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This thesis contains three theoretical works about certain aspects of the interplay of electronic correlations and topology in the Hubbard model.
In the first part of this thesis, the applicability of elementary band representations (EBRs) to diagnose interacting topological phases, that are protected by spatial symmetries and time-reversal-symmetry, in terms of their single-particle Matsubara Green’s functions is investigated. EBRs for the Matsubara Green’s function in the zero-temperature limit can be defined via the topological Hamiltonian. It is found that the Green’s function EBR classification can only change by (i) a gap closing in the spectral function at zero frequency, (ii) the Green’s function becoming singular i.e. having a zero eigenvalue at zero frequency or (iii) the Green’s function breaking a protecting symmetry. As an example, the use of the EBRs for Matsubara Green’s functions is demonstrated on the Su-Schriefer-Heeger model with exact diagonalization.
In the second part the Two-Particle Self-Consistent approach (TPSC) is extended to include spin-orbit coupling (SOC). Time-reversal symmetry, that is preserved in the presence of SOC, is used to derive new TPSC self-consistency equations including SOC. SOC breaks spin rotation symmetry which leads to a coupling of spin and charge channel. The local and constant TPSC vertex then consists of three spin vertices and one charge vertex. As a test case to study the interplay of Hubbard interaction and SOC, the Kane-Mele-Hubbard model is studied. The antiferromagnetic spin fluctuations are the leading instability which confirms that the Kane-Mele-Hubbard model is an XY antiferromagnet at zero temperature. Mixed spin-charge fluctuations are found to be small. Moreover, it is found that the transversal spin vertices are more strongly renormalized than the longitudinal spin vertex, SOC leads to a decrease of antiferromagnetic spin fluctuations and the self-energy shows dispersion and sharp features in momentum space close to the phase transition.
In the third part TPSC with SOC is used to calculate the spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature. The spin Hall conductivity is calculated once using the conductivity bubble and once including vertex corrections. Vertex corrections for the spin Hall conductivity within TPSC corresponds to the analogues of the Maki-Thompson contributions which physically correspond to the excitation and reabsorption of a spin, a charge or a mixed spin-charge excitation by an electron. At all temperatures, the vertex corrections show a large contribution in the vicinity of the phase transition to the XY antiferromagnet where antiferromagnetic spin fluctuations are large. It is found that vertex corrections are crucial to recover the quantized value of −2e^2/h in the zero-temperature limit. Further, at non-zero temperature, increasing the Hubbard interaction leads to a decrease of the spin Hall conductivity. The results indicate that scattering of electrons off antiferromagnetic spin fluctuations renormalize the band gap. Decreasing the gap can be interpreted as an effective increase of temperature leading to a decrease of the spin Hall conductivity.
A powerful technique to distinguish the enantiomers of a chiral molecule is the Coulomb Explosion Imaging (CEI). This technique allows us to determine the handedness of a single molecule. In CEI, the molecule becomes charged by losing many electrons in a very short period of time by interacting with the light. The repulsion forces between the positive charged particles of the molecule leads the molecule to break into parts-fragments. By measuring the three vector momentum of (at least) four fragments, the handedness observable can be determined. In this thesis, CEI is induced by absorption of a single high energy photon, which creates an inner-shell hole (K shell) of the molecule. The subsequent cascade of Auger decays lead to fragmentation. We decided to work with the formic acid molecule in this thesis. Two different experiments were conducted. The first experiment focused on exciting electrons to different energy states, while the second experiment focused on extracting directly a photoelectron to the continuum and measure the angular distribution of the photoelectron in the molecular frame. The primary goal was to search for chiral signal in a pure achiral planar molecule under the previous electron processes. The results of these findings were further implemented to two more molecules.
