Analysis of laser accelerated ion foci
created with permanent magnet
quadrupoles
Derya Taray
München 2017
Analyse laserbeschleunigter
Ionenfokusse erzeugt durch
Permanentmagnet Quadrupole
Derya Taray
Bachelorarbeit
an der Fakultät für Physik
der Ludwig–Maximilians–Universität
München
vorgelegt von
Derya Taray
aus Hannover
München, den 14.7.2017
Gutachter: Prof. Dr. Jörg Schreiber
Betreuer: Thomas Rösch
Contents
List of Figures
vii
List of Tables
viii
Zusammenfassung
ix
Abstract
xi
1. Introduction
1
2. Theoretical Framework
2.1. Laser accelerated Ions (LIONs) . . . . . . . . . . . . . . . . . . . .
2.1.1. Generating Ion beams with high power laser systems . . . .
2.1.2. LION beam properties . . . . . . . . . . . . . . . . . . . . .
2.1.3. Conventionally accelerated ion beams . . . . . . . . . . . . .
2.2. Focusing and Transport of Ion Beams . . . . . . . . . . . . . . . . .
2.2.1. Charged Particles in Magnetic fields . . . . . . . . . . . . . .
2.2.2. Magnetic ion spectrometer . . . . . . . . . . . . . . . . . . .
2.2.3. Focusing LION bunches . . . . . . . . . . . . . . . . . . . .
2.2.4. Acceptance and transfer function of an ion transport system
2.3. Image Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1. Detection Mechanism . . . . . . . . . . . . . . . . . . . . . .
2.3.2. Repeated Read-outs . . . . . . . . . . . . . . . . . . . . . .
2.3.3. Particle Number and Dose Calculation . . . . . . . . . . . .
2.3.4. Other Detection Systems . . . . . . . . . . . . . . . . . . . .
3. Experiment with LIONs
3.1. Laboratory for extreme photonics (LEX photonics)
3.2. LION focusing setup at LEX . . . . . . . . . . . . .
3.2.1. Dipole Magnet . . . . . . . . . . . . . . . .
3.3. Deflection measurement . . . . . . . . . . . . . . .
3.4. Parameters for particle number calculation . . . . .
3.4.1. Focus Definition . . . . . . . . . . . . . . . .
3.4.2. Background Subtraction . . . . . . . . . . .
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vi
Contents
3.4.3. Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4. Evaluation and Results
4.1. Spectrometer measurements . . . . . . . . . .
4.1.1. Energy Derivation . . . . . . . . . . .
4.1.2. Evaluation of focus energies . . . . . .
4.2. Particle Number Calculations . . . . . . . . .
4.3. Qualitative Observations and first deductions
4.3.1. Image plate pictures . . . . . . . . . .
4.3.2. Particle number calculations . . . . . .
4.3.3. Laser focus . . . . . . . . . . . . . . .
4.3.4. Focus Structures . . . . . . . . . . . .
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5. Experiment with conventionally accelerated ions
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5.1. Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2. Measurements and Results . . . . . . . . . . . . . . . . . . . . . . . . . . 37
6. Discussion
6.1. Steering . . . . . . . . . . . . . . . . .
6.2. Particle Number and Dose Calculation
6.3. Geometric properties of the focus . . .
6.4. Energy Resolution of the Spectrometer
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7. Outlook
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A. List of Abbreviations
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B. Data Tables
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C. Overview of Codes
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Bibliography
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Danksagung
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Erklärung
53
List of Figures
2.1.
2.2.
2.3.
2.4.
2.5.
2.6.
Deflection of a particle by a dipole field . . . . . . . . . . . . .
Ideal QP field . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trajectories of 2 particles of the same energy in a dipole field.
Setup used to simulate the QP doublet in [1]. . . . . . . . . .
Simplified energy levels of the IP-material. . . . . . . . . . . .
Three successive scans of an IP. . . . . . . . . . . . . . . . . .
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3.1. The setup, as used for the LEX experiment evaluated in this work. . . .
3.2. The vacuum exit window on which the IPs were attached. . . . . . . . .
3.3. Comparison of the deflection calculation in equation 2.4 and the program
’StartSpectraCalculation.m’ . . . . . . . . . . . . . . . . . . . . . . . . .
3.4. IP scans 1 and 7 of shot 220. . . . . . . . . . . . . . . . . . . . . . . . . .
3.5. Measurement of the focus deflections . . . . . . . . . . . . . . . . . . . .
3.6. Particle number maps with dose (left) and geometrical defined focus(right)
for two shots. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7. Particle number maps of shot 217 with and without subtracted background.
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4.1. Derivation of focus energy from the deflection shown for two examples. .
4.2. Calculated and measured deflections of the foci, plotted against the QP
energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3. Deflections v.s. QP energies. . . . . . . . . . . . . . . . . . . . . . . . . .
4.4. PNs of different shots, calculated with different methods. . . . . . . . . .
4.5. Normalized PNs calculated with different methods . . . . . . . . . . . . .
4.6. Focus images of the seven shots evaluated in this work . . . . . . . . . .
4.7. The target holder, used for the experiments. . . . . . . . . . . . . . . . .
4.8. Image of the beam profile without the dipole on 4 layers of a RCF stack
with 0.4m TFD. Spacial variations of the focus spot are due to the cutout
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5.1.
5.2.
5.3.
5.4.
5.5.
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The setup used in the Tandem experiment. . . . . . . .
Measures of the PP . . . . . . . . . . . . . . . . . . . . .
Image of the ion beam through the PP. . . . . . . . . . .
Horizontal and vertical line focus, created by single QPs.
Foci, created by both QP in the Tandem experiment . .
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List of Tables
3.1. QP properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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4.1. Deflections and corresponding energies of all shots . . . . . . . . . . . . .
4.2. Final focus energies and error boundaries . . . . . . . . . . . . . . . . . .
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B.1.
B.2.
B.3.
B.4.
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Used Drift lengths in the QP setup .
Particle numbers . . . . . . . . . . .
Mean PNs and PSL reduction factors
Dose transmitted to the focus . . . .
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Zusammenfassung
Pakete Laser beschleunigter Ionen, zeigen eine Vielzahl interessanter Eigenschaften, und
übertreffen konventionell beschleunigte Ionenstrahlen hinsichtlich Emittanz und Fluenz.
Aufgrund dieser Eigenschaften, werden zahlreiche Anwendungen in Forschung oder Technik diskutiert. Bisher sind diese aber durch das breite Energiespektrum, die hohe Divergenz des Strahls und die starke Hintergrundstrahlung, die bei der Beschleunigung
produziert wird, limitiert. Eine Möglichkeit diese Probleme zu lösen ist, die Ionen durch
ein effektives Transportsystem aus der Umgebung starker Hintergrundstrahlung zu entfernen. Ein solches System soll den Ionenstrahl kollimieren und je nach Aufbau nur
für Ionen einer bestimmten Energie durchlässig sein. Dadurch sind Magnetfelder besonders geeignet, da ihr Einfluss auf die Bahn eines Teilchens stark von dessen Energie
abhängt.
Eine vielversprechende Möglichkeit eines solchen Systems bietet ein Paar aus Permanentmagnet Quadrupolen. Am Laboratory for extreme photonics (LEX photonics)
in München wurde ein solcher Aufbau realisiert. In einer Reihe von Experimenten
wurde versucht einen energetisch schmalbandigen Ionenfokus in 1.5m Abstand zur Quelle
herzustellen. Die erzeugten Foki zeigten unerwartet komplexe Strukturen. Dadurch
wurde der quantitative Vergleich verschiedener Experimente unmöglich. In dieser Arbeit
wird eine Methode eingeführt um diese Fokusstrukturen sinnvoll nach Teilchenzahlen
zu quantisieren und so Vergleichbarkeit herzustellen. Dazu werden zwei verschiedene
Fokusdefinitionen anhand der Teilchenzahlen verglichen und das Experiment aus LEX
photonics danach ausgewertet. Dabei wurde ein Programm implementiert, das aus den
benuzten Detektordaten für verschiedene Parameter die Teilchenzahlen berechnet.
Außerdem wurde der Ursprung der Strukturen untersucht. Dafür wurde ein weiteres
Experiment am Tandem Beschleuniger des Maier Leibniz Laboratoriums durchgeführt.
Dieser Beschleuniger bot durch seinen monoenergetischen und gut bekannten Strahl
die perfekte Möglichkeit zu überprüfen ob die Strukturen aus der Quelle der Ionen
enstanden oder durch die Quadrupole verursacht wurden. Durch Untersuchen verschiedener Fehlpositionierungen der Quadrupole wurden für einen Teil der Strukturen
mögliche Erklärungen gefunden. Es besteht aber weiterhin die Möglichkeit, dass diese
Strukturen durch die Form des Laserfokus hervorgerufen werden. Eine weitere Erklärung
könnten das breite Energiespektrum des Eingangsstrahls oder Randeffekte der Quadrupolfelder
sein.
x
Zusammenfassung
Zuletzt werden weitere Entwicklung und Anwendungsmöglichkeiten des Quadrupol Duplets diskutiert. Dazu zählt die Entwicklung einer Transferfunktion durch das System,
um es zur Analyse der Ionenquelle zu nutzen.
Abstract
Laser accelerated ion bunches offer numerous interesting properties and outgo conventionally accelerated ion beams in emittance and fluence. That is why a wide range of
applications in science and technology is discussed. So far their applicability is limited
by the broad energy spectrum, high divergence and strong background radiation, that
is produced during the acceleration process. One way of solving this problem is creating
an ion tranport system, that transfers the ions away from the area of strong radiation.
Such a system would also have to collimate the beam and accept only ions of a certain
energy. Magnetic fields offer a good possibility to achieve this, because their influence
on a particles trajectory strongly depends on its energy.
A doublet of permanent magnet quadrupoles offers a promising possibility of such a system. In the laboratory for extreme photonics (LEX photonics) in Munich such a setup
was realized. In a series of experiments, an energetically thin focus was created 1.5m
away from the ion source. The created foci exhibited unexpected, complex structures.
