 1, 2 and 4 channels.
The problem was traced to the mode of use of the two voltage sources LM4140
components (Fig. 5.10) mounted on the test board. These devices are current sources
used to provide the Vp- and Vp+ constant voltages. However, the Vp- was used as a
current sink.
Fig. 5.10: The pin-out of the LM4140 voltage reference. The right one provides Vp+, whiles the
left one, provides Vp- .
From the graphs in figure 5.11, taken from the data sheets, it is possible to note that,
if an LM4140 is used in source current mode, the output voltage is kept constant up to
milliamperes whereas if it is used in sink current mode, as it was done for Vp-, the
voltage changes at a much smaller current. This is shown in figure 5.11 where the
voltage is shown as a function of the sink current.
122
Fig. 5.11: The work behaviour for the source current and the sink current configurations of the
LM4140 components.
The problem was fixed by adding a 120 Ω resistance on the test board, between the
Vp- and the ground terminals (Fig. 5.13). In this way the point of work of the LM4140
device is changed such that, in condition of no input current to the chip, it provides a
current source of 100μA. When the count rate increases, the LM4140 device will
provide less current, since an amount of current comes from the TERA chip and goes to
ground.
Fig. 5.12: The LM4140 configurations: a) Source mode, b) Sink mode, c) Sink mode with the
applied resistances, in red.
123
Fig. 5.13: A snapshot of the down side of the test board. It is possible to notice the welded
resistance of 10KΩ; it is later replaced with a 120Ω resistance.
At this point, the measurements were repeated using an input resistance for each
channel Rp= 10 MΩ, a data acquisition time Δt=100 ms and the welded resistance
between Vp- and the ground terminal RVp-_Gnd = 120Ω.
The linearity tests for one channel and for all the chip channels are shown in figures
5.14 to 5.18.
Fig. 5.14: The linearity test for one channel.
124
Fig. 5.15: Deviation from the linearity fit, for one channel.
In the Fig. 5.15, the maximum deviation from linearity is shown. For positive input
currents the maximum deviation found is Δfreq. =0.11 MHz that corresponds to 0.55%
of the measured frequency; whereas, for negative currents, the maximum deviation is
found to be Δfreq. =0.18 MHz, that corresponds to 0.96% of measured frequency.
Fig. 5.16: The linearity test for the 64 channels.
For an estimation of the linearity, the difference between the experimental frequency-ofcounts data and the linear fit for 64 channels, are reported in figure 5.17
125
Fig. 5.17: Deviation from the linearity fit, for 64 channels.
The maximum deviation for positive input currents is Δfreq. =0.012 GHz that
corresponds to 1.02% of the experimental value; whereas, for negative currents, the
maximum deviation is Δfreq. =0.012 GHz, that corresponds to 1.06% of the
experimental value.
In Fig. 5.18 all the linearity results obtained by using up to 64 channels in parallel are
shown. It is found that, by connecting several channels in parallel, the very good
linearity of the TERA chip is preserved. It is also shown that the dynamic range
increases allowing to use the readout at currents up to ±250 𝜇𝐴. The count frequency
saturation appears to shift, with the increasing of the number of parallel connected
channels. As expected from Eq. (5.6), with a single channel connected, the current
saturation is at ±4 𝜇𝐴 while, with the increasing of the number of channels NCh, the
saturation occurs at 𝑁𝐶ℎ ∙ (±4 𝜇𝐴 ).
126
Fig. 5.18: The complete linearity test for 1, 2, 4, 8, 16, 32 and 64 channels in parallel.
127
5.2.3 Count resolution
For any readout system it is important to know the accuracy of the data collected. For
this reason, we studied how the channels work.
If a current is directed in input to our read-out electronics, we can make the
assumption that it will be almost equally divided for each parallel-connected channel of
the chip, (i.e. to assume that all the channels have approximately the same input
impedance). We suppose in addition that the counting rate of one channel does not
depend on the other channels. Under these assumptions, the expected trend for the
standard deviation of the total number of counts is,
𝜎 = 𝜎1𝑐ℎ �𝑁𝑐ℎ
(5.7)
and for 𝜎1𝑐ℎ we expect to find half a count.
In order to test this assumption, we developed a Monte Carlo model of our readout
which is described in the following.
