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Magnetische Quadrupole und Solenoide sind ein elementarer Bestandteil einer Beschleunigeranlage und begrenzen die transversale Ausdehnung eines Teilchenstrahls durch eine Reflexion der Teilchen in Richtung der Beschleunigerachse. Die konventionelle Bauweise als Elektromagnet besteht aus einem Eisenjoch welches mit Spulen umwickelt ist. In dieser Arbeit werden diese Magnetstrukturen auf Basis von Permanentmagneten designt und hinsichtlich ihrer Qualität zum Strahltransport optimiert, sowie Feldmessungen an permanentmagnetischen Quadrupolen durchgeführt. Diese wurden mit 3D-gedruckten Halterungen aus Kunststoff gefertigt, was eine Vielzahl von Formvariationen ermöglicht. Darauf aufbauend wurde ein im Vakuum befindlicher Aufbau entwickelt, mit welchem die Strahlenvelope im inneren eines permanentmagnetischen Quadrupol Tripletts diagnostiziert werden kann. Dies greift auf ein am Institut für angewandte Physik entwickeltes System zur nicht-invasiven Strahldiagnose mithilfe von Raspberry Pi Einplatinencomputern und Kameras in starken Magnetfeldern zurück.
Die in dieser Arbeit vorgestellte Konfiguration eines PMQ’s ist eine Weiterentwicklung des am CERN im Linac4, einem Alvarez-Driftröhrenbeschleuniger zur Beschleunigung von H– , verwendeten Designs. Bei diesem sind je acht quaderförmige Permanentmagnete aus Samarium Cobalt (SmCo) in die Driftröhren des Beschleunigers integriert.
Darauf aufbauend wurden die geometrischen Designparameter hinsichtlich ihres Einflusses auf die Qualität des Magnetfelds untersucht. In einem magnetischen Quadrupol zur Strahlfokussierung wird dies durch einen linearen Anstieg des Magnetfeldes von Quadrupolachse zu Polflächen charakterisiert. Das Design wurde im Zuge dessen zur Verwendung von industriellen Standardgeometrien von Quadermagneten und der Erhöhung der magnetischen Flussdichte erweitert. Dazu wurde untersucht wie sich das Hinzufügen von zusätzlichen Magneten auswirkt und ob eine bessere Feldqualität durch andere Magnetformen erreicht wird.
Die Kombination mehrerer PMQ in geringem Abstand (<10 mm) führt abhängig von der Geometrie der PMQ-Singlets zu einer erheblichen Verschlechterung der Feldlinearität, was eine Erhöhung des besetzten Phasenraumvolumens der Teilchen nach sich zieht.
Am Beispiel von PMQ-Tripletts werden die zu beachtenden Designparameter analysiert und Lösungsansätze vorgestellt. Die auftretenden Effekte werden anhand von Strahldynamiksimulation veranschaulicht. Für eine Anwendung der vorgestellten Designs wurde eine Magnethülle mit einer Wabenstruktur zur Aufnahme der Einzelmagnete entwickelt. Diese besteht aus zwei Halbschalen, welche jeweils den Kompletteinschluss aller Magnete garantiert und eine einfache Montage um ein Strahlrohr ermöglicht. Diese wurden in der Institutswerkstatt aus Kunststoff via 3D-Druck gefertigt. Aufgrund der höheren erreichbaren Magnetisierung wurden Neodym-Eisen-Bor-Magnete (Nd2F14B, Br =1,36 T) für den Bau der entwickelten Strukturen verwendet. Für eine Magnetfeldmessung zur Bestätigung der magnetostatischen Simulationen und einer Bewertung der Druckqualität wurde eine motorisierte xyz-Stage zur Bewegung einer Hallsonde aufgebaut. Die Messungen zeigen eine gute Zentrierung des Magnetfeldes, sodass PMQ mit einer Kunststoffhalterung eine schnelle und billige Möglichkeit sind, kurzfristig eine Quadrupol-Konfiguration aufzubauen. Die Kosten belaufen sich für einen einzelnen PMQ je nach Länge auf 50€ bis 100€.
Basierend auf der PMQ-Struktur wurde ein PMQ-Triplett in ein Vakuum versetzt und mit Raspberry Pi Kameras im Zwischenraum der Singlets ausgestattet. Dies ermöglichte die Aufnahme der Strahlenvelope innerhalb des Tripletts anhand der durch einen Heliumstrahl induzierten Fluoreszenz und erste Erkenntnisse für notwendige Weiterentwicklungen wurden gesammelt. Auf den genauen technischen Aufbau wird im abschließenden Kapitel der Arbeit detailliert eingegangen.