Hence it was not possible to compare the experiments quantitatively. In this work, a
method to quantify the ion foci by their particle number is introduced, to enable comparions among the different experiments. For that purpose two different focus definitions
are compared, regarding particle numbers and used to evaluate the experiment at LEX
photonics. For this, a program was implemented, that calculates the particle numbers
from the detector signal for different paramters.
Additionally, the origin of the focus structures was analyzed. Therefore a second experiment was conducted at the tandem accelerator of the Maier Leibniy laboratory. The well
known, stable and monoenergetic beam, provided by this accelerator, offered a perfect
possibility to test if the structures were created by the ion source or the quadrupoles.
Scanning different positioning errors, an explanation for a part of the structures was
found. Anyway, there still is the possibility, that the structures were created by the
form of the laser foucs. Another explanation might be the broad energy spectrom of the
incoming beam or fringe effects of the quadrupole fields.
Finally, further developements and applicatios of the quadrupole doublet are discussed.
These include the derivation of a transfer function through the quadrupole system and
this using the doublet as imaging device for the ion source.
Introduction
Laser Ion acceleration is a promising technique to create high energy ion beams with
unique properties [2]. Worldwide, applications ranging from research usability like laser
driven fusion to contributions to radiation therapy are discussed [3].
One of the special properties of Laser accelerated Ion (LION) bunches is their very
small emittance, resulting from the small size of the particle source. It is around a
hundred times smaller, compared to conventional accelerators [4]. A low emittance is an
important property of high quality ion beams, as it limits possibility to focus the beam.
LION bunches, also offer extremely high particle fluences of up to 1021 particles per ps
[2].
Nevertheless LION bunches exhibit a large, energy dependent divergence angle and broad
energy spectrum [1].As well, during the acceleration mechanism, electromagnetic radiation ranging from x-rays to gamma rays, fast electrons and neutrons are produced [2].
But for most applications a paralel, monoenergetic beam, with no additional radiation
of other types is required. Hard electromagnetic radiation might damage diagnostic devices or undesiredly increase the dose, transmitted to a tissue. Ions of different energies
within one bunch, result in a spread of penetration depth and energy deposition into an
irradiated probe. Due to the large divergence angle, the fluence of the particles reduced
rapidly with distance to the source. That is why the applications of LION bunches are
currently limited.
To increase their applicability and access their unique properties, an ion focusing and
transport system is required. This system has to transfer the ion bunches away from the
area of strong background radiation, sort out particles of undesired energies and focus
the beam.
A doublet of permanent magnet Quadrupoles (QPs) offers a compact and effective way
of focusing and monochromatizing ion beams [5]. The construction and analysis of such
a system is described in [1]. In 2016 a series of experiments with this system was conducted LEX photonics in Munich, to analyze the behavior of the QP system in a LION
experiment. The experiment is described in chapter 3. The theoretical models for the
experiments are explained in chapter 2. This experiment yielded unexpectedly complex
focus structures, whose origins are not understood yet. Also a reliable quantification of
the foci, allowing comparisons of different experiments did not exist.
2
1. Introduction
The laser system in LEX photonics is currently being updated to the Center of Advanced
Laser Applications (CALA), where the QP system will be applied for further LION
experiments. Hence, the properties of the QP doublet have to be understood. In this
work first an attempt is made to quantify the focus structures, to enable closer analysis
and comparisons between different experiments. As the structures vary strongly from
experiment to experiment, a comparable parameter that is reasonably enforceable on
every focus, had to be defined. To achieve this, two different definitions of the focus
region are established and compared in chapters 3 and 6. In order to compare the shots,
the particle number inside the different focus regions is calculated. This was realized
by implementing a MATLAB script to calculate the particle numbers with different
parameters.
Second in this work, the origin of the focus structures is investigated. The basic problem
here was, that neither the source properties, nor the behavior of the QPs was known
precisely. An experiment at a Tandem-accelerator provided a reliable and homogeneous
ion beam, necessary to identify if the structures were created by the LION source or by
the QPs. It is described in chapter 5.
Third, the validity of the measurements and possible origins of the focus structures
are discussed in chapter 6. The development of a transfer function through the QPs
system and further applications of this system are mentioned in chapter 7. Here also the
development of a transfer function through the QP system and resulting from this, the
possibility to use the QP system for LION spectrometry will shortly be discussed.
Theoretical Framework
2.1. Laser accelerated Ions (LIONs)
Laser ion acceleration is a technique, currently getting an increasing research effort, due
to the unique ion beam properties it offers. It is usually realized by focusing a high
power laser on a thin target foil. Ions will be accelerated on the rear side of the foil and
emitted as a divergent beam.
There is no summarizing model of the acceleration process but several different models
describe the mechanism in different regimes. The difference between the regimes is
defined by the experimental parameters, like the laser intensity and target thickness [3].
A complete discussion of all regimes and models is far beyond the scope of this work,
so only the target normal sheath acceleration (TNSA) will be discussed, because it is
currently the best understood and commonly used model. A more detailed description
of other models can be found in [3]
2.1.1. Generating Ion beams with high power laser systems
TNSA was firstly introduced by Wilks et al. in [6] to explain experimental results
published by Snavely et al [7]. A laser prepulse creates a plasma on the laser side of the
foil. The main, high intensity pulse is reflected in this plasma, but still heats it up with
different absorption mechanisms like inverse bremsstrahlung and resonant absorption [2].
The laser mainly affects the electrons in the plasma as they have a much lower mass than
the remaining ions, heating and pushing them towards the target rear side. The strong
acceleration of electrons creates a x-ray flash, that propagates through the experimental
chamber [6]. The hot electrons start penetrating through the target and exit on the rear
side, leaving behind positive charged ions. In the surrounding vacuum, they are stopped
by the quasistatic electric field of the remaining ions, forming a bell shaped electron
sheath, following a Boltzmann distribution with electric potential [2]. The dimension of
the electron cloud, normal to the target can range from nm to µm.
The sheath remains stable as long as the laser keeps heating up the plasma. This negative charge density now creates an electric field of several T V /m, pulling the positively
4
2. Theoretical Framework
charged ions out of the target and accelerating them within nanoseconds to several
MeV.
This process is most effective on protons, because they have the lowest mass of all ions
and though are accelerated first [2]. To generate beams of heavier ions, the target has to
be cleared from protons, often appearing as surface impurities or as a part of the target
molecules [6].
A second possible acceleration regime is the so called radiation pressure acceleration
(RPA). It requires nm-thin targets and uses the momentum of the electromagnetic wave
to accelerate ions, comparable to the light-sail principle. Thus RPA is said to be more
efficient than TNSA, produces a narrower spectrum of ions and a less divergent beam.
An important prerequisite for reaching this regime is a very sharp and intense laser
pulse. It was achieved by Henig et al in [8]. Unfortunately the conditions necessary
for RPA are currently not reliably available in experiments, so TNSA is nowadays the
most commonly used mechanism [1]. In one bunch up to 1010 protons are accelerated
[7].
2.1.2. LION beam properties
LION bunches exhibit properties different from conventionally accelerated ion beams
like e.g. from radio frequency (RF) accelerators. First, their energy spectrum is very
broad, decaying exponentially towards higher energies, with a cutoff energy usually at
several tens of MeV[3].
Second, the divergence angle of the beam is very large and energy dependent (up to 40
degrees) [9]. Higher energetic protons have a lower divergence angle because of the form
of the electron sheath accelerating the ions. Ostensively speaking, the protons traveling
through a larger potential difference and thus gaining more energy, have to have a lower
transverse momentum, because the high potential - hence dense - area of the sheath
is very small due to its bell-shape. The form of the electron sheath can be influenced,
by shaping the surface of the target foil. The relation between the form of the electron
sheath and the beam profile was studied in [4]. It was observed that the transverse beam
profile can be modified by shaping the target rear surface. By means of this, focusing
the beam is possible, too. The latter is discussed briefly in chapter 2.2.
Even though the divergence angle is large, the emittance of LION beams is very small
due to their little source area. Emittance is a phase space quantity of particle beams,
often used to indicate the quality of an accelerator. A low emittance is a characteristic
of a high quality ion beam. It specifies the correlation between divergence angle and
position of the particles in the beam profile. As the source of LIONs is very small,
the emittance is low. Emittance is proportional to a phase space volume and is thus
conserved through all changes, the beam undergoes, according to Liouvilles theorem [10].
Conventional RF accelerators reach several mm · mrad. For LION beams, an emittance
of 0.004 mm·mrad has been observed [4].
2.1 Laser accelerated Ions (LIONs)
5
Third, LION beams are intrinsically pulsed, as their source, is usually a pulsed laser.
Pulses with > 1010 particles and durations of several ps have been recorded [2]. These
short pulse durations result from the short acceleration times during a single laser pulse
yielding very small longitudinal emittances and a high particle fluence.
During the electron heating, the plasma also emits a very intense x-ray flash , gamma
radiation and relativistic electrons [2], who have to be blocked for most applications, as
they might damage control or diagnostic devices.
2.1.3. Conventionally accelerated ion beams
Conventionally ion beams are produced in electrostatic or electrodynamic accelerators,
e.g. a Tandem van-de-Graaff accelerator. These accelerators offer well defined and
reproducible ion beams.
The Tandem van-de-Graaff accelerator uses the principle of Tandem accelerators to
create different ions with up to 20 MeV per proton in very stable beams. In the ion
source, negative ions are created and transfered to the accelerator tank. There they run
through an electric potential of e.g. 10 MV. In the middle of the acceleration process,
their electrons are stripped off and now positively charged ions run through the same
potential one more time, ending up with 20MeV. Stripping off the electrons, allows to
use the same acceleration potential twice, yielding a higher efficiency of the system.
After the accelerator, several focusing and steering electromagnets, transfer the ion beam
to the experiment chamber. A 90 degrees deflection magnet and other energetic filters
are employed for beam cleaning and to ensure a monoenergetic spectrum.
The properties of a Tandem van-de-Graaff accelerator beam are summarized here as
comparison with the LION bunches [10].
First the beam is monoenergetic, the energy is adjustable up to 20M eV per proton.
Second the beam is approximately parallel, hence the divergence is negligible. There
also is no energy dependency of the divergence angle. Nevertheless, the emittance is
around 1mm · mrad.