Called 𝐼𝑇 the total current provided in input, the current that flows in a single channel
i, is assumed to be:
𝐼𝑖 =
where
𝐼𝑇
∙𝐾
𝑁𝑐ℎ 𝑖
(5.8)
𝐾𝑖 , is the current partition coefficient which is assumed to vary by ±2%
depending on the channel
𝑋𝐿 < 𝐾𝑖 < 𝑋𝐻
(5.9)
𝐾𝑖 = 1 + (𝑋𝐻 − 𝑋𝐿 )(𝑅 − 0.5)
(5.10)
where 𝑋𝐿 =0.98, 𝑋𝐻 =1.02 and 𝐾𝑖 is randomly selected according to
R is a randomly generated number between 1 and 0. The boundary condition for K is:
𝑁𝑐ℎ −1
𝐾𝑁𝑐ℎ = 𝑁𝑐ℎ − � 𝐾𝑖 → 𝐼𝑇 = � 𝐼𝑖 .
1
𝑖
(5.11)
128
Now, we have to describe the current-to-counts conversion. Let’s call 𝑄𝑖𝑗 the charge
integrated by channel i and the acquisition loop j.
𝑄𝑖𝑗 = 𝐼𝑖 𝛥𝑡 + 𝑄𝑖𝑗
𝑄𝑖𝑗
𝑙𝑒𝑓𝑡
𝑙𝑒𝑓𝑡
(5.12)
is the residual charge, i.e. the charge that remains after a discrete detection and
𝛥𝑡 is the data acquisition time for a loop. The number of counts will be the integer part
of the ratio between the charge 𝑄𝑖𝑗 and the charge quantum 𝑄𝑐 .
𝑁𝑖𝑗 = 𝑖𝑛𝑡 �
𝑄𝑖𝑗
�.
𝑄𝑐
(5.13)
For the first loop, the initial charge is assumed to be
𝑄𝑖0 𝑙𝑒𝑓𝑡 = 𝑅 𝑄𝑐
(5.14)
with R, a randomly generated number between 1 and 0.
For the second and further loops
𝑄𝑖𝑗
𝑙𝑒𝑓𝑡
= �
𝑄𝑖𝑗
𝑄𝑖𝑗
− 𝑖𝑛𝑡 � �� 𝑄𝑐 .
𝑄𝑐
𝑄𝑐
(5.15)
Finally, the total number of counts in each loop is
𝑖
� 𝑖𝑛𝑡 �
1
𝑄𝑖𝑗
� → 𝑁𝑗 .
𝑄𝑐
(5.16)
The graph in Fig. 5.17 shows the results of the model, considering a constant input
current and 1000 acquisition loops. The standard deviation value is obtained as follows:
𝜎𝐶ℎ
� 2
∑1000
𝑗=1 �𝑁𝑗 − 𝑁𝚥 �
=�
𝑁𝐿𝑜𝑜𝑝 − 1
(5.17)
�𝚥 , is the average value of counts over 1000 loops.
where 𝑁
129
The value of the σ is taken ten times for each channel configuration (1, 2, 3, 4…64)
and the fit is done on the average value of these standard deviations.
Fig. 5.19: Model results of the counts standard deviation in function of the number of channels.
Iin = Itot= 227.975 μA, Qc = 200 fC, Δt = 10 μs and 1000 loops.
Then, we have tried to verify this predicted behaviour by measuring the standard
deviation with the test setup. In order to do this, initially, we connected the Keithley to
our readout system but we soon realized that, it was necessary to use a battery as power
supply, because the electrical noise from the current generator is higher than the
statistical effect studied.
We have also used a metal box with as a Faraday’s cage and put the chip board and
the upper board for the resistance connections into it.
With the first version of the upper board (Fig. 5.8) we could not connect all the
channels. The new board has 64 integrated-10MΩ resistances and therefore is smaller
and less subject to electrical noise than the previous one.
130
Fig. 5.23: A picture of the upper board mounted on the readout board of the TERA08.
With these improvements, we did the data acquisition for 1, 2, 4, 6, 10, 12, 16, 24,
32, 64 channels. The results are shown below.