In der einfachsten Form wird ein PM-Solenoid anhand eines einzelnen axial magnetisierten Hohlzylinders realisiert und erzeugt näherungsweise die Feldverteilung einer Zylinderspule. Durch die radialen Magnetfeldkomponenten an den Rändern des Solenoiden erhalten Teilchen eine tangentiale Geschwindigkeitskomponente und führen eine Gyrationsbewegung entlang der Solenoidachse aus. Diese reduziert den Strahlradius und die Teilchen behalten eine Geschwindigkeitskomponente, welche zur Solenoidachse zeigt. Für eine Maximierung dieser Fokussierung muss das Magnetfeld auf die Zylinderachse konzentriert werden. Insbesondere bei einer Verlängerung des Hohlzylinders wird die Kopplung der Polflächen über das Innenvolumen abgeschwächt. Aufgrund dessen wurde ein Design bestehend aus drei Hohlzylindersegmenten entwickelt. Dieses setzt sich aus zwei radial und einem axial magnetisierten Hohlzylinder zusammen und erhöht die mittlere magnetische Flussdichte für ausgewählte Geometrien um einen Faktor zwei im Vergleich zu einem einzelnen Hohlzylinder gleicher Geometrie. Dies ist gleichzusetzen mit einer Vervierfachung der Fokussierstärke, welche quadratisch mit der mittleren magnetischen Flussdichte skaliert. Die Strahldynamischen Konsequenzen werden anhand von Simulationen mit generierten Magnetfeldverteilungen erläutert. Für eine kostengünstige Bauweise wurde eine Design basierend auf quaderförmigen Magneten entwickelt.
Investigation of the kinematics involved in compton scattering and hard X-ray photoabsorption
(2023)
The present work investigates the kinematics of Compton scattering at gaseous, internally-cool helium and molecular nitrogen targets in the high- and the low-energy regime. Additionally, photoionization at molecular nitrogen with high-energy photons is investigated. These exeprimental regimes were previously inaccessible due to the extremely small cross sections involved. Nowadays, the third- and fourth-generation synchrotron machines produce sufficient photon flux, enabling the investiagtion of the above processes. The utilized cold-target recoil-ion momentum spectroscopy (COLTRIMS) technique further increases the detection efficiency of the observed processes, since it enables full-solid-angle detection by exploiting momentum conservation.
Compton scattering is investigated at both high (helium and N2) and low (helium) photon energies. In the high-energy regime, the impulse approximation is mostly valid, which is not the case for the low-energy regime. The impulse approximation assumes that the Compton-scattering process takes place at a free electron with a momentum distribution as if it was bound, thus ignoring the binding energy of the system. In the low-energy regime, the impulse approximation is not valid.
Photoionization is investigated at high photon energies, where the linear momentum of the photon cannot be neglected, as is the fashion of the commonly used dipole approximation.
This thesis deals with several aspects of non-perturbative calculations in low-dimensional quantum field theories. It is split into two main parts:
The first part focuses on method development and testing. Using exactly integrable QFTs in zero spacetime dimensions as toy models, the need for non-perturbative methods in QFT is demonstrated. In particular, we focus on the functional renormalization group (FRG) as a non-perturbative exact method and present a novel fluid-dynamic reformulation of certain FRG flow equations. This framework and the application of numerical schemes from the field of computational fluid dynamics (CFD) to the FRG is tested and benchmarked against exact results for correlation functions. We also draw several conclusions for the qualitative understanding and interpretation of renormalization group (RG) flows from this fluid-dynamic reformulation and discuss the generalization of our findings to realistic higher-dimensional QFTs.
The topics discussed in the second part are also manifold. In general, the second part of this thesis deals with the Gross-Neveu (GN) model, which is a prototype of a relativistic QFT. Even though being a model in two spacetime dimensions, it shares many features of realistic models and theories for high-energy particle physics, but also emerges as a limiting case from systems in solid state physics. Especially, it is interesting to study the model at non-vanishing temperatures and densities, thus, its thermodynamic properties and phase structure.
First, we use this model to test and apply our findings of the first part of this thesis in a realistic environment. We analyze how the fluid-dynamic aspects of the FRG realize themselves in the RG flow of a full-fledged QFT and how we profit from this numeric framework in actual calculations. Thereby, however, we also aim at answering a long-standing question: Is there still symmetry breaking and condensation at non-zero temperatures in the GN model, if one relaxes the commonly used approximation of an infinite number of fermion species and works with a finite number of fermions? In short: Is matter (in the GN model) in a single spatial dimension at non-zero temperature always gas-like?
In general, we also use the GN model to learn about the correct description of QFTs at non-zero temperatures and densities. This is of utmost relevance for model calculations in low-energy quan- tum chromodynamics (QCD) or other QFTs in medium and we draw several conclusions for the requirements for stable calculations at non-zero chemical potential.
The Compressed Baryonic Matter (CBM) is one of the core experiments at the future Facility for Anti-proton and Ion Research (FAIR), Darmstadt, Germany. Its goal is to investigate nuclear matter characteristics at high net-baryon densities and moderate temperatures. The Silicon Tracking System (STS) is a central detector system of CBM.