The strong force is one of the four fundamental interactions, and the theory of it is called Quantum Chromodynamics (QCD). A many-body system of strongly interacting particles (QCD matter) can exist in different phases depending on temperature (T) and baryonic chemical potential (µB). The phases and transitions between them can be visualized as µB−T phase diagram. Extraction of the properties of the QCD matter, such as compressibility, viscosity and various susceptibilities, and its Equation of State (EoS) is an important aspect of the QCD matter study. In the region of near-zero baryonic chemical potential and low temperatures the QCD matter degrees of freedom are hadrons, in which quarks and gluons are confined, while at higher temperatures partonic (quarks and gluons) degrees of freedom dominate. This partonic (deconfined) state is called quark-gluon plasma (QGP) and is intensively studied at CERN and BNL. According to lattice QCD calculations at µB=0 the transition to QGP is smooth (cross-over) and takes place at T≈156 MeV. The region of the QCD phase diagram, where matter is compressed to densities of a few times normal nuclear density (µB of several hundreds MeV), is not accessible for the current lattice QCD calculations, and is a subject of intensive research. Some phenomenological models predict a first order phase transition between hadronic and partonic phases in the region of T≲100 MeV and µB≳500 MeV. Search for signs of a possible phase transition and a critical point or clarifying whether the smooth cross-over is continuing in this region are the main goals of the near future explorations of the QCD phase diagram.
In the laboratory a scan of the QCD phase diagram can be performed via heavy-ion collisions. The region of the QCD phase diagram at T≳150 MeV and µB≈0 is accessible in collisions at LHC energies (√sNN of several TeV), while the region of T≲100 MeV and µB≳500 MeV can be studied with collisions at √sNN of a few GeV. The QCD matter created in the overlap region of colliding nuclei (fireball) is rapidly expanding during the collision evolution. In the fireball there are strong temperature and pressure gradients, extreme electromagnetic fields and an exchange of angular momentum and spin between the system constituents. These effects result in various collective phenomena. Pressure gradients and the scattering of particles, together with the initial spatial anisotropy of the density distribution in the fireball, form an anisotropic flow - a momentum (azimuthal) anisotropy in the emission of produced particles. The correlation of particle spin with the angular momentum of colliding nuclei leads to a global polarization of particles. A strong initial magnetic field in the fireball results in a charge dependence and particle-antiparticle difference of flow and polarization.
Anisotropic flow is quantified by the coefficients vₙ from a Fourier decomposition of the azimuthal angle distribution of emitted particles relative to the reaction plane spanned by beam axis and impact parameter direction. The first harmonic coefficient v₁ quantifies the directed flow - preferential particle emission either along or opposite to the impact parameter direction. The v₁ is driven by pressure gradients in the fireball and thus probes the compressibility of the QCD matter. The change of the sign of v₁ at √sNN of several GeV is attributed to a softening of the EoS during the expansion, and thus can be an evidence of the first order phase transition. The global polarization coefficient PH is an average value of the hyperon’s spin projection on the direction of the angular momentum of the colliding system. It probes the dynamics of the QCD matter, such as vorticity, and can shed light on the mechanism of orbital momentum transfer into the spin of produced particles.
In collisions at √sNN of several GeV, which probe the region of the QCD phase diagram at T≲100 MeV and µB≳500 MeV, hadron production is dominated by u and d quarks. Hadrons with strange quarks are produced near the threshold, what makes their yields and dynamics sensitive to the density of the fireball. Thus measurement of flow and polarization, in particular of (multi-)strange particles, provides experimental constraints on the EoS, that allows to extract transport coefficients of the QCD matter from comparison of data with theoretical model calculations of heavy-ion collisions.
For continuation of the annotation see the PDF of thesis
Im Rahmen dieser Doktorarbeit werden drei Schwerpunkte behandelt: 1) Die hocheffektive Beschleunigung von Elektronen und Protonen durch die Wechselwirkung von relativistischen Laserpulsen mit Schäumen. 2) Die Erzeugung und Messung hochintensiver Betatronstrahlung von direkt laserbeschleunigten (DLA-) Elektronen. 3) Die Anwendung von DLA-Elektronen für den biologischen FLASH-Effekt mit einer rekordbrechenden Dosisrate.
Die direkte Laserbeschleunigung von Elektronen wurde durch die Wechselwirkung eines sub-ps-Laserpulses mit einer Intensität von ~ 10^19 W/cm^2 mit einem Plasma nahe kritischer Elektronendichte (NCD) untersucht. Ein sub-mm langes NCD-Plasma wurde durch Erhitzen eines Schaums mit einer niedrigen Dichte mit einem ns-Puls von 10^13-10^14 W/cm^2 erzeugt. Die Experimente wurden an der PHELIX-Anlage (Petawatt Hoch- Energie Laser für Schwerionenexperimente) in den Jahren 2019 – 2023 durchgeführt. Während der Suche nach optimalen Bedingungen für die Beschleunigung von Elektronen und Protonen wurden die Parameter des ns-Pulses variiert und verschiedene Targets verwendet. Es wurde gezeigt, dass das Plasma im Schaum gute Voraussetzungen für die Erzeugung gerichteter, ultrarelativistischer DLA-Elektronen mit Energien von bis zu 100 MeV bietet. Die Elektronen weisen eine Boltzmann-ähnliche Energieverteilung mit einer Temperatur von 10-20 MeV auf.