Third, the beam is continuous. If a pulsed beam is required, it has to be introduced
artificially.
Finally, there is no background radiation of other types and the beam profile is homogeneous without any imprint of the source.
6
2. Theoretical Framework
2.2. Focusing and Transport of Ion Beams
In order to use the ion bunches, produced in the laser acceleration, in any application,
they certainly will have to be transfered away from the target foil because of the intense
background radiation occurring during the acceleration process. So an ion tranport
system is needed. Commonly magnetic fields are used to guide ion beams through a
transport system, as their influence on the trajectory of fast, charged particles is more
effective than electric fields [10].
2.2.1. Charged Particles in Magnetic fields
A charged particle flying through an electromagnetic field, is deflected by the Lorenz
force FL :
E + q · (vv × B )
FL = qE
(2.1)
where E is the vector of the electric field, q is the particles charge, v its velocity and B
the magnetic field [10]. Here, and in all further calculations, the convention is used, that
vectors are bold and their absolute length is written in the same letter, but not bold.
B | = B)
(E.g.: |B
For a pure magnetic field, E = 0 and the particle is forced onto a circular path. Its
radius R can be calculated using the centripetal force [10]:
qB
q
1
=
=√
· B⊥
R
p
2mE
(2.2)
with the particle momentum p, or its kinetic energy E, mass m and the absolute value
of the magnetic field perpendicular to the particle trajectory B⊥ . Using a multipole
expansion of the magnetic field in a direction y, By can be written like this [10]:
dBy
1 d2 By 2
By (x) = By0 +
x+
x + ...
dx
2! dx2
(2.3)
where x and y are the directions perpendicular to the beam In this work, only pure
y
) fields will be discussed, because only these are used
dipole (By0 ) and quadrupole ( dB
dx
in linear particle optics.
2.2 Focusing and Transport of Ion Beams
7
Dipole field
In a dipole field, an ion beam is forced in a circular path with the radius calculated in
equation 2.2. A field, shorter than this radius can be used to deflect particles according
to their energy. The deflection y of a proton from an undeflected line in the detection
plane can be calculated in two parts y1 and y2 . y1 is the downwards deflection inside the
dipole field on the circular path, whereas y2 is caused by the deflection angle α during
the drift after the dipole field (see figure 2.1).
y = y1 + y2
√
y1 = R − R2 − l2
y2 = √
d4 l
R2 − l 2
(2.4)
Figure 2.1.: Deflection of a particle by a dipole field
These formulas can be derived from figure 2.1. y1 is calculated using pythagoras theorem
and y2 uses the tangent of the deflection angle. After the dipole, the central beam axis
will be shifted downwards (y1 ) and continue with an energy dependent divergence angle
( dy24 ).
8
2. Theoretical Framework
Quadrupole field
An ideal quadrupole (QP) field is shown in figure 2.2. It consists of two north and two
south poles. It exhibits a gradient, that increases with distance to the middle axis.
Along the middle axis, perpendicular to the image plane in Figure 2.2, the magnetic
field is zero, so a particle flying along the central axis is not deflected. The field is
characterized by the QP strength k:
k=√
q dBy
2mE dx
(2.5)
y
where x and y are the two dimensions perpendicular to the beam axis z. dB
is also
dx
called ’grad QP’. The QP strength strongly depends on the properties of the incoming
particle. Also if the magnet is longer, it’s effect on the beam will be stronger.
Figure 2.2.: Ideal QP field (blue). Lorenz forces acting on a proton flying through the
image plane (green) show a focusing effect along the y axis and a defocussing
effect along the x axis for positively charged particles. Image taken from [1]
In a positively charged ion beam, passing through the image plane in Figure 2.2, particles
off the center in x direction, will be deflected away from the center, hence defocused.
In contrast, particles that are off the center in y direction, will be deflected towards the
center, hence focused. Both deflections occure due to the lorentz force. Therefore a
single QP has a focusing and a defocusing plane and thus will only create a line focus.
A second QP rotated 90 degrees relative to the first one, is needed to create a focus in
both planes. The alignment of these two QP has to be such, that the focus positions in
both planes are at the same position along the beam axis. Otherwise two line foci, at
different positions will be created. The setup of the QPs is shown in Figure 2.4.
Solving the equations of motion, one can derive a matrix formalism to calculate the
trajectory of a particle through a system of dipoles, QPs and field free drifts. An
accurate derivation and explanation of this formalism can be found in [10]. It is used in
[1] to optimze the setup of the QP system for the experiment at LEX.
2.2 Focusing and Transport of Ion Beams
9
2.2.2. Magnetic ion spectrometer
In a dipole field a charged particle beam, will be deflected according to its energy (see
Figure 2.1). So a polychromatic beam will be split up. With a particle number sensitive
detection system like image plates, described in chapter 2.3, an approximate spectrum
can be derived.
But this is only possible, if the entrance position of the particle is known very precisely.
In Figure 2.3 it is shown, how 2 particles with the same energy will be detected on
different deflection positions, resulting in a finite energy resolution.
Figure 2.3.: Trajectories of 2 particles of the same energy in a dipole field. An uncertainty in entrance position results in an energy error (schematic picture).
Right: graph of equation 2.4
Using an aperture in front of the dipole field, the entrance position of the particles can be
determined, and thus the energy resolution is increased. However, there will always be a
finite energy resolution ∆E of the spectrometer, that is limited by the size of the entrance
aperture. (See Figure 2.3) The localization uncertainty ∆y in the detection plane will
always be as big as the entrance aperture if the detection plane is perpendicular to
the incoming beam. As the correlation between energy and deflection is not linear, the
energy resolution also depends on the absolute energy value. Higher energies will always
be resolved worse than low ones, because y(E) flattens towards higher energies.
To measure the energy of a particle, detected at the deflection y the energies Emin and
Emax , related to the deflections y + ∆y and y − ∆y, have to be derived from equation
2.4. The particles energy has to be within the interval [Emin , Emax ].
To approximate the spectrum of a polychromatic beam with a magnetic ion spectrometer, a convention has to be chosen. Here a suggestion is made, that was developed
during this work: Choose energy intervals, covering the desired range, whose width is
approximately the energy resolution for the according absolute value. The middle of
10
2. Theoretical Framework
each interval is chosen as the mean energy in this interval. Calculate the minimum and
maximum deflection of the mean energy y ± ∆y
. These deflection values are used as
2
boundaries of horizontal energy belts, that cover the whole detection plane. Here it is
important to choose the intervals such, that the belts do not overlap. The spectrum can
now be derived by counting the particles within one belt, and associating this number
with the mean energy of this belt.
2.2.3. Focusing LION bunches
The large divergence and broad energy spectrum of LION bunches make a reliable
focusing and energy selection system crucial for their application in most fields.
Different Focussing Devices
Several methods to focus LION beams have been proposed. Target shaping, plasma
microlenses and solenoid fields were mentioned in [1].
Target shaping could only create a focus within millimeters behind the target [1] and
is thus not appropriate for applications.Plasma microlenses require a very precise coordination of two high intensity laser pulses and are therefore not suitable for a reliable
experimental setup [11].
QP fields are a very common technique to focus ion beams. They can be produced
by electromagnets (EM). But due to the large divergence angle and high energies, very
strong fields are required. These could only be achieved with pulsed high current or
superconductive coils. Both types require an external electricity supply, and superconductive coils would also need cooling. Both supply systems would have to resist the
strong electromagnetic pulse, that occurs during the plasma heating and be operated in
vacuum. Also the required EMs are very large [5].
An alternative to EMs are permanent magnet quadrupoles (PMQs). They do not need
an electricity supply, making them resistive to the strong electromagnetic pulses occuring
in the LION chamber and improving their applicability in vacuum. Also, the possibility
of high magnetization allows a very compact design [12]. As well in [13] it was shown,
that the proton flux of a LION beam can be significantly increased with PMQs. That
is why PMQs were chosen for the experiment, analyzed in this work.
2.2 Focusing and Transport of Ion Beams
11
Focusing with PMQs
The Halbach design, used to generate a QP field with permanent magnets is explained
in detail in [12]. It consists of either 12 or 16 permanent magnet dipoles, assembled
such, that their collective field resembles an ideal QP field.
As seen before, the influence of the QPs on a particle strongly depends on the particles
kinetic energy. Thus, each QP doublet can only be designed to focus particles of one
energy and a small bandwidth around this energy.
In general, for a setup of two PMQs, one big (BQP) and a smaller one (SQP) are
required, because the focal planes of both have to overlap to create a focus in vertical
and horizontal direction. Using two identical QPs, the focal lengths will be the same
and the focal planes will never be in the same position along the beam axis, because the
QPs can not be placed onto each other. Using two different sized QPs, still an alignment
algorithm is required, because the defocussing effect of one QPs in the focussing direction
of the other one affects the focal lengths of the latter. In a properly aligned setup, the
focal plane on the side of the BQP will always be closer to the setup and the focal plane
on the side of the SQP will be further away. So to focus a divergent source, like a LION
beam, where the focussing device should be as close as possible to the source, to collect
more particles, it is important to have first the BQP [1]. To focus a parallel ion beam,
wichs source can assumed to be in infinite distance, first the SQP is needed, because the
focus to create will be closer to the QP doublet.
To focus a divergent ion beam, the first QP of the system has to be as long as possible,
because the longer it is, the closer it can be installed to the source, and thus collect more
particles. Also, a longer QPs is more restrictive to energies, the system is not designed
to focus, so the monochromatization is better. The only tradeoff for the length of the
first QP is, that a longer QP can not focus low energetic protons, as these are so strongly
deflected, that they turn around inside the QP. [1].
The second QP should in principle be as short as possible to ensure maximum efficiency.
It only has to be long enough, to ensure a high quality QP-field without disturbing fringe
effects. The analysis that yielded these results was done in [1].
In [1], the properties of the setup shown in Figure 2.4 were analyzed. It was for the first
time applied in the experiment evaluated in this work. As the aperture of both QPs
is quite small, particles with energies the system is not designed to focus mostly crash
into the walls of the QP. So the system is quite restrictive and creates a thin energy
bandwidth focus structure, even if the incoming spectrum is broad [1]. The analysis
yielded, that Drift 1 mainly selects the particle energy that is focused and Drift 2 sets
the position of the focal plane.