It is placed inside a 1Tm magnet and operated at a temperature of about −10 °C to keep radiation-induced bulk current in the 300μm double-sided microstrip silicon sensors low. The design of the STS aims to minimize the material budget in the detector acceptance (2.5° < θ < 25°). In order to do so, the readout electronics is placed outside the active area, and the analog signals are transported via ultra-thin micro-cables. The STS comprises eight tracking stations with 876 modules. Each module is assembled on a carbon fiber ladder, which is subsequently mounted in the C-shaped aluminum frame.
The scope of the thesis focused on developing a modular control system framework that can be implemented for different sizes of experimental setups. The developed framework was used for setups that required a remote operation, like the irradiation of the powering modules for the front-end electronics (FEE), but also in laboratory-based setups where the automation and archiving were needed (thermal cycling of the STS electronics).
The low voltage powering modules will be placed in the vicinity of the experiment, therefore they will experience a total dose of up to 40mGy over the 10 years of STS lifetime.
To estimate the effects of the radiation on the low-voltage module performance, a dedicated irradiation campaign took place. It aimed at estimating the rate of radiation induced soft errors, that lead to the switch off of the FEE.
Regular power cycles of multiple front-end boards (FEBs) pose a risk to the experiment operation. Firstly, such behavior could negatively influence the physics performance but also have deteriorating effects on the hardware. It was further assessed what are the limitations of the FEBs with respect to the thermal cycling and the mechanical stress. The results served as an indication of possible failure modes of the FEB at the end of STS lifetime. Failure modes after repeated cycles and potential reasons were determined (e.g., Coefficient of Thermal Expansion (CTE) difference between the materials).
Due to the conditions inside the STS efficient temperature and humidity monitoring and control are required to avoid icing or water condensation on the electronics or silicon sensors. The most important properties of a suitable sensor candidate are resilience to the magnetic field, ionizing radiation tolerance, and fairly small size.
A general strategy for ambient parameters monitoring inside the STS was developed, and potential sensor candidates were chosen. To characterize the chosen relative humidity sensors the developed control framework was introduced. A sampling system with a ceramic sensor and Fiber Optic Sensors (FOS) were identified as reliable solutions for the distributed sensing system. Additionally, the industrial capacitive sensors will be used as a reference during the commissioning.
Two different designs of FOS were tested: a hygrometer and 5 sensors multiplexed in an array. The FOS hygrometer turned out to be a more reliable solution. One of the possible reasons for a worse performance is a relatively low distance between the subsequent sensors (15 cm) and a thicker coating. The results obtained from the time response study pointed out that the thinner coating of about 15μm should be a good compromise between the humidity sensitivity and the time response.
The implementation of the containerized-based control system framework for the mSTS is described in detail. The deployed EPICS-based framework proved to be a reliable solution and ensured the safety of the detector for almost 1.5 years. Moreover, the data related to the performance of the detector modules were analyzed and significant progress in the quality of modules was noted. Obtained data was also used to estimate the total fluence, which was based on the leakage current changes.
The developed framework provided a unique opportunity to automate and control different experimental setups which provided crucial data for the STS. Furthermore, the work underlines the importance of such a system and outlines the next steps toward the realization of a reliable Detector Control System for STS.
This thesis is concerned with the investigation of static and dynamic properties of quantum Heisenberg paramagnets in the absence of a magnetic field and therefore for vanishing magnetization. For this purpose a new formulation of the spin functional renormalization group (SFRG) is employed. The first manifestations of the SFRG were developed by Krieg and Kopietz, motivated by the FRG approach to ordinary field theories and the older works of Vaks, Larkin and Pikin on diagrammatic methods for spin operators.
The main idea is to study quantum spin systems by considering the evolution of correlation functions under a continuous deformation of the interaction between magnetic moments, starting from a solvable limit. This leads to nonperturbative results for quantities like the spin-spin correlation function. After a basic introduction to the phenomena and concomitant problems discussed in this thesis, a detailed description of the SFRG method in its initial formulation is given in the second chapter. We start with the generating functional of connected imaginary-time spin-correlation functions GΛ [h], for which an exact flow equation is derived. A particular issue, already pointed out by Krieg and Kopietz, arises here, namely the singular non-interacting limit of its subtracted Legendre transform ΓΛ [m]. As a consequence the initial condition of that functional does not have a proper series expansion in powers of m. This prevents us from working directly within a pure one-particle irreducible (1-PI) parametrization of the correlation functions, as is often done in the context of field theories. Thus motivated, we develop a workaround explicitly tailored to paramagnets, which provides us with a functional that has a well-behaved Legendre transform. The new approach is based on a different treatment of fluctuations at zero and finite frequencies, analogous to a previous hybrid formulation for the symmetry-broken phase. Certain properties, considered to be highly relevant for isotropic paramagnets, as well as previous observations, already made in the study of simpler spin systems like the Ising model, serve as additional justifications for choosing this construction.