Optimale Bedingungen für eine effektive Beschleunigung von DLA-Elektronen wurden bei der Kombination eines CHO-Schaums mit einer Dichte von 2 mg/cm3 und einer Dicke von 300-500 µm mit einer Metallfolie erreicht. Die Gesamtladung der detektierten Elektronen mit Energien über 1,5 MeV erreichte 0,5-1 µC mit der Umwandlungseffizienz der Laserenergie von ~ 20-30%.
Außerdem wird die Beschleunigung von Protonen durch DLA-Elektronen anders verursacht als bei typischer Target Normal Sheath Acceleration (TNSA). Für die Untersuchung der lokalen Protonenenergieverteilung wurden Magnetspektrometer unter verschiedenen Winkeln zur Laserachse verwendet. Dafür wurde eine Filtermethode entwickelt, welche es ermöglicht, Spektren von Protonen mit Energien von bis zu 100 MeV zu rekonstruieren. Es wurde gezeigt, dass am PHELIX durch die Kombination von einem ~ 300-400 µm dicken CHO-Schaum mit einer Dichte von 2 mg/cm^3 und einer 10 µm dicken Au-Folie bei einer Intensität des sub-ps-Pulses von ~ 10^19 W/cm^2 und unter Verwendung eines optimierten ns-Vorpulses eine optimale Protonenbeschleunigung erreicht wurde. Es wurde ein TNSA-ähnliches Regime mit einer maximalen Cut-off-Energie von 34±0,5 MeV beobachtet. Im Vergleich dazu wurde bei der typischen TNSA unter Verwendung einer 10 µm dicken Au-Folie als Target und derselben Laserintensität eine maximale Cut-off-Energie von 24±0,5 MeV gemessen. Darüber hinaus beobachteten wir einen sehr schwachen Abfall der Protonenanzahl in Abhängigkeit von der Protonenenergie (anders als bei der typischen TNSA) und eine sehr regelmäßige Protonenstrahlverteilung in einem breiten Winkelbereich bis zu hohen Energien. Dies könnte zur Verbesserung der Qualität der Protonenradiographie von Plasmafeldern genutzt werden.
Beim DLA-Prozess (im NCD-Plasma) entsteht Betatronstrahlung durch die Oszillationen von Elektronen in quasi-statischen elektrischen und magnetischen Feldern des Plasmakanals. Um diese Strahlung zu untersuchen, wurde ein neues modifiziertes Magnetspektrometer (X-MS) konstruiert. Das X-MS ermöglicht die 1D-Auflösung mehrerer Quellen. Dank dieser Spezifikation war es möglich, Betatronstrahlung von Bremsstrahlung der ponderomotorischen Elektronen im Metallhalter zu trennen und zu messen.
Im Experiment mit einem CHO-Schaum mit einer Dichte von 2 mg/cm^3 und einer Dicke von ~ 800 µm als Target wurde die von den optimierten DLA-Elektronen erzeugte Betatronstrahlung gemessen. Bei einer Peak-Intensität des dreieckigen ns-Pulses von ~ 3·10^13 W/cm^2 und des sub-ps-Pulses von ~ 10^19 W/cm^2, welcher 4±0,5 ns gegenüber dem ns-Puls verzögert war, betrug der Halbwinkel im FWHM-Bereich des Elektronenstrahls 17±2°. Unter diesen Bedingungen war die Betatronstrahlung mit einem Halbwinkel im FWHM-Bereich von 11±2° für die Photonen mit Energien über 10 keV ebenfalls gerichtet. Die Photonenanzahl mit Energien über 10 keV wurde auf etwa 3·10^10 / 3·10^11 (gerichtete Photonen / Photonen im Halbraum entlang der Laserstrahlrichtung) abgeschätzt. Die maximale Photonenanzahl pro Raumwinkel betrug ~2·10^11 photons/sr. Die Brillanz der registrierten Betatronstrahlung erreichte ~ 2·10^20 photons/s/mm^2/mrad^2/(0.1% BW) bei 10 keV.