12
2. Theoretical Framework
Figure 2.4.: The setup used to simulate the QP doublet in [1]. Image taken from there.
In [1] an extensive study of positioning errors of the QPs was conducted. This yielded
that the relative rotation of the QPs is the most sensitive parameter. The QP fields have
to be rotated exactly 90 degrees relative to each other. Errors of ±0.1 degrees already
strongly affect the form of the focus and particle fluence. If such an error exists, the
beam profile in the focal plane is much larger. Instead, askew line foci are created, upand downstream of the focal plane. Both line foci are exactly mirrored, such that a scan
along the beam axis would yield a rotating line focus.
Another positioning error is the relative position of the magnetic axes of the QPs. If
they are not aligned exactly on one axis, a particle flying through the dupled sees a
dipole moment. This results in a lateral steering of the focus position. The focal plane
is not affected.
2.2.4. Acceptance and transfer function of an ion transport system
The transfer function of an ion transport system, simulates the whole system. It takes
an incoming beams phase space as argument and calculates the beams phase space after
the system. So by inverting the transfer function, it is possible to derive the phase space
of the incoming beam from the beam profile at the end of the system.
The transverse phase space of an ion is usually defined as x, ppxz and y, ppyz , where x
and y are the axes perpendicular to the propagation direction z. px , py and pz are the
corresponding pulses of the particle. Hence the phase space is the position of the particle
in one dimension and its divergence angle in the other, for x and y directions. So every
particle is a point in this phase space, and the beam bounding covers an area [10].
An ion transport system can be any system of dipole or quadrupole magnets, field free
drifts and also apertures. The latter can either be there for technical reasons, like
the diameter of a QP magnet, or be installed on purpose e.g. to improve the energy
resolution of a spectrometer.
The acceptance of such a system is the area in transverse phase space in front of the
2.3 Image Plates
13
system, in which a particle can start and will be transported through the entire system,
without being absorbed in an aperture or wall. It is usually calculated for a monoenergetic beam.
2.3. Image Plates
Measuring LIONs poses a difficult challenge to detection systems because of the very
high particle flux, wide energy spectrum and strong background signal that is typical for
such experiments [14]. We wanted to evaluate both, areas hit only by a few particles and
high intensity areas, to quantify the difference between the ion focus and other regions.
So a high dynamic range (HDR) of the detector was required, which is a typical property
of image plates (IPs).
2.3.1. Detection Mechanism
IPs are photo-stimulable luminescence (PSL) detectors, offering a HDR and linear response to the dose they receive, being sensitive to any kind of radiation.
The sensitive material of IPs is BaF Br0.85 I0.15 : Eu2+ , a Eu-doped phosphor incorporated in a binding angend of urethane, with an energy level distribution as shown
simplified in Figure 2.5.
The most relevant property of this energy level distribution is the bandgap, containing
many traps. An electron excited by incoming radiation to the conduction band will end
up in one of these traps with a high probability. These electrons will mostly be attributed
to the dopant Eu2+ ions, turning them into Eu3+ . An image of the incoming radiation
is stored in meta-stable states of electrons, and can be read out by illuminating the IP
with red light (635nm). This excites the trapped electrons back to the conduction band,
as this photon energy matches exactly this transition. From the conduction band the
electrons will partly recombine via several excited states of Eu2+ . During this recombination process amongst others, light with a central wave length of 385nm is emitted.
This is detected by the read-out system with a photo multiplier tube(PMT), yielding
the so-called PSL-intensity value( PSL value, IP SL ) [14]
2.3.2. Repeated Read-outs
The measurement range of the IP detector system is mainly restricted by saturation of
the PMT readout. The light intensity from the IP fades exponentially with the read-out
laser irradiation time [14] because after each scan, less electrons will be left in the traps
and hence in the next scan less recombinations will occur. Several scans with fixed laser
irradiation times were performed on the same IP, exhibiting more and more areas where
14
2. Theoretical Framework
Figure 2.5.: Simplified energy levels of the IP-material. It consists of a large bandgap,
with many traps. Image taken from [14]
the PMT-chip is not oversaturated and provides an evaluable signal. Figure 2.6 shows
images of three successive scans.
Due to the fading of signal between two scans i and i+1 of one IP, a reduction factor λi
can be defined. It is possible to measure this factor by comparing the PSL value in an
unsaturated region in both scans:
P
IP SLi+1
λi = P
IP SLi
i = 1, 2, ...
(2.6)
where the sums represent a sum over the values of all pixels in the rectangles shown
in Figure 2.6. Repeating this for all n scans of one image, the PSL values required for
further calculations IP SLf inal can be calculated as:
IP SLf inal = λ1 · λ2 · ...λn ∗ IP SLn
(2.7)
where IP SLn is the PSL value in the last scan. For reasons of clarity, IP SLf inal is from
now on refered to as IP SL .
The PSL value also fades with time if the IP is not read out immediately. This fading
reduces the PSL value to around 93% of its initial value after two hours [14].
2.3 Image Plates
15
Figure 2.6.: Three successive scans of an IP. Areas with weak signal are only resolved
in the first scan, strongly irradiated areas are only resolved in the last scan.
Rectangles indicate areas used to calculate the reduction factors.
2.3.3. Particle Number and Dose Calculation
Over a wide range the PSL-value per pixel is proportional to the dose deposited in an
area of the IP [14], respectively the volume beneath this area. Here dose is defined as
the energy E per mass M deposited in matter by irradiation:
D=
dE
dM
(2.8)
The dose D, received by a pixel with the PSL-value IP SL , can be calculated like this:
D=
IP SL
m
(2.9)
with the proportionality factor m = 1597.0 ± 31.5Gy −1 for the used TR-IP with the
FLA5100 readout system. [14]
The Bethe Bloch formula describes the energy deposition per path-length of radiation
in matter due to its stopping power [15] . The measured PSL-value is proportional to
the deposited dose - and hence energy - under a certain area of the IP. Therefore the
PSL value (IPnorm
SL ) induced in a pixel by a single particle with a known energy E can be
estimated with a simplified Bethe-Bloch formula. In the PhD Thesis by Sabine Reinhard
a simplified model with two parameters was fitted to measured PSL values, induced by
protons of known energies. The fitted model is:
16
2. Theoretical Framework
IPnorm
SL =
A
ln(B · E)
E
(2.10)
The fit yielded the parameters A = 0.498±0.200P SL/M eV and B = 15.108±29.840M eV −1
for the used IP and read-out system.
Knowing the kinetic energy of the particles, one can calculate the particle number per
n
:
pixel pixel
n
IP SL
= norm
pixel
IP SL
(2.11)
2.3.4. Other Detection Systems
Radiochromic films
Radiochromic films (RCF) offer an alternative to IPs in detection of ion beams. They
also enable two dimensional imaging of the beam profile. RCF have an active layer made
of Lithium salt of pentacosa-10,12-diynoic acid, a monomeric molecule, that is broken up
under incident radiation. It recombines either to a butatrien-like structured polymer or
an acetylen-like structured polymer. The latter creates a change in the optical density
of the material and reduces light transmission. As the reduction in transmission is
proportional to the energy and hence dose deposited in the active layer, it is possible
to quantify the incident radiation by measuring the transmission of the irradiated film
[14]
Often RCF are used in a stack of several layers. As lower energetic particles are absorbed
in the first layers and higher energetic particles also create signal in the rear layers, it is
possible to derive a energy profile of the beam [14].
RadEye1 detectors
RadEye1 detectors, are commercially available CMOS pixel detector chips using Si as
active medium with a pixel size of 48µm. Their size is 1024×2046 pixels, hence 51.2mm×
102.4mm, but several detectors can be installed next to each other, to increase the
detection plane. They are read out digitally and allow online evaluation. This makes
them very attractive for qualitative experiments because the effect of a change in the
setup can be seem immediately. They can be read out with a frequency of 2.7Hz. A
quantitative evaluation is not easily possible due to the limited dynamic range compared
to IPs [14].
Experiment with LIONs
To test the real behavior of LIONs in a QP dublet and to investigate the properties of the
setup proposed in [1], an experiment in LEX photonics was performed. In this chapter,
the experimental setup and the developed evaluation methods are described.
3.1. Laboratory for extreme photonics (LEX photonics)
In LEX photonics a pulsed Ti:Sa laser delivered 2J in 30fs pulses on thin foil targets
W
of various materials, leading to intensities of about 1020 cm
2 in the focus with a size of
several µm. The whole setup was in vacuum, because these high laser intensities and
short pulse lengths are impossible to maintain in ambient conditions. Additionally the
propagation of the resulting ion beam would be disturbed by air.
This work is dedicated to the evaluation of the experiment performed on 11/18/2017,
where protons of up to 10M eV were accelerated out of 250nm thin gold foils. The foils
were destroyed during the laster-target interaction. The proton bunches resulting from
the laser shots, were focused with a PMQ doublet and used for different experiments.
To study the properties of the focus itself, the bunches were focused on IPs.
Because of changes in the target, and laser instabilities, the accelerated spectrum is
not completely reproducible from shot to shot. Different bunches are distinguished
by increasing numbers. In this work shots 12, 91, 116, 129, 213, 217 and 220 are
evaluated.
3.2. LION focusing setup at LEX
The ion beam was focused and energy selected with a set of two PMQs, installed, as
shown in figure 3.1. This experiment is now referred to as LEX experiment, the setup is
called LEX setup. The details of both QPs are summarized in Table 3.1 and discussed
in [1]. Drift 1 was used to select the focused proton energy. Drift 2 was adjusted
such, that the target focus distance (TFD) always remained at 153, 1cm, because the
detection plane was fixed. Drift lengths 1 and 2 can be found in the appendix table B.1.
18
3. Experiment with LIONs
Table 3.1.: QP properties
length [mm] grad QP [T/m]
BQP
40
334 ± 2
SQP
20
333 ± 1
The position of the dipole, thus Drift 4, was constant for all shots: 78.6cm before the
detection plane. Drift 3 was the result of the former settings.