In the third chapter our new method is assessed by calculating the dynamic susceptibility G(k, iω) and thus the dynamic structure factor S(k, ω) in the symmetric phase. For this purpose an approximate integral equation for the dynamic polarization function Π̃(k, iω) was derived. This equation results from a truncation of the hierarchy of flow equations and contains static quantities, that are assumed to be known from another source. Our first application is the high-temperature limit T → ∞ in d ≤ 3 dimensions. Salient features, believed to be part of the spin dynamics in isotropic Heisenberg magnets are also exhibited by our solution, like (anomalous) diffusion in a suitable hydrodynamic limit. Moreover we obtain the same order of magnitude for the diffusion coefficient D as in experiments and other theoretical calculations. Other aspects do not entirely agree with previous approaches.
Afterwards we continue by investigating systems close to the critical point Tc. Dynamic scaling forms for Π̃(k, iω) and S(k, ω), which, like spin diffusion, are postulated on the basis of quite general physical arguments, are reproduced. Agreement of the line-shapes 2with neutron scattering experiments at T = Tc is found to be satisfying, with deviations for ω → 0, that may be attributed to the simplicity of the approximation, like at infinite temperature.
Finally, we focus our attention on the thermodynamic properties of isotropic Heisenberg paramagnets by calculating the static susceptibility G(k). For this purpose we employ simple truncation schemes of the flow equations for the static self-energy ΣΛ (k) and four-spin vertex ΓΛ , together with a basic ansatz for the dynamic polarization Π̃(k, iω) in quantum systems. As a result we obtain transition temperatures Tc of three-dimensional nonfrustrated magnets within an accuracy of 5 percent compared to established benchmark values from Quantum Monte Carlo and high temperature expansion series. We conclude this chapter by giving an outlook on the application of our method to frustrated systems, which may require a combined non-trivial calculation of static and dynamic properties.
The main focus of this thesis is the application of the nonperturbative Functional Renormalization Group (FRG) to the study of low-energies effective models for Quantum Chromodynamics (QCD). The study of effective field theories and models is crucial for our understanding of physics, especially when we deal with fundamental interaction theories like QCD. In particular, the ultimate goal is the understanding of the critical properties of these models in such a way that we can have an insight on the actual critical phenomena of QCD, with a special focus on its chiral phase transition. The choice of the FRG method derives from the fact that it belongs to the class of functional non-perturbative methods and has also the advantage of linking physics at different energy scales. These features make FRG perfectly compatible with the task of studying non-perturbative phenomena and in particular phase transitions, like the ones expected for strongly interacting matter. However, the functional nature of the FRG approach and of the Wetterich equation has a consequence that its exact resolution is hardly possible, and an ansatz for the effective action is generally needed. In this work we choose to adopt the local-potential approximation (LPA), which prescribes to stop at zeroth order in the expansion in derivative operators of the quantum effective action, including only the quantum effective potential. In this work we exploited the key observation that the FRG flow equation can be cast, for specific models and truncation schemes, in the form of an advection-diffusion, possibly with a source term. This type of equation belongs to the class of problems faced in the context of viscous hydrodynamics. Therefore, an innovative approach to the solution of the FRG flow equation consists in the choice of a method developed specifically for the resolution of this class of hydrodynamic equations. In particular, the Kurganov-Tadmor finite-volume scheme is adopted. Throughout this work we apply this scheme to the study of different physical systems, showing the reliability and the flexibility of this approach.
In the first part of the thesis, we discuss the well-known O(N) model, using the hydrodynamic formulation to solve the FRG flow equation in the LPA truncation. We focus on the study of the critical behaviour of the system and calculate the corresponding critical exponents. Particular attention is given to the error estimation in the extraction of critical exponents, which is a needed and not widely explored aspect. The results are well compatible with others in the literature, obtained with different perturbative and nonperturbative methods, which validates the procedure. In the second part of the thesis, we introduce the quark-meson model as a low-energy effective model for QCD, with a specific focus on its chiral symmetry-breaking pattern and the subsequent dynamical quark-mass generation. The LPA flow equation is of the advection-diffusion type, with an extra source contribution which is due to the inclusion of fermionic degrees of freedom. We thus adopt the developed numerical techniques to derive the phase diagram of the model, which is in agreement with the one obtained with other techniques in the literature.
We also follow another possible way for the study of the critical properties of the quark-meson model: the so-called thermodynamic geometry. This approach is based on the interpretation of the parameter space of the system as a differential manifold. One can then obtain relevant information about the phase transitions from the Ricci scalar. We studied the chiral crossover investigating the behavior of the Ricci scalar up to the critical point, featuring a peaking behavior in the presence of the crossover. We then repeated this analysis in the chiral limit, where the phase transition is expected to be of second order. Via this geometric technique it is possible to have a different view on the chiral phase transition of QCD. This is the case since this approach is based on the calculation of quantities which are influenced by higher-order momenta of the thermodynamic potential, thus allowing for a more comprehensive analysis of the phase transition.