Die Verwendung eines Hochstromstrahls aus DLA-Elektronen für die FLASH-Strahlentherapie ermöglicht das Erreichen einer Dosis von bis zu 50-70 Gy während eines sub-ps-Laserpulses. Im Jahr 2021, während der P213-Strahlzeit am PHELIX wurde der Sauerstoffkonzentrationsabfall bei der Bestrahlung von Medien (Wasser und andere biologische Medien) mit DLA-Elektronen in Abhängigkeit von der Dosis untersucht. Die Strahlendosis wurde hierbei indirekt gemessen. Hierfür wurde eine Rekonstruktionsmethode entwickelt, die es ermöglicht, die Dosis innerhalb des „Wasser-Containers“ auf Basis von Messungen außerhalb des Containers mit einem untersuchten Medium zu ermitteln. Es wurde eine gute Übereinstimmung zwischen dem Experiment und einer Monte-Carlo-Simulation für Wasser gezeigt. Die registrierte Dosisrate erreichte einen Rekordwert von ~ 70 TGy/s.
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.
Artificial intelligence in heavy-ion collisions : bridging the gap between theory and experiments
(2023)
Artificial Intelligence (AI) methods are employed to study heavy-ion collisions at intermediate collision energies, where high baryon density and moderate temperature QCD matter is produced. The experimental measurements of various conventional observables such as collective flow, particle number fluctuations, etc. are usually compared with expensive model calculations to infer the physics governing the evolution of the matter produced in the collisions. Various experimental effects and processing algorithms can greatly affect the sensitivity of these observables. AI methods are used to bridge this gap between theory and experiments of heavy-ion collisions. The problems with conventional methods of analyzing experimental data are illustrated in a comparative study of the Glauber MC model and the UrQMD transport model. It is found that the centrality determination and the estimated fluctuations of the number of participant nucleons suffer from strong model dependencies for Au-Au collisions at 1.23 AGeV. This can bias the results of the experimental analysis if the number of participant nucleons used is not consistent throughout the analysis and in the final model-to-data comparison. The measurable consequences of this model dependence of the number of participant nucleons are also discussed. In this context, PointNet-based AI models are developed to accurately reconstruct the impact parameter or the number of participant nucleons in a collision event from the hits and/or reconstructed track of particles in 10 AGeV Au-Au collisions at the CBM experiment. In the last part of the thesis, different AI methods to study the equation of state (EoS) at high baryon densities are discussed. First, a Bayesian inference is performed to constrain the density dependence of the EoS from the available experimental measurements of elliptical flow and mean transverse kinetic energy of mid rapidity protons in intermediate energy collisions. The UrQMD model was augmented to include arbitrary potentials (or equivalently the EoSs) in the QMD part to provide a consistent treatment of the EoS throughout the evolution of the system. The experimental data constrain the posterior constructed for the EoS for densities up to four times saturation density. However, beyond three times saturation density, the shape of the posterior depends on the choice of observables used. There is a tension in the measurements at a collision energy of about 4 GeV. This could indicate large uncertainties in the measurements, or alternatively the inability of the underlying model to describe the observables with a given input EoS. Tighter constraints and fully conclusive statements on the EoS require accurate, high statistics data in the whole beam energy range of 2-10 GeV, which will hopefully be provided by the beam energy scan programme of STAR-FXT at RHIC, the upcoming CBM experiment at FAIR, and future experiments at HIAF and NICA. Finally, it is shown that the PointNet-based models can also be used to identify the equation of state in the CBM experiment. Despite the uncertainties due to limited detector acceptance and biases in the reconstruction algorithms, the PointNet-based models are able to learn the features that can accurately identify the underlying physics of the collision. The PointNet-based models are an ideal AI tool to study heavy-ion collisions, not only to identify the geometric event features, such as the impact parameter or the number of participant nucleons, but also to extract abstract physical features, such as the EoS, directly from the detector outputs.