Fig. 5.24: The experimental standard deviation of the counts, in function of the number of
channels connected. Vbatt = 1.56 V, Vota = 1.64 V, Rp = 10 MΩ; Rin = 10 MΩ; Qc = 200 fC;
∆t= 1 ms; 2000 loops.
With a battery in current configuration (an additional resistance Rin is connected in
series), the current provided changes with the number of connected channels:
𝐼𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 =
𝑉𝑂𝑇𝐴 − 𝑉𝑏𝑎𝑡𝑡𝑒𝑟𝑦
.
𝑅𝑃
𝑅𝑖𝑛 + 𝑁
𝐶ℎ
(5.18)
131
Taking into account these input current variations, we changed the simulation model
using the same values of current, which were measured in the experimental data
acquisitions. The result is shown in figure 5.21.
Fig. 5.21: Standard deviation of the counts, in function of the number of channels, with a
variable input current provided by a 1.5V battery. Vbatt = 1,56 V, I= 75.88 ÷155.77 nA, Qc=
200 fC, Δt= 1 ms, 2000 Loops.
Then, to get a better comparison between the simulation and the experimental results,
it was decided to subtract the effect of the electronic noise which is not included in the
simulation. The noise was measured acquiring data with the input source disconnected
and without the upper board. The results of the standard deviation of the background are
reported in the next figure. It can be seen that the electronic noise is also increasing with
the number of channels and like the square root of this number.
Fig. 5.25: Standard deviation of the background counts, in function of the number of channels.
Vbatt = 0 V, Vota = 1.64 V, Rp = 10 MΩ; Rin = 10 MΩ; Qc = 200 fC; ∆t= 1 ms; 2000 loops.
132
With the quadrature subtraction between the sigma counts values (Fig. 5.21) and the
background values (Fig. 5.24), it is possible to get a better estimation of the standard
deviation effects only related to the charge quantum.
Fig. 5.26: The experimental standard deviation of the counts, with the background correction .
Vbatt = 1.56 V, Vota = 1.64 V, Rp = 10 MΩ; Rin = 10 MΩ; Qc = 200 fC; ∆t= 1 ms; 2000
loops.
A comparison between the simulation results and the experimental data, corrected
taking out the noise is shown in figure 5.27:
Fig. 5.27: The comparison between the simulation (in red) and the experimental results (blue).
133
Observing the plots reported in this section, it is possible to say that the counts
standard deviation increases in function of the number of the channels following the
expected statistics.
5.2.4 Rest fluctuations
In order to check the assumption that each channel is counting independently, the
study of the ratio between the total number of counts and the number of connected
channels was performed.
With N channels connected in parallel, if, as we expect, each channel counts
independently, the rest of the division by N of the number of counts, obtained after any
given data acquisition time, will be an integer number included between 0 and N-1 with
a uniform probability distribution. Whereas if there are some recurring structures in the
rest distribution, it means that some channels count together. If the last condition were
true, our readout system would have a lower precision than the one of the single
channel, as explained in the Fig. 5.28.
The rest is obtained from this equation:
𝑅=
𝐶𝑜𝑢𝑛𝑡𝑠𝑡𝑜𝑡
𝐶𝑜𝑢𝑛𝑡𝑠𝑡𝑜𝑡
− 𝑖𝑛𝑡 �
�
𝑁𝐶ℎ
𝑁𝐶ℎ
(5.19)
Fig. 5.28: A representation of the two opposite ways to count: channels that count
independently (blue) and channels that count all together (red).
134
If we plot the periodicity of these rest values obtained from a large number of
readout software iteration loops, it is possible to analyse the rest distribution; thus we
have to check if some values recur with a higher probability than others.
Fig. 5.29: This figure explains how the rest fluctuations plots are realized. On the x-axis, the
rests value included by 0 and 𝑁𝐶ℎ − 1 and the number of times that each value comes up from
the ratio on the ordinate.
Observing the graphs in Fig. 5.30 it is clear that the rest distribution does not indicate
structures with higher probabilities than others, to confirm that the channels count
independently.
135
Fig.5.30: Rest fluctuations of the number of counts divided by 64, 32, 16, 8, 4 and 2. The data
acquisition times was Δt = 1ms, for 20.000 loops.