Finally, we exploit the numerical advancement to face the issue of the regulator choice in the FRG calculations. This is one of the most delicate issues which arise when using approximations to solve the FRG flow equation and deserves extensive investigation. In particular, we performed a vacuum parameter study and used the RG consistency requirement to determine the impact of the choice of the regulator on the physical observables and on the phase diagram of the model. Via this study we develop a systematic method to comparison the results obtained via different regulators. We show the importance of the choice of an appropriate UV cutoff in the determination of UV-independent IR observables and, consequently, the impact on the latter that the truncation of the effective average action and the choice of the regulator have.
Die Arbeit behandelt die Messung von Photonen mit Teilchendetektoren, die auf digitalen Silizium-Pixelsensoren basieren. Diskutiert werden zwei wesentliche Schritte in den Upgrade-Programmen des ALICE-Experiments am CERN-LHC:
1. FOCAL-Detektor-Upgrade (2027): Untersuchung der Detektorantwort des elektromagnetischen Pixel-Kalorimeters EPICAL-2 und der Form elektromagnetischer Schauer durch Teststrahl-Messungen und Monte Carlo Simulationen.
2. ALICE 3-Upgrade (2035): Simulationsstudien zum Untergrund in der Messung von Photonen mit sehr kleinem Transversalimpuls.
Teil 1: Performance des elektromagnetischen Pixel-Kalorimeters EPICAL-2
Detektordesign und Testmessungen: EPICAL-2, ein SiW-Sandwich-Design-Kalorimeter mit ALPIDE Sensoren, besitzt eine Tiefe von ca. 20 Strahlungslängen und etwa 25 Millionen Pixel. Testmessungen wurden an der Universität Utrecht (kosmische Myonen) sowie am DESY und CERN-SPS (Elektronen) durchgeführt.
Simulation und Validierung: Das EPICAL-2 wird im Simulationspaket Allpix2 implementiert, um die Testmessungen zu validieren und das Detektorverhalten zu untersuchen. Systematische Variationen bestätigen die Stabilität und Reproduzierbarkeit der Simulation.
Datenaufbereitung und Schauerprofile: Im Rahmen der Datenanalyse werden fehlerhafte Pixel ausgeschlossen, Pixel-Treffer zu Clustern gruppiert, Chips kalibriert und der Strahlwinkel korrigiert. Das longitudinale Profil elektromagnetischer Schauer zeigt, dass das Schauermaximum in der Simulation etwas tiefer liegt als in den Testdaten, was auf zusätzliches Material oder eine unvollständige Beschreibung der Schauerentwicklung in der Simulation zurückzuführen sein könnte. Das laterale Profil zeigt, dass eine Schauertrennung im Millimeter-Bereich möglich ist.
Energieantwort und -auflösung: Die nicht-lineare Energieantwort wird sowohl in Testdaten als auch in Simulationen beobachtet. Die Energieauflösung des EPICAL-2 für Cluster ist besser als für Pixeltreffer und vergleichbar mit dem analogen CALICE-Prototypen. Simulationen ohne Strahlenergie-Fluktuationen zeigen eine bessere Energieauflösung als in den Testdaten.
Teil 2: Untergrund in der Messung von Photonen in ALICE 3
Simulationssetup: Die ALICE 3-Detektorgeometrie wird in GEANT4 implementiert, um den Untergrund in der Messung weicher Photonen zu untersuchen. Simulationen mit PYTHIA und GEANT4 zeigen, dass der Untergrund hauptsächlich aus Zerfallsphotonen und Photonen aus externer Bremsstrahlung besteht.
Ergebnisse der Untergrundstudien: Der Untergrund durch Photonen aus externer Bremsstrahlung dominiert und liegt im Akzeptanzbereich des FCT um einen Faktor von 5 bis 10 über dem theoretischen Signal weicher Photonen. In der Simulation wird das Material zu 8%—14% X0 in ALICE 3 bestimmt, wobei bereits bei 5% X0 der Untergrund genauso stark ist wie das erwartete Signal.
Möglichkeiten zur Untergrundreduzierung: Untersuchungen zeigen, dass ein Elektron-Veto das Signal-zu-Untergrund-Verhältnis um den Faktor 30 verbessern und eine Materialreduktion durch ein optimiertes Strahlrohr um den Faktor 7.
Die Ergebnisse des ersten Teils dieser Arbeit demonstrieren insgesamt die gute Performance des EPICAL-2 in Bezug auf die Energiemessung und die Bestimmung der Schauerform. Darüber hinaus unterstützen sie den Einsatz digitaler Kalorimeter im FOCAL-Upgrade des ALICE-Experiments und zeigen das Potenzial der digitalen Kalorimetertechnologie für zukünftige Hochenergiephysik-Experimente.