In the experiment evaluated in this work, Fujifilm TR-IPs and a FLA5100 readout
system were used as detectors for the deflected ion foci. The IPs were placed outside
the vacuum chamber, directly on the window shown in figure 3.2, covered with 50µm
thin capton. This yielded the sharp cut of the signal on the fringe as visible e.g. in the
image of shot 91 (see figure 4.6).
Figure 3.1.: The setup, as used for the LEX experiment evaluated in this work. Image
adapted from [1].
3.2.1. Dipole Magnet
The dipole magnet behind the QP doublet was used to create an energy dependent
deflection y(E) of the focus, allowing an estimation of the focused energies (see chapter
3.3). In front of the dipole, an aperture was installed to improve the energy resolution.
The aperture could be varied between a pinhole with 5mm diameter or a 1.5mm slit.
The dipole length was l = 12cm. Dipole and aperture combined are from now on referred
to as spectrometer.
The MATLAB program ’StartSpectraCalculation.m’ written by Florian Lindner was
used to calculate the expected deflections of certain energies in the field of the dipole.
It applies particle tracking though the measured magnetic field of the dipole. Figure 3.3
shows, that it fits very well with the model in equation 2.4 using an effective magnetic
field of 0.13T .
3.2 LION focusing setup at LEX
19
Figure 3.2.: The vacuum exit window on which the IPs were attached. Rectangle indicates
the approximate position of the IPs
Figure 3.3.: Comparison of the deflection calculation in equation 2.4 and the program
’StartSpectraCalculation.m’
20
3. Experiment with LIONs
3.3. Deflection measurement
In order to derive the approximate particle energy of the focus, the deflections due to
the dipole field were measured. At first a virtual ’zeroline’ at the theoretical position of
an uncharged beam had to be defined.
As described in chapter 2.1.1 a x-ray flash is produced during the laser plasma interaction, that also propagates along the beam axis. The circular projection in the first IP
scan, shown in figure 3.4, is the image of the pinhole, used in the spectrometer, produced
by this x-ray flash. The image is taken with an IP, that was read out multiple times.
As the x-ray signal is much weaker, than the signal of the protons, it is only visible
in the first IP scan. The ion focus is most accurately visible in the last scan. So the
first and last scan images had to be combined in order to measure the focus deflection
precisely.
Figure 3.4.: IP scans 1 and 7 of shot 220. In scan 1 the x-ray spot is visible, in scan 7
the focus position.
The x-ray spot did still not give a precise localization of the zeroline. While the pinhole
diameter was 5mm, its image in the IP is about 1.6cm. The foci are mostly quite small
and can be localized approximately with a precision of ±1mm. So a zeroline definition
3.3 Deflection measurement
21
with similiar precision would be favorable. For shot 12 a slit with a width of 1.5mm was
used in the spectrometer aperture. Its image is partly visible on the upper margin of
the IP. For all other shots, at least a part of the pinhole image is visible. The lower end
of the vacuum exit window is visible in all shots, so it could be used as reference point.
The deflection measurement was performed as follows:
1. In shot 12 scan 1 the distance from the lower margin of the slit image to the bottom
s12 1 is measured
2. In shot 12 scan 6 the distance from the bottom of the exit window projection to
the focus center: s12 6 is measured
3. d1 = s12 1 − s12 6 yields the distance from the margin to the focus.
4. One shot (here 220) with the same QP positions as shot12 (i.e. same deflection)
is used to measure the distance from the lower margin of the pinhole image to the
focus: d2
5. x = d1 − d2 yields the distance from the lower margin of the slit image to the lower
margin of the pinhole image, wich is assumed to be the same in all shots.
6. Measure for all shots the distance from the lower margin of the pinhole image to
the focus: d2
7. d2 + x yields the distance from the lower margin of the slit image to the foci
Figure 3.5.: Measurement of the focus deflections
22
3. Experiment with LIONs
This procedure is partly visualized in figure 3.5. With this routine, the deflection value
of shot 220 is not representative, because it is used for calibration. Nevertheless it will
be included in the further analysis for comparison.
So far, the distance from the lower margin of the slit to the focus (d2 + x) was measured
for every shot. The zeroline is supposed to be in the center of the slit image, which is
not visible on the IP, because the slit is not completely imaged (see figure 3.5). However
in the image of shot 28, which is not evaluated in this work, but was recorded with the
same setup, the image of the pinhole is fully visible. So, its diameter could be measured
to be dphIm = 1.6cm. As the magnification of slit and pinhole image must be equivalent,
the equation:
dslIm
dphI
=
dph
dsl
(3.1)
must hold. With the diameter of the pinhole dph , the slitwidth dsl and the width of the
slits image dslIm could be calculated:
dslIm = dsl ·
dphI
dph
(3.2)
3.4. Parameters for particle number calculation
In [14] a formula to calculate particle number (PN) from the IP data is established. In
order to apply it in this experiment, two parameters were introduced to clarify definitions. There are two options for each parameter yielding four methods to calculate the
PN in the focus and two options to calculate the PN on the whole IP. These parameters
are explained in the next sections.
As described in chapter 2.3 the kinetic energy of the incoming protons is needed to
calculate the particle number from the PSL value. For this calculation the energy,
derived from the deflections, was used. (see Chapter 4.1.1)
3.4.1. Focus Definition
As the images of the ion beam show very diverse structures, the definition which pixels
belong to the focus was not trivial. However, a proper focus definition was important to
quantify the particle number transmitted to the focus. So two different focus definitions
were applied in order to compare the results.
In the geometric definition (g-focus) (see figure 3.6 right hand side), the focus is a circle
with 0.75mm radius, placed around the center of the structure. The radius was chosen
3.4 Parameters for particle number calculation
23
such that the circle covered the brightest area in most shots. Its position was defined by
marking it manually in the picture, so there is a potential error coming from placement
inaccuracies. This error was measured by recounting the particle number in the focus of
one shot four times and calculating the mean value. A maximum deviation of less than
8% was found.
In the dose definition (d-focus) (see figure 3.6 left hand side), every pixel in the image,
that received a dose higher than half the maximum dose on one pixel is counted as a
part of the focus. It was also used in a previous experiment by Bin et al. [16]. This
definition yields no positioning or similar errors like the geometric definition.
Figure 3.6.: Particle number maps with dose (left) and geometrical defined focus(right)
for two shots.
3.4.2. Background Subtraction
Images of some shots exhibited a quite intense background signal around the focus. It
is not certain if this background is produced by ions of different energies than the focus,
passing through the QPs or by scattered radiation e.g. from the x-ray flash. In the first
case, it would be a relevant signal, influencing the quality of the focus. In the latter case,
it has to be subtracted because it yields an offset to the particle number, that should
not be evaluated. Although it is not certain if this signal is background, it will be called
background signal from now on as a simplified expression.
24
3. Experiment with LIONs
Figure 3.7.: Particle number maps of shot 217 with and without subtracted background.
So a second parameter was introduced for the particle number calculation. The two
options in this case are no background (nobg) and background(bg). Figure 3.7 shows
exemplary the focus of shot 217 with and without subtracted background.
The background subtraction was done by calculating the arithmetic mean of the PSL
value in a rectangle and subtracting this mean value from all pixel values. As the
rectangle was selected manually, an additional error introduced. It was calculated in the
same way as the error from the geometrical focus definition (see Chapter 3.4.1), yielding
less than 12%.
3.4.3. Implementation
To realize the described analysis, the program ’IPReader.m’ was updated to ’IPReader2.m’
during this work. It now reads the ’.img’-files, produced by the IP scanner system, scans
the necessary metadata from a ’.inf’ file of the same name and asks the user for the desired parameters. Then a ’PartNumb*.txt’ file is written to the folder of the ’.img’ file,
containing the particle numbers per pixel array. * represents the specified parameters.
The PNs in the focus and summed over the entire IP are calculated as well. More
information about this program can be found in the appendix C
Also the dose, transmitted to the volume, underlying the focal area for both focus
definitions was calculated. For this, equation 2.9 was applied pixelwise, then the dose
per pixel was summed over the focus area.
Evaluation and Results
The LEX experiment yielded the focus images shown in figure 4.6. To analyse and
quantify these structures, different methods were introduced above. In this chapter,
they will be applied and the results are interpreted.
4.1. Spectrometer measurements
4.1.1. Energy Derivation
The half slit-image-width (2.4mm) calculated in equation 3.2 was added to the deflections of all shots. This yielded the final deflections y, shown in table 4.1. The table also
contains the energies, the QP setup was designed to focus (QP energies).
The program ’StartSpectraCalculation.m’ was used to calculate expected deflections of
certain energies in the dipole. The energies corresponding to the measured deflections
were extrapolated, as shown in figure 4.1. The focus energies obtained by this extrapolation are also documented in table 4.1.
To estimate the error of the whole deflection, the contribution of all three measurements
that added to the deflection had to be considered. An error of ∆d = ±1mm was assumed
for all length measurements in the IP pictures due to uncertainties of locations in the
images and misplacement of cursors. A Gaussian error calculation was used to estimate
the error in the total deflection y:
∆y =
p
3 ∗ (∆d)2 = ±1.7mm
(4.1)
This is larger than the dimension of most foci (see Section 3.4.1), so the deflection-, and
therewith the energy error due to the focus size is negligible. Errors of the slit image
width were also neglected, because the dimensions of the pinhole and slit are known very
precisely.
26
Table 4.1.: Deflections
shot no
12
91
deflection [cm]
3.00 2.49
QP energy [MeV]
7.0
10.0
13.8
focus energy [MeV] 9.4
4. Evaluation and Results
and corresponding
116 129 213
2.78 2.59 3.01
8.0
9.0
7.0
11.1 12.6 9.3
energies of all shots
217 220
2.90 3.00
7.0
7.0
10.2 9.4
Figure 4.1.: Derivation of focus energy from the deflection shown for two examples.
Graph calculated with ’StartSpectraCalculation.m’
4.1.2. Evaluation of focus energies
Obviously, there is a discrepancy between the measured focus energies and the QP
energies in table 4.1. Furthermore, especially the higher energies above 11 MeV are
rather unlikely to occur in the LEX-LION experiment. The incoming spectrum, partly
visible in figure 4.4, fades around 10 MeV.