A synchrotron is a particular type of cyclic particle accelerator and the first accelerator concept to enable the construction of large-scale facilities [10], such as the largest particle accelerator in the world, the 27-kilometre-circumference Large Hadron Collider (LHC) by CERN near Geneva, Switzerland, the European Synchrotron Radiation Facility (ESRF) in Grenoble, France for the synchrotron radiation, the superconducting, heavy ion synchrotron SIS100 under construction for the FAIR facility at GSI, Darmstadt, Germany and so on. Unlike a cyclotron, which can accelerate particles starting at low kinetic energy, a synchrotron needs a pre-acceleration facility to accelerate particles to an appropriate initial value before synchrotron injection. A pre-acceleration can be realized by a chain of other accelerator structures like a linac, a microtron in case of electrons, for example, Proton and ion injectors Linac 4 and Linac 3 for the LHC, UNLAC as the injector for the SIS18 in GSI and in future the SIS18 as injector for the SIS100. The linac is a commonly used injector for the ion synchrotron and consists of some key components. The three main parts of a linac are: An ion source creating the particles, a buncher system or an RFQ followed by the main drift tube accelerator DTL. In order to meet the energy and the beam current requirement of a synchrotron injector linac, its cost is a remarkable percentage of the total facility costs.
However, the normal conducting linac operation at cryogenic temperatures can be a promising solution in improving the efficiency and reducing the costs of a linac. Synchrotron injectors operate at very low duty factor with beam pulse lengths in 1 micros to 100 micros range, as most of the time is needed to perform the synchrotron cycle. Superconducting linacs are not convenient, as they cannot efficiently operate at low duty factor and high beam currents.
The cryogenic operation of ion linacs is discussed and investigated at IAP in Frankfurt since around 2012 [1, 37]. The motivation was to develop very compact synchrotron injectors at reduced overall linac costs per MV of acceleration voltage. As the needed beam currents for new facilities are increasing as well, the new technology will also allow an efficient realization of higher injector linac energies, which is needed in that case. Operating normal conducting structures at cryogenic temperature exploits the significantly higher conductivity of copper at temperatures of liquid nitrogen and below. On the other hand, the anomalous skin effect reduces the gain in shunt impedance quite a bit[25, 31, 9]. Some intense studies and experiments were performed recently, which are encouraging with respect to increased field levels at linac operation temperatures between 30 K and 70 K [17, 24, 4, 23, 5, 8]. While these studies are motivated by applications in electron acceleration at GHz-frequencies, the aim of this paper is to find applications in the 100 to 700 MHz range, typical for proton and ion acceleration. At these frequencies, a higher impact in saving RF power is expected due to the larger skin depth, which is proportional to the frequency to the power of negative half with respect to the normal skin effect. On the other hand, it is assumed that the improvement in maximum surface field levels will be similar to what was demonstrated already for electron accelerator cavities. This should allow to find a good compromise between reduced RF power needs for achieving a given accelerator voltage and a reduced total linac length to save building costs.
A very important point is the temperature stability of the cavity surface during the RF pulse. This is of increasing importance the lower the operating temperature is chosen: the temperature dependence of the electric conductivity in copper gets rather strong below 80 K, as long as the RRR - value of the copper is adequate. It is very clear, that this technology is suited for low duty cycle operated cavities only - with RF pulse lengths below one millisecond. At longer pulses the cavity surface will be heated within the pulse to temperatures, where the conductivity advantage is reduced substantially. These conditions fit very well to synchrotron injectors or to pulsed beam power applications.
H – Mode structures of the IH – and of the CH – type are well-known to have rather small cavity diameters at a given operating frequency. Moreover, they can achieve effective acceleration voltage gains above 10 MV/m even at low beam energies, and already at room temperature operation[29]. With the new techniques of 3d – printing of stainless steel and copper components one can reduce cavity sizes even further – making the realization of complex cooling channels much easier.
Another topic are copper components in superconducting cavities – like power couplers. It is of great importance to know exactly the thermal losses at these surfaces, which can’t be cooled efficiently in an easy way.
In this thesis, we use lattice QCD to study a part of the QCD phase diagram, specifically the QCD phase transition at mu=0, where the QCD matter changes from hadron gas to quark-gluon plasma (QGP) with increasing temperature.
This phase transition takes place as a crossover, but when theoretically changing the masses of the quarks, the order of the phase transition changes as well.
We focus on the region of heavy quark masses with Nf=2 flavours, where we investigate the critical quark mass at the second order phase transition in the form of a Z2 point between the first-order and the crossover region.