Die Ergebnisse des zweiten Teils dieser Arbeit liefern einen wesentliche Beitrag zum geplanten ALICE 3-Upgrade. Weiterhin veranschaulichen sie, wie ein Elektron-Veto und die Reduzierung des Materials zusammen eine vielversprechende Messstrategie bilden können.
Efficient modeling and mitigation of quadrupole errors in synchrotrons and their beam transfer lines
(2023)
This thesis investigates the problem of estimating quadrupole errors on synchrotrons as well as how to minimize the influence of quadrupole errors for beam transfer lines (beamlines). It emphasizes the importance to treat possible error sources in all parts of an accelerator in order to provide constantly high beam quality to the experimental stations. While the presented methods have been investigated by using the example of the SIS18 synchrotron and the HEST beamlines at GSI Helmholtz Centre for Heavy Ion Research, they are equally relevant for the future synchrotrons and beamlines of the Facility for Antiproton and Ion Research in Europe (FAIR).
Part 1 discusses the problem of estimating quadrupole errors via orbit response measurements at synchrotrons. An emphasis is put on investigating the influence of the availability of steerer magnets and beam position monitors (BPMs) on the solvability of the inverse problem as well as on the propagation of measurement uncertainty for the estimation of quadrupole errors. The problem is approached via analytical considerations as well as via dedicated simulation studies. By developing an analytical expression for the Jacobian matrix, the theoretical boundaries for the solvability of the inverse problem are derived. Moreover, it is shown that the analytical expressions for the Jacobian matrix can be used during the fitting procedure to achieve a significant improvement in the computational efficiency by a factor $N_{steerers} \times N_{quadrupoles}$, where $N$ denotes the number of lattice elements of the respective type. The presented results are tested via dedicated measurements at the SIS18 synchrotron.
Part 2 discusses – complementary to part 1 – the influence of quadrupole errors in beam transfer lines with respect to the beam quality requirements given by the experimental stations. A preventive approach is presented which allows to minimize the influence of possible quadrupole errors on the degradation of beam quality. By identifying and selecting robust quadrupole configurations, a stable operation of the beamline can be enabled and the time needed by operators to readjust the beamline parameters can be reduced. The concept of beamline robustness is developed and is studied with the help of dedicated simulations. The simulation results are used to identify certain properties that distinguish robust from nonrobust quadrupole configurations. Also, various methods for improving the computational process of identifying robust quadrupole configurations are presented. The methods and results are tested via dedicated measurements at two different beamlines at GSI Helmholtz Centre for Heavy Ion Research and at Forschungszentrum Jülich.
The theoretical and experimental investigation of exotic hadrons like tetraquarks is an important branch of modern elementary particle physics. In this thesis I investigate different four-quark systems using lattice QCD and search for evidence of stable tetraquark states or resonances.
Lattice QCD as a non-perturbative approach to QCD allows an accurate and reliable determination of the masses of strongly bound hadrons.
However, most tetraquarks appear as weakly bound states or resonances, which makes a theoretical investigation using lattice QCD difficult due to the finite spatial volume. A rigorous treatment of such systems is feasible using the so-called Lüscher method. This allows to calculate the scattering amplitude based on the finite-volume energy spectrum determined in a lattice QCD calculation. Similarly to the analysis of experimental data, this scattering amplitude can be used to determine the binding energies of bound states or the masses and decay widths of resonances in the infinite volume.
In my work I calculate the low-energy energy spectra of different four-quark systems and use - if necessary - the Lüscher method to determine the masses of potential tetraquark states.
I focus on systems consisting of two heavy antiquarks and two light quarks, where at least one of the heavy antiquarks is a bottom quark.
Even though such tetraquarks have not yet been experimentally detected, they are considered promising candidates for particles that are stable with respect to the strong interaction.
A decisive step for successfully calculating low-lying energy levels for such four-quark systems is a carefully chosen set of creation operators, which represent the physical states most accurately. In addition to operators that generate a local structure where all four quarks are located at the same space-time point, I also use so-called scattering operators that resemble two spatially separated mesons. These scattering operators turned out to be relevant for successfully determining the lowest energy levels and are therefore essential, especially if a Lüscher analysis is carried out.
In my work, I considered two different lattice setups to study the four-quark systems $\bar{b}\bar{b}ud$ with $I(J^P)=0(1^+) $, $\bar{b}\bar{b}us$ with $J^P=1^+ $ and $\bar{b}\bar{c}ud$ with $I(J^P)=0(0^+) $ and $I(J^P)=0(1^+) $ and to predict potential tetraquark states. In both setups, I considered scattering operators. While in the first setup I used them only as annihilation operators, in the second setup they were included both as creation and annihilation operators. Additionally, in the second lattice setup, I performed a simplified investigation of the $\bar{b}\bar{b}ud$ system with $I(J^P)=0(1^-) $, which is a potential candidate for a tetraquark resonance. The results of the investigation of the mentioned four-quark systems can be summarized as follows:
For the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^+) $ I found a deeply bound ground state slightly more than $ 100\,\textrm{MeV} $ below the lowest meson-meson threshold. The existence of a corresponding $\bar{b}\bar{b}ud$ tetraquark in the infinite volume was confirmed using a Lüscher analysis and possible systematic errors due to the use of lattice QCD were taken into account.