To explain these unexpectedly low absolute deflection values an upwards steering introduced by positioning errors of the QPs was assumed (see chapter 2.2.3). This is probable,
as the QPs were aligned manually [1]. This steering could produce an upwards shift of
all foci, resulting in lower absolute deflection values, with respect to the x-ray flash since
the latter is not affected by the QPs. To visualize this effect, the measured deflections
were plotted against the QP energies. The computed deflections of protons of these
energies were included in the plot as well. As visible in figure 4.2, the measured val-
4.1 Spectrometer measurements
27
ues and the computed curve run approximately parallel, reasoning the theory of a QP
steering. The average vertical distance between the data points and the computed line
was calculated yielding a steering of 4.6mm. Subtracting this from the computed line,
yielded the second line in figure 4.2.
Figure 4.2.: Calculated and measured deflections of the foci, plotted against the QP energies. A steering was assumed to explain the discrepancy in the deflections.
Shots 91 and 217 were assumed to have slightly different focus energies because of their big deflection deviations.
Only shots 91 and 217 still exhibited a deviation of more than the measurement error
of ∆y = ±1.7mm. Hence it was assumed, that their foci contained energies slightly
different from the QP energy. Their energy was adjusted, according to the calculated line.
This is also illustrated in figure 4.2. A slight change in the focused energy might occur,
if the incoming spectrum of this shot contained more or less high energetic particles or if
there are small positioning errors of the QPs. Both options are possible in the analyzed
setup.
This closer evaluation yielded the energy values in table 4.2. The minimum and maximum deflections, resulting from the calculated error of the measurement (see equation
28
4. Evaluation and Results
4.1), were used to estimate the energy error boundaries in table 4.2. To find the minimum and maximum energies, the method presented in figure 4.1 was applied on the
deflections y ± ∆y.
Figure 4.3.: Deflections v.s. QP energies. Some images of shot foci were inserted at their
corresponding positions, to visualize the size of the foci, compared to the
deflections. Green spots indicate the actually measured positions. Red line
shows the calculated deflection of different energies (see equation 2.4) with
4.6mm steering subtracted and B = 0.13T. Inset shows the same equation
on a larger scale to visualize its evolution.
Table 4.2.:
12
shot
QP energy [MeV]
7.0
focus energy [MeV] 7.0
Emin [MeV]
6.35
Emax [MeV]
7.69
Final
91
10.0
9.7
8.7
10.9
focus energies and error boundaries
116 129 213 217 220
8.0
9.0
7.0
7.0 7.0
8.0
9.0
7.0
7.5 7.0
7.3
8.00 6.35 6.8 6.35
8.90 10
7.69 8.3 7.69
4.2 Particle Number Calculations
29
Figure 4.3 visualizes the relation between deflection and final focus energy, and shows
the size of the foci, compared to the deflections. One can see, that the focus sizes
are much smaller than the differences in focus positions. So the focus positions are
definitely energy dependent. This observation justifies the usage of the focus deflections
for calculations.
4.2. Particle Number Calculations
Figure 4.4 shows all calculated focus PN for all seven shots and all four methods. The
energy plotted along the horizontal axis is calculated from the deflection of the focus as
described above. This is not necessarily the energy of all particles in the focus but a
good approximation. For the errorbars the minimum and maximum energies from tab
4.2 are applied.
PNs can be found in the appendix in tables B.2 and B.3. Space resolved PN data of
the analyzed shots can be found in ’Y:/project/agschreiber/Derya.Taray/IP analysis’
split up in one folder for each shot. The ’partNumb*.txt’ files contain arrays with the
number of particles of the corresponding pixel in an image. Table B.4 contains the dose
transmitted to the volume, underlying the different focus areas of all shots.
Figure 4.4.: PNs of different shots, calculated with different methods. A representative
LION spectrum from an other shot is included to compare PNs. Errorbars
result from minimum and maximum energies in 4.2. For reasons of clarity,
they were only inserted once per energy, since they are identical for all spots
of one energy
30
4. Evaluation and Results
The results spread roughly over one order of magnitude even within one shot. Although
the incoming LION spectrum is not accurately reproduced in every shot, it can be used
as an approximation and represents an average shot. A difference in the PNs of different
shots is expected, due to shot to shot fluctuations.
However, the focus PNs are almost all one order of magnitude higher than the PN of
the incoming LION spectrum at the particular focus energy. Shot to shot fluctuations
of an order of magnitude were not expected to occur in this stage of the LEX photonics
experiment. Also, almost all focus PNs are higher than the incoming spectrum. If the
deviation from the incoming spectrum would be introduced by shot to shot fluctuations,
some shots would provide PNs lower than the incoming spectrum. So the foci probably
contain particles of a broad energy interval.
Figure 4.4 provides an overview of the absolute PNs provided by the different methods,
but the systematical influences of the parameters can better be discussed with the help
of figure 4.5. PNs were normalized to each shots average and the horizontal axis is no
longer the energy, as it not relevant for the method comparison. Each line in both plots
corresponds to one method. So the influence of the parameters focus definition and
background subtraction on different shots can be compared.
Figure 4.5 a) and b) show the same plot, but in a) the PN is summed only over the
focus region, while in b) the PN is summed over the whole image. In b) there are only
two options (bg and nobg) because the focus definition is not applied any more.
Figure 4.5.: PNs were normalized to each shots average and plotted together, to show the
influence of the different parameters. Each line corresponds to one method.
In a) the focus PNs are plotted, in b) the PN was summed over the entire
IP.
4.3 Qualitative Observations and first deductions
31
4.3. Qualitative Observations and first deductions
4.3.1. Image plate pictures
Figure 4.6.: Focus images of the seven shots evaluated in this work.
Figure 4.6 shows the last scan IP pictures of all evaluated shots. All of them besides
shot 12 expose a characteristic downwards wing and a cross structure in the upper part.
For shot 12 the spectrometer aperture was a slit with only 1.5mm width, while for the
other shots, a 5mm pinhole was used.
The cross structure in the upper part consists of two diagonal wings and a horizontal
bar. The latter is missing in shots 213 and 217, for wich the target foil was placed
slightly outside the laser focus. In most shots the maximum dose was deposited in the
point where all wings meet. Thus this point is the brightest area in the image. Only in
shots 91 and 217 the brightest pixels are somewhere in the downward wing.
As the junction of the wings probably is the center of the ion acceleration sheath, it was
used as focus point for the deflection measurements described in chapter 3.3. This is
justified, because the laser focus, hence the center of the acceleration sheath, the QPs
and the spectrometer aperture were aligned on one line. This line defines the zeroline of
no deflection.
32
4. Evaluation and Results
4.3.2. Particle number calculations
As expected, the background subtraction yields always lower PNs. This is visible in
both plots in figure 4.5. For the g-focus, the background subtraction yields more or less
a constant offset with both lines beeing almost parallel. Fluctuations only occur because
of different background signal intensities. For the d-focus, the difference between bg and
nobg shows higher fluctuations. Generally, the difference between bg and nobg is higher
for larger focus areas like in shots 217 and 91.
For most shots, the geometrical focus definition yields lower PNs, because the dose
defined foci are larger, and always contain the pixels with highest fluences. The g-focus
is not necessarily located at the spot of strongest signal. But for shots 12, 116 and
220 the geometrical definition yields a higher PN, because the area with strong signal
is quite small and therefore the geometrical defined focus contains more pixels. This is
also visible in figure 3.6 for shot 116.
Shots 213 and 217, for which the target foil was placed slightly away from the laser focus,
yield a lower PN for the g-focus definition. On the other hand, the d-focus definition
yields especially high PNs for these shots. As also the vertical bar is missing, probably
in this case more particles were transfered to the downwards wing, hence away from the
g-focus region, but increasing the dose in the downwards wing such,that a larger area
contributed to the d-focus region.
Another important observation is, that for optically well-focused shots, the results of the
different methods differ less. Well-focused in this case means that the area of strongest
signal is small, and concentrated in the spot where the wings meet (see figure 4.6). Also
the wings should not contain a strong signal and maybe even some of them do not exist.
(e.g. shots 12, 116)
4.3.3. Laser focus
In order to explain the structures visible in figure 4.6, one option was to study the ion
source hence the laser focus. The latter was not imaged during the LEX experiment,
but left a burned flag on the target holder, containing the foils, as shown in figure 4.7.
Each hole contains one target foil and is irradiated separately. The picture was taken on
the laser-focus side of the target after irradiation. There is a burned flag visible on the
downside of the hole, giving reason to the theory, that the laser focus has a downwards
pointing wing, similar to the structures of the ion foci in figure 4.6.
4.3 Qualitative Observations and first deductions
33
Figure 4.7.: The target holder, used for the experiments. Green arrows indicate the
burned areas outside the target holes. Image courtesy Jens Hartmann.
4.3.4. Focus Structures
The structures visible in figure 4.6 were not expected in the LEX experiment, and are
not yet explained. They were also recorded in an earlier experiment in front of the
dipole. In this experiment, the QPs were used to focus the ion beam on a stack of
RCFs, installed in front of the dipole in the LEX setup, shown in figure 3.1 with 0.4m
TFD. This yielded the images shown in figure 4.8. The structure looks similar, in all
layers of the stack, so it has to be monoenergetic. As well, if the structure visible on the
RCFs would contain a broad energy spectrum, its appearance would change after the
dipole. But the IP pictures exhibited a very similar structure (see figure 4.6).
Figure 4.8.: Image of the beam profile without the dipole on 4 layers of a RCF stack with
0.4m TFD. Spacial variations of the focus spot are due to the cutout
So the focus structures are definitely not produced by the dipole. This leaves only two
possible options for their origin. Either the acceleration sheath, hence the ion source has
34
4. Evaluation and Results
a shape, that results in the observed focus structures or they are created by field effects
of the QPs. The basic problem here is, that neither the source area, nor the effect of the
QPs on a polychromatic, divergent beam is known precisely. A closer characterization of
the ion source was not yet possible, due to the intense and variable radiation occurring in
this area and the non negligible shot to shot fluctuations. Therefore first the behavior of
the QPs had to be understood better, in order to eliminate one uncertainty in the setup.