The first-order region is positioned at infinitely heavy quarks. As the quark masses decrease, the associated Z3 centre symmetry breaks explicitly, causing the first-order phase transition to weaken until it turns into the Z2 point and finally into a crossover.
We study this Z2 point using simulations at Nf=2 and lattices of the sizes Nt = {6, 8, 10, 12}, partially building on previous work, in which the simulations for Nt = {6, 8, 10} were started.
The simulations for Nt=12 are not finished yet though, but we were able to draw some preliminary conclusions. These simulations are run on GPUs and CPUs, using the codes Cl2QCD and open-QCD-FASTSUM, respectively. Afterwards, the data goes through a first analysis step in the form of the Python program PLASMA, preparing it for the two techniques we use to analyse the nature of the phase transition.
As a first, reliable analysis method, we perform a finite size scaling analysis of the data to find the location of the Z2 point. Since we are using lattice QCD, performing a continuum extrapolation is necessary to reach the continuum result.
In regard to this, the finite size scaling analysis method is hampered by the excessive amount of simulated data that is needed regarding statistics and the total number of simulations, which is why this thesis is only an intermediate step towards the continuum limit.
This also leads to the second analysis technique we explore in this thesis.
We start to design a Landau theory which describes the phase boundary for heavy masses at Nf=2 based on the simulated data.
We develop a Landau functional for every Nt we have simulation data for.
Albeit the results are not at the same precision as the ones from the finite size scaling analysis, we are able to reproduce the position of the Z2 point for every Nt.
Even though we are not able to take a continuum extrapolation right now, after more development takes place in future works, this approach might, in the long run, lead to a continuum result that won't need as many simulations as the finite size scaling analysis.
In the last twenty years, a variety of unexpected resonances had been observed within the charmonium mass region. Although the existence of unconventional states has been predicted by the quantum chromodynamics (QCD), a quantum field theory describing the strong force, a clear evidence was missing. The Y(4260) is such an unexpected and supernummerary state, first observed at BaBar in 2005, and aroused great interest, because it couples much stronger to hidden charm decays (charm-anticharm states like J/Psi or h_c) instead of open charm decays (D meson pairs). This is unusual for states with masses above the D anti-D threshold. Furthermore, it decays into a charged exotic state Y(4260)->Z_c(3900)^+- pi^-+. The charge of the Z_c(3900)^+- is an indication that it comprises of two more quarks than the charm-anticharm pair, and could therefore be assumed to be a four-quark state. Due to these still not understood properties of these QCD-allowed states, they are referred to as exotic XYZ states to emphasize their particularity.
In 2017, the collaboration of the Beijing Spectrometer III (BESIII) investigated the production reaction of the Y(4260) resonance based on a high-luminosity data set. This significantly improved precision of the measurement of the cross-section sigma(e+e- -> J/Psi pi^+ pi^-) permitted a resolution into two resonances, the Y(4230) and the Y(4360). The Z_c(3900)^+- had been discovered by the BESIII collaboration in 2013, thus this experiment at the Beijing Electron-Positron Collider II (BEPCII) is a top-performing facililty to study exotic charmonium-like states.
In this work, an inclusive reconstruction of the strange hyperon Lambda in the charmonium mass region is performed to study possible decays of Y states in order to provide further insight into their nature. Finding more states or new decay channels may provide crucial hints to understand the strong interaction beyond nonperturbative approaches.
Three resonances are observed in the energy dependent cross-section: the first with a mass of (4222.01 +- 5.68) MeV and a width of (154.26 +- 28.16) MeV, the second with a mass of (4358.88 +- 4.97) MeV and a width of (49.58 +- 13.54) MeV and the third with a mass of (4416.41 +- 2.37) MeV and a width of (23.88 +- 7.18) MeV. These resonances, with a statistical significance Z > 5sigma, can be interpreted as the states Y(4230), Y(4360) and psi(4415).
Additionally, a proton momentum-dependent analysis strategy has been used in terms of the inclusiveness of the reconstruction and to address the momentum discrepancies between generic MC and measured data.
Im Rahmen dieser Arbeit wurde ein verbessertes Buncher-System für Hochfrequenzbeschleuniger mit niedrigem und mittlerem Ionenstrom entwickelt. Die entwickelte