Similar results were obtained for the $ \bar{b}\bar{b}us $ four-quark system with $ J^P=1^+ $. Again, I found a ground state well below the lowest meson-meson threshold, but slightly weaker bound than for the $ \bar{b}\bar{b}ud $ system. Effects due to the finite volume turned out to be negligible for this system, as already predicted for the $ \bar{b}\bar{b}ud $ system. \item For the $ \bar{b}\bar{c}ud $ four-quark systems with $ (J^P)=0(0^+) $ and $ (J^P)=0(1^+) $ I was able to rule out the existence of a deeply bound tetraquark states based on the energy spectrum in the finite volume. However, by means of a scattering analysis using the Lüscher method, I found evidence a broad resonance for both channels.
In the case of the $ \bar{b}\bar{b}ud $ four-quark system with $ I(J^P)=0(1^-) $, I could neither confirm the existence of a resonance, nor rule out its existence with certainty.
In particular, my investigations showed that the results of the two different lattice simulations are consistent. The theoretical prediction of the bound tetraquark states $\bar{b}\bar{b}ud$ and $\bar{b}\bar{b}us$ as well as the tetraquark resonances in the $\bar{b}\bar{c}ud$ system in this work represent an important contribution to the future experimental search for exotic hadrons and can support the discovery of previously unobserved particles.
The equation of state (EoS) of matter at extremely high temperatures and densities is currently not fully understood, and remains a major challenge in the field of nuclear physics. Neutron stars harbor such extreme conditions and therefore serve as celestial laboratories for constraining the dense matter EoS. In this thesis, we present a novel algorithm that utilizes the idea of Bayesian analysis and the computational efficiency of neural networks to reconstruct the dense matter equation of state from mass-radius observations of neutron stars. We show that the results are compatible with those from earlier works based on conventional methods, and are in agreement with the limits on tidal deformabilities obtained from the gravitational wave event, GW170817. We also observe that the resulting squared speed of sound from the reconstructed EoS features a peak, indicating a likely convergence to the conformal limit at asymptotic densities, as expected from quantum chromodynamics. The novel algorithm can also be applied across various fields faced with computational challenges in solving inverse problems. We further examine the efficiency of deep learning methods for analyzing gravitational waves from compact binary coalescences in this thesis. In particular, we develop a deep learning classifier to segregate simulated gravitational wave data into three classes: signals from binary black hole mergers, signals from binary neutron star mergers, or white noise without any signals. A second deep learning algorithm allows for the regression of chirp mass and combined tidal deformability from simulated binary neutron star mergers. An accurate estimation of these parameters is crucial to constrain the underlying EoS. Lastly, we explore the effects of finite temperatures on the binary neutron star merger remnant from GW170817. Isentropic EoSs are used to infer the frequencies of the rigidly rotating remnant and are noted to be significantly lower compared to previous estimates from zero temperature EoSs. Overall, this thesis presents novel deep learning methods to constrain the neutron star EoS, which will prove useful in future, as more observational data is expected in the upcoming years.
Terahertz (THz) radiation lies between the micro and far-infrared range in the electromagnetic spectrum. Compared with microwave and millimeter waves, it has a larger signal bandwidth and extremely narrow antenna beam. Thus, it is easier to achieve high-resolution for imaging and detection applications. The unique properties, such as penetration for majority non-polar materials, non-ionizing characteristic and the spectral fingerprint of materials, makes THz imaging an appealing artifice in the military, biomedical, astronomical communications, and other areas. However, THz radiation’s current low power level and detection sensitivity block THz imaging system from including fewer optical elements than the visible or infrared range. This leads to imaging resolution, contrast, and imaging field of view degenerate and makes the aberration more serious. THz imaging based on the space Fourier spectrum detection is developed in this thesis to achieve high-quality imaging. The main concept of Fourier imaging is by recording the field distribution in the Fourier plane (focal plane) of the imaging system; the information of the target is obtained. The numerical processing method is needed to extract the amplitude and phase information of the imaged target. With additional process, three-dimensional (3D) information can be obtained based on the phase information. The novel recording and reconstructing ways of the Fourier imaging system enables it to have a higher resolution, better contrast, and broader field of view than conventional imaging systems such as microscopy and plane to plane telescopic imaging system.