For this reason, a second experiment, with a well known ion beam was necessary.
Experiment with conventionally accelerated ions
To analyze whether the structures seen in figure 4.6 are produced by the QP or are a
real property of the ion source, an experiment at the Tandem accelerator of the Maier
Leibniz Laboratory (MLL) in Garching was performed. The aim was to study influences
of positioning errors on the focus form. This experiment also offered the chance to
retest the QP setup and show the possibility to create a high quality ion focus using
PMQs.
5.1. Experimental Setup
For the experiment, the Tandem van-de-Graaff accelerator of the MLL was adjusted to
produce 20M eV protons in a continuous beam.
The setup of the experiment is shown in figure 5.1. The incoming beam firstly passed
through a small 3x3 quadratic pinhole array, called pepperpot (PP) (see figure 5.2 for
measures). Like this 9 parallel beams were created, that should be focused to one point
by the QPs. To achieve the focusing, drift 2 and 3 were optimized. The used QPs were
the same as in the LEX-experiment (see chapter 3.2). The distance from the PP to
the SQP was irrelevant, as the beam before the SQP can be regarded parallel with a
diameter between 1 and 2mm.
36
5. Experiment with conventionally accelerated ions
Figure 5.1.: The setup used in the Tandem experiment.
As the parallel beam can be interpreted as coming from a point source in infinite distance,
and the focus should be close to the QPs, in this experiment the ions had to pass first
through the SQP (see chapter 2.2.3)
The ions were detected with two RadEye1 detectors, offering online evaluation and thus
easier focus optimization. QPs and RadEye1 detectors were mounted on motorized
stages to adjust drifts 2 and 3. The QPs could also be moved in x and y directions,
perpendicular to the beam. All experiments were conducted in vacuum to reduce ion
scattering on air molecules and hence the divergence of the beam.
Figure 5.2.: Measures of the PP
5.2 Measurements and Results
37
5.2. Measurements and Results
Figure 5.3 is an image of the ion beam through the PP. It was used as reference image for
the focus position and to align the QPs. The holes are not all homogeneously imaged,
because the PP was not installed perfectly perpendicular to the beam.
Figure 5.3.: Image of the ion beam through the PP. Holes are not imaged homogeneously.
Pixel values in arbitrary units (AU)
38
5. Experiment with conventionally accelerated ions
First, both QPs were installed separately, to create line foci and adjust the lateral
alignment of the QPs. This was done, by overlaying the line foci positions with the
unperturbed image of the PP. Like this, the steering due to positioning errors was
eliminated. This yielded the pictures, visible in figure 5.4. Both line foci are compact
and exhibit no unexpected structures.
Figure 5.4.: Horizontal and vertical line focus, created by single QPs.
Second, both QPs were adjusted together to create a point focus in the detection plane.
For this, the ion beam had to be aligned along the magnetic axis of the QPs. Scanning
along the beam axis through the focus, a rotating line structure was observed, as it would
be expected for a QP rotation missalignment as introduced in [1] (see chapter 2.2.3).
Therefore one can derive, that the QP rotation alignment, was not precise enough to
eliminate imaging errors neither in the Tandem experiment, nor in the previous LEX
experiment.
5.2 Measurements and Results
39
Then a slight lateral misplacement of the QPs was introduced to analyze the influence
of positioning errors of the complete setup. Both QPs were moved simultaneously, along
the axes perpendicular to the ion beam (x and y). The focus without misplacement,
and two foci with misplaced QPs are shown together in figure 5.5.
Figure 5.5.: Foci, created by both QPs. Two foci were imaged in a larger scale; x=45mm
y=0 also with readjusted colorbar. x and y indicate the lateral positions of
the QPs
The focus without misplacement has a diameter of approximately 200µm. The positioning errors increase the size it a bit, and decrease the absolute particle number, hence
the intensity. In the image of the focus x=45mm, y=0mm a small, downwards pointing
wing structure can be observed. This increases the focus size to approximately 1mm in
this direction. Horizontally, it is still around 200µm wide.
Also a downwards shift is visible in the x=45mm, y=0mm focus although, the QPs were
not moved in y direction. So a horizontal misalignment of the QPs can apparently create
a vertical shift of the focus.
Discussion
In order to explain the experimental results, several assumptions were made and also
some outcomes did not fit with the expectations. These critical points will be discussed
in this chapter.
6.1. Steering
The steering of 4.6mm of the QPs, introduced to explain the low deflection values
(see chapter 4.1.2), was assumed to be constant for all shots. It might be created by
a dipole moment produced by the QP fields due to inaccuracies in the design or a
relative misplacement of the QPs. Then, the deflection would be energy dependent,
as higher energetic particles are deflected less. So the constant offset approximation,
would underestimate the deflection of the 7 MeV and overestimate the deflection of the
10M eV protons. Even if such a tendency is visible in figure 4.3, it is not to a degree
that would allow a quantitative evaluation. Especially because three of the four 7 MeV
shots perfectly fit to the computed line.
The steering could also result from misalignment of the QPs relative to the source. In
the Tandem experiment, in figure 5.5 a vertical shift of the focus is introduced by a
horizontal misalignment.
6.2. Particle Number and Dose Calculation
An algorithm to calculate particle numbers per area from IP data was derived and implemented. Details can be found in C. Two different focus definitions were applied.
The g-focus definition is probably more appropriate to characterize the applicability
of the bunch. since for most applications, the beam will have to be focused within a
defined area. Thus the fluence through this area will be of interest. However, the d-focus
definition provides more reliable information about the transport efficiency of the QPs
doublet. In the g-focus, not all high fluence areas are necessarily covered and therefore,
it might underestimate the PN delivered to the detection plane.
6.2 Particle Number and Dose Calculation
41
In the g-focus, mean particle fluences of up to 1.3 · 106 mm−2 were calculated. This is
better than the expectations in [1] and around 1000 times higher, than the fluence without any focusing device. In summary, the g-focus should be used to analyze applications
of the LION beam, while the d-focus is better used to characterize the QP system or
the LION bunch.
The calculated particle numbers, that are documented in the PN maps and in table B.2
are of very low precision. Errors occuring from the applied methods, explained in chapter
3.4 were neglected, because of the huge errors in the calibration factors, of 100% and
more, introduced in [14]. But the order of magnitude agrees with previous experiments,
an can thus be used for further analyses.
The wide spread of the absolute PN, of around 100 % for the same shot, shows the
importance of an adequate choice of the calculation method. To reduce this spread, a
clarification of the background signal source would be useful. Eliminating this parameter,
would only leave the focus definition as free parameter which can be chosen appropriate
to the application. Also, it is not affecting the absolute PN per area.
A significant feature in figure 4.4 is the extremely low particle number of shot 217,
with 7.5 MeV. This is also one of the two shots, where the measured energy deviates
significantly from the QP energy. Although the QP energy is still within the error
boundaries, one might deduce that whatever caused the deviation of the focused energy
also caused a less efficient focusing. The reason might be positioning errors of the QPs or
a change in the incoming spectrum, due to instabilities in the acceleration mechanism.
But this is not a very strong hint, because the absolute particle number of this shot,
could also have been lower, such that the focusing efficiency still was the same. And shot
91, whose focus energy also deviated from the QP energy, exhibited a higher particle
number. The other shot to shot fluctuations in the particle number are within the error
boundaries of the calculation.
For the PN calculation, it was assumed, that the whole focus structure only contained
particles of a thin energy interval (see chapter 3.4), although it spread over roughly
1.6cm. Because of the dipole field, such a long structure should be polyenergetic, because
of the energy dependent deflection. The assumption of a thin energy spectrum is anyway
justified by the fact, that the structures were also detected without a dipole (see chapter
4.3.4). Another reason for the assumption of a thin energy spectrum was the energy
selecting effect of the QP system in the focus. So the wide spread of the structure would
be explained with different entrance positions and angles in the dipole field.
The dose values, documented in table B.4 are much higher than expected. In [16] Bin
et al reported focus doses of several Gy with a very similar setup. Also the dose does
not fit with the PNs. Using the areal density of the IPs ρ , the g-focus area A, the
calculated PN n and the dose transmitted to the focus D, the average deposited energy
per particle E can be expressed as:
42
6. Discussion
E=
D·A·ρ
= 0.3GeV
n
(6.1)
with the values of shot 12. This is impossible for maximum 10 MeV protons. As the
PNs are reasonable, probably the dose calculation yields wrong results. This might be
due to a problem with the calibration factor derived for protons in [14]. Maybe the
electromagnetic radiation, is not negligible in the PSL value, and therefore the proton
calibration factor can not be applied anymore. For this reason also the dose maps, in
the folder ’Y:/project/agschreiber/Derya.Taray/IP analysis’ are probably wrong.
6.3. Geometric properties of the focus
The size of the g-focus is the same for all shots (1.8mm2 ), while the d-focus size varies
strongly from shot to shot. It’s vertical length is between 2mm and 1cm. That is
also why the g-focus definition is much more sensitive to background subtraction. All
foci observed in the Tandem experiment, are smaller than the diameter of the g-focus
definition. They would fit entirely in this definition. So the d-focus definition would
cover a smaller area for these foci. This is an indication, that the foci, created in the
LEX experiment are not the minimum size, that is achievable with the QPs, as the
tandem focus was smaller. Additionally, the focus at tandem was as well affected by
positioning errors (see chapter 5.2 . So probably a more precise alignment could create
an even smaller focus.
As the wing structures, especially the downwards pointing one, are most certainly not
created by the dipole magnet, the question of their origin is still a topic to be discussed.
During the Tandem experiment, a small downwards wing in the focus was seen, when
the QPs were misplaced sidewards, such that the beam axis no longer was along the QP
magnetic axis. A similar, undesired misplacement of the QPs in the LEX experiment
could have caused the downward wing. This would indicate a lack of precision in the
QP alignment in the LEX experiment. But the cross structures in the upper part
can not be explained like this, because nothing similar was observed in the Tandem
experiment.
A second explanation for the wing structures could be the form of the ion source. In
figure 4.7 a similar structure was seen in the laser focus. This laser focus structure could
be reproduced in the acceleration sheath, hence the ion source. In [4] a change in the
beam profile, induced by a modification of the acceleration sheath was already reported.