136
Concluding remarks
This thesis focuses on the development of beam monitor ionization chambers for
hadrontherapy accelerators. The trend of development in this field is towards compact
accelerators, which produce pulsed high intensity particle beams. The main difficulty in
monitoring high intensity beams is the ion recombination and, consequently, the
inefficiency of the charge collection in the chamber.
The University of Torino and the INFN are developing an innovative multiple gap
ionization chamber with the aim of measuring the intensity of charged particle beams
and simultaneously determine the collection efficiency.
The work described in this thesis is part of this project and, specifically, it
concentrates on the readout front-end electronics of this detector. The main idea of this
part of the project has been to use the latest version of the 64 channels TERA ASIC,
current-to-frequency converter (developed by the INFN and the University of Torino)
and to connect all its channels in parallel configuration, in order to overcome the
problem of current saturation for a single channel in high intensity regime.
The first three chapters of this thesis consist in a review of the main concepts of
hadrontherapy (Chapter 1), an overview of the latest developments in medical
accelerator with specifications of the most advanced technologies and the future
perspectives (Chapter 2), and the operating principles and specifications of the gas-filled
detectors (Chapter 3). In Chapter 4, I analysed the problem of the collection efficiency f
for high intensity, pulsed beams and I developed the graphical method that will be used
in the measurement of the collection efficiency with the multiple gap chamber.
The results indicate that with this method it will be possible to measure the collection
efficiency with an uncertainty of 1-2% in a large range of beam intensities for each
beam pulse.
The readout of the chamber, based on the TERA08 chip, is presented in Chapter 5,
together with the measurements of the linearity of current-to-frequency of counts
conversion which I have performed; a good linearity in a range up to 250μA was
achieved, that is much more than required for the application. I also made a detailed
study of the resolution of the readout, comparing the results to a Monte Carlo model
137
that assumes that all channels are behaving independently; a very good agreement was
found, thus confirming the assumptions of the model.
138
Acknowledgments
Al termine di questo percorso accademico, ci tengo a ringraziare le persone che, in un
modo o nell’altro, mi hanno seguito contribuendo così al raggiungimento di
quest’obiettivo.
Per quanto riguarda il progetto di tesi, ringrazio tutto il gruppo di fisica medica del 3°
piano per il sostegno, l’aiuto e il clima famigliare. Ringrazio quindi Roberto e Simona,
per avermi valorizzato durante il lavoro. Grazie ai dottorandi Mohammed, Abdul, Amin
e un grazie speciale per Leslie, per l’amicizia e l’aiuto, fin dai primi giorni.
Per il capitolo torinese, ringrazio gli amici nonché colleghi Marco e Alberto, con i quali
ho potuto ritrovare un dimensione che più mi si confà, nell’ambiente universitario.
Grazie a tutti gli amici marzialisti del gruppo taekwondo della Stella Polare: Roberto,
Fil, Cristian, Giulio, Dino, Sophie, Veronica, Valentina, Davide e Barbara, per la
condivisione, le botte, la passione e l’allegria.
Da studente fuori sede, ho avuto la fortuna di avere molti coinquilini speciali, pezzi
importanti di questo puzzle. Perché la convivenza è stata forse la parte più innovativa e
che più mi ha arricchito, in questa transumanza BS→TO. Ringrazio quindi Marco, Juan,
Giampiero, Giangavino e i miei attuali cdm Alessandro, Claudio e Stefano per le
innumerevoli risate, per le chiacchiere notturne, e per il clima casalingo ideale.
Ora la parte dei famigliari, quella del sostegno “primordiale”. Grazie a mamma e papà,
non solo per aver permesso che portassi avanti le mie scelte ma anche per avermi
sempre sostenuto; grazie a Stefano e Gemma, perché da fratellino, sono sempre stato
coccolato. Grazie a tutta la grande famiglia di cugini zii, nonni, con un pensiero
particolare alla nonna Annetta che con grande empatia ha seguito il mio percorso di
studi e al nonno Massimo perché, col suo: “cala mia le braghe prima del tep”, mi ha
spronato a superare le difficoltà.
In fine, il grazie più speciale di tutti a Giulia, ci sei sempre stata ed ho potuto contare su
di te in ogni momento! Inoltre, sei stata tu, più o meno volontariamente, a spronarmi per
quest’avventura da “fuori sede”.
Grazie, grazie, grazie.
139
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