The work presented in this thesis consists of two imaging systems, one is working at 300 GHz based on the fundamental heterodyne detection of the THz radiation, the other is operated at 600 GHz by utilizing the sub harmonic heterodyne detection technique. The realization and test of the heterodyne detection are based on the THz antenna-coupled field-effect transistor (TeraFET) detector developed by Dr. Alvydas Lisauskas. Both systems use two synchronized electronic multiplier chains to radiate the THz waves. One radiation works as the local oscillator (LO), the other works as illumination with a slight frequency shift, the radiations are mixed on the detector scanning in the Fourier plane to record the complex Fourier spectrum of the imaged target. The LO has the same frequency range as the illuminating radiation for fundamental heterodyne detection but half the frequency range for the sub-harmonic heterodyne detection. The 2-mm resolution, 60-dB contrast, and 5.5-cm diameter imaging area at 300 GHz and the of 500-μm resolution, 40-dB contrast, and 3.5-cm diameter imaging area at 600 GHz are achieved (the 300-GHz illuminating radiation has the approximate power of 600 μW , the 600-GHz illuminating radiation has the approximate power of 60 μW ).
The thesis consists of 6 parts. After the introduction, the second chapter expands on the topic of Fourier optics from a theoretical point of view and the simulations of the Fourier imaging system. First, the theory of the electromagnetic field propagation in free space and through an optical system are investigated to elicit the Fourier transform function of the imaging system. The simulation is used for theoretical considerations and the implementation of a Fourier optic script that allows for numerical investigations on reconstruction. The preliminary imaging field of view and resolution are also demonstrated. The third chapter describes the Fourier imaging system at 300 GHz based on the fundamental heterodyne detection, including the experimental setup, the 2D, and 3D imaging results. The following fourth chapter reports the integration of the TeraFET detector with two substrate lenses (one is a Si lens on the back-side Si substrate, the other is a wax/PTFE lens on the front side containing the bonding wires) for sub-harmonic heterodyne detection at 600 GHz. The characteristic of the wax/PTFE lens at THz range is presented. After that, the compared imaging results between the detector with and without the wax/PTFE lens are shown. The fifth chapter extends the demonstration on the lateral and depth resolution of the Fourier imaging system in detail and uses the experimental results at 600 GHz to validate the analytical predictions. The comparison of the resolution between the Fourier imaging system and the conventional microscopy system proves that the Fourier imaging system has better imaging quality under the same system configuration. The last chapter in this thesis concludes on the findings of the THz Fourier imaging and gives an outlook for the enhancement of the Fourier imaging system at THz range.
Precise intensity monitoring at CRYRING@ESR: on designing a Cryogenic Current Comparator for FAIR
(2023)
In the field of today’s beam intensity diagnostic there is a significant gap in the non-interceptive, calibrated measurement of the absolute intensity of continuous (unbunched) dc beams with current amplitudes below 1 μA. At the Facility for Antiproton and Ion Research (FAIR) low-intensity DC beams will occur during slow extraction from the synchrotrons as well as for coasting beams of highly-charged or exotic nuclei in the storage rings. The lack of adequate beam instrumentation limits the experimental program as well as the accuracy of experimental results.
The Cryogenic Current Comparator (CCC) can close the diagnostic gap with a high-precision dc current reading independent of ion-species and of beam parameters. However, the established detector design based on a core with high magnetic permeability and on a radial shield geometry has well-known weaknesses concerning magnetic shielding efficiency and intrinsic current noise. To eliminate these weaknesses, a novel coreless CCC with a co-axial shield was constructed and combined with a high-performance SQUID contributed by the Leibniz-Institute of Photonic Technology (Leibniz-IPHT Jena). The new axial CCC model was compared to a radial CCC with the established design provided by the Friedrich-Schiller-University Jena. According to numerical simulations prepared at TU Darmstadt and test measurements of the detectors in the laboratory, the new design offered a significant improvement of the shielding factor – from 75dB to 207dB at the required dimensions – and eliminated all noise contributions from the core material, promising an improved current resolution. Although the lower inductance of the pickup coil reduced the coupling to the beam significantly, the noise properties of the new CCC type were comparable to the classical version with a high-permeability core. However, the expected decrease of the low-frequency noise and thus an increase of the current resolution could not be observed at this stage of development.
Consequently, the classical CCC based on the radial shielding and high-permeability core had to be installed in CRYRING@ESR to provide best possible intensity measurements for the upcoming experimental campaign. In CRYRING the CCC was operated with beam currents between 1nA and 20μA and with different ion species (H, Ne, O, Pb, U). It was shown that the CCC provides a noise-limited current resolution of better than 3.2 nArms at a bandwidth of 200 kHz as well as a noise level below 40 pA/√Hz above 1 kHz. During the operation, the main noise sources of the accelerator environment had to be identified and suitable mitigation strategies were developed. Temperature and pressure fluctuations were suppressed with a newly-designed cryogenic support system based on a 70 l helium bath cryostat, developed and built in collaboration with the Institut für Luft- und Kältetechnik Dresden, in combination with a helium re-liquefier. The cryogenic operating time was restricted to around 7 days, which must be expanded significantly in the future. Digital filters were developed to remove the perturbations of the helium liquefier and of the neighboring dipole magnets. Given the promising results the CCC system can be considered as a prototype for future CCCs at FAIR.