So the laser focus structure could be imaged in the ion focal plane by the QPs. This
would mean, that the QP system actually produced an image of the ion source, similar
to an optical image with lenses. This was already proposed in [1], but not yet expected
to be achieved in the LEX experiment. The observation of the missing horizontal bar in
shots 213 and 217, for which the target foil was placed outside the laser focus, supports
the theory, that the observed structures result from the laser focus.
6.4 Energy Resolution of the Spectrometer
43
Cross structures, similar to the images recorded during the LEX experiment were also
reported by Schillaci et al in [17], while applying and simulating a PMQ focusing setup
for polychromatic LION bunches. Cross structures were observed in measurements and
simulations. The structures observed by Schialli et al. exhibit mostly wings of the same
length. They explained the structures by errors in the QP fields, especially in the fringe
regions, already announced in [18]. To explain the longer downwards stretch, observed
in the LEX experiment the rotation error of the QPs, described in 2.2.3 could be applied.
This would create an askew line focus, and thus increase the length of one arm of the
cross, creating the long downwards wing. The difference in the focus structures might
also result from the fact, that Schillaci et al used a system of four PMQs instead of
two.
To summarize, the focus structures, probably are generated by a combination of QP
effects and the ion source shape. To explain them precisely, a more detailed knowledge
of the QPs is required.
6.4. Energy Resolution of the Spectrometer
As explained in chapter 2.2.2 the spectrometer had a finite energy resolution, created by
the size of the entrance aperture. For most shots, this was a pinhole with 5mm diameter,
resulting in an energy resolution of approximately 3M eV .
But the imaged structures do consist of more than one particle or one point. They
stretch over approximately 1.6cm in the detection plane. Only in shot 12, instead of the
pinhole, a 1.5mm slit was used. This smaller aperture reduced the acceptance region of
the whole system such, that the downwards pointing wing was cut off. As the pinhole
did not cut off the wing, one can derive, that this bigger acceptance was necessary to
transfer the whole structure through the system. If the structure entered the whole ion
transport system, significantly lower or higher, parts of it would have been cut off like
in shot 12.
To quantify this tolerance of the structure position, and thus derive the absolute energy
resolution, the acceptance of the whole system is required. Comparing its size, with
the size of the ion source, and projecting the difference in the focal plane, would yield
the maximum possible deviation in deflection, hence the energy resolution of the whole
system. To calculate this projection, also the transfer function of the system, especially
the magnification is required.
For this work, the energy resolution was assumed to be limited by the deflection measuring accuracy ∆y = 1.7mm calculated in equation 4.1. So it was around 1 − 2M eV ,
depending on the absolute value. But as the focus energies and the QP energies fit very
well, this probably underestimates the quality of the spectrometer.
Outlook
For a further evaluation of the LEX experiment e.g. to calculate the energy resolution,
the acceptance and transfer function of the whole system are required. In [1] the acceptance function of a PMQ doublet was calculated already. This formalism could be
expanded for the setup in the LEX experiment. Calculating these, would also be beneficial, because then the exact energy interval of the focused structure can be derived.
Using this and the particle number calculation, it would be possible to use the QP system with different design energies to measure the entire spectrum of the LION source.
If the spectrum is reproduced in every shot, the QP system with IPs could be used as a
LION spectrometer with very broad energy band and high dynamic range.
If no other explanation for the high dose values is found, the calibration factor, introduced in [14] should be checked again.
For most applications of ion beams a sharp contrast is required, because in the focus
region the irradiation shall be intense, while probes outside the focus should not be
affected. In this work, it was shown, that the diverse structures of the beam can be cut
out in the focal plane by inserting a smaller aperture, as done in shot 12. Like this the
focus contrast can be increased. So from the results of this work, a small aperture slit
instead of the large pinhole is recommended for future LION applications.
Future experiments could investigate the imaging properties of the QPs. Using them
as imaging devices, seems to be within reach. This would be another application of
the transfer function, respectively its inversion. Magnification and transport efficiency
would be of interest.
If the focus structures really are the image of the ion source, the QPs can also be used
to study the source region with high spatial resolution. For example, the reason for
the missing horizontal bar in shots 213 and 217 could be investigated. Also in the last
layer of the RCF-stack (figure 4.8) a very faint horizontal structure is visible. In the
images recorded by Schillaci et al in [17] also an underlying structure of higher energy is
recorded. The origin of these higher energetic ions could also be explained by the transfer
function or a better knowledge of the source region. For these applications, certainly the
pinhole aperture in the dipole would be favorable instead of the slit, because it enables
an imaging of the whole structure.
45
As the process of ion acceleration is not fully understood yet, powerful experimental
imaging methods are required.
Also the focusing and monochromatizing effect of the PMQ doublet was demonstrated
in this work. So PMQs can certainly be used to shape LION bunches to fit future
applications. In further developements, QPs could also be used to compress ion bunches
even further and reduce their longitudinal emittance. But firstly, it is necessary to
improve the rotational and position alignment of the QPs. Both, the steering in the
LEX experiment, and the imaging artifacts in the tandem experiment showed, that
currently reached precision is not enough to perform reliable imaging.
To summarize, PMQs offer an excellent option to analyze LION beam properties in
scientific experiments and as well are a key technology for pushing LIONs further towards
application. So the progress in future LION experiments will probably be closely related
to developments in PMQ focusing systems.
List of Abbreviations
Abbreviation
long term
TNSA
IP
TFD
QP
BQP
SQP
RCF
RF
PN
g-focus
d-focus
MLL
PP
LION
PMQ
AU
LEX photonics
bg
nobg
PSL
target normal sheath acceleration
image plate
target focus distance
quadrupole
big quadrupole (l=40mm)
small quadrupole (l=20mm)
radiochromic film
radio frequency
particle number
geometrical focus; parameter for PN calculation
dose focus; parameter for PN calculation
Maier Leibniz Laboratory
pepper pot (3x3 pinhole array)
laser accelerated ion
permanent magnet Quadrupole
arbitrary units
Laboratory for extreme photonics
without background subtraction; parameter for PN calculation
with background subctraction; parameter for PN calculation
photon stimulated luminescence
Data Tables
Table B.1.:
QP energy [MeV] 7
drift 1 [mm]
33.783
19.644
drift 2 [mm]
Used Drift lengths in the QP setup
8
9
10
36.580 39.211 41.700
22.735 25.684 28.512
Table B.2.: Calculated P N s/106 for all shots and methods. ”whole” indicates
the sum over all particles on the IP.
method bg whole bg, g-focus bg, d-focus nobg whole nobg, g-focus nobg, d-focus
shot 12
3.43
1.07
0.691
3.40
1.02
0.691
shot 91
62.6
1.41
2.68
9.62
0.884
1.09
shot 116
37.2
3.66
2.24
17.5
3.44
2.06
shot 129
42.2
1.31
1.43
5.21
0.877
0.675
shot 213
3.90
0.133
0.361
0.814
0.0963
0.21
shot 217
1.05
0.0486
0.0968
0.408
0.0405
0.0658
shot 220
46.4
2.65
1.63
1.63
2.27
1.09
Table B.3.: Calculated mean P N s/106 and PSL reduction factors from first
to last scan ”whole” indicates the sum over all particles on the
IP.
whole mean focus mean PSL red. fact.
shot12
3.43
8.77
27
shot 91
31.4
1.47
40
shot 116
25.9
2.88
64
shot 129
20.1
1.04
31
shot 213
1.99
0.198
3.1
shot 217
0.631
0.0608
3.1
shot 220
26.3
1.89
48.8
48
B. Data Tables
Table B.4.: Dose transmitted to the volume underlying the focus area for all
shots in both focus definitions
g-focus dose[Gy] d-focus dose [Gy]
shot12
217
143
shot 91
238
435
shot 116
685
424
shot 129
226
247
shot 213
29
75
shot 217
10
19
shot 220
540
337
Overview of Codes
StartSpectraCalculation.m
IPReader2.m
This program was written by Florian Lindner, it uses
particle tracking, to calculate the deflection of a protons or carbon ions in the measured magnetic field of
the dipole used in the experiment described in 3.2. It
yields a two dimensional mesh, of datapoints with the
positions of particles of different energies and transverse entrance positions.
This code was implemented in the scope this work,
starting from IPReader.m. It takes ’.img’ files of different scans, produced by the IP scanner and the
energy of the detected particles as input parameters
and calculates a particle number map. The calculation of the reduction factor between the different
scans is optional. If it is not calculated, it has to
be provided manually. In the latter case, the last
scan ’.img’ file has to be selected. In the first case,
the first scan ’.img’. It also has the option to select a rectangle, that is defined as background signal
and subtracted. It was used in all particle number
calculations described in this work. The programm
uses the scripts ’img2PSL.m’, ’comparePSL.m’
and ’subtract0.m’. They are all located in the
folder ’Y:/project/agschreiber/Derya.Taray/IP analysis/IPReader2’ and only work if they are located in
the same folder. It writes out the PN and dose map
as a ’.txt.’ files. The ’.txt’ files contain an array with
the particles or Gy per pixel. Further explanations
can be found in the comments of the code itself.
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Danksagung
Zuerst gilt mein Dank Prof. Jörg Schreiber, der mir mit seinem Seminar einen ersten
Einblick in das Forschungsgebiet von Laser Plasma Interaktion gab und anbot, meine
Bachelorarbeit in seiner Gruppe zu schreiben.
Außerdem möchte ich mich bei meinem Betreuer Thomas Rösch bedanken. Er half mir
bei Fragen in allen Bereichen mit viel Geduld und gab mir die Möglichkeit am Tandem
Experiment teilzunehmen. Diese Erfahrung sehe ich als einen wertvollen Teil meiner
Bachelorarbeit an.
Des Weiteren möchte ich mich bei der ganzen Gruppe bedanken, die mich immer unterstützte und mir stets das Gefühl gab willkommen zu sein.
Erklärung
Hiermit erkläre ich, die vorliegende Arbeit selbständig verfasst zu haben und keine anderen als die in der Arbeit angegebenen Quellen und Hilfsmittel benutzt zu haben.
Derya Taray , München den 14.07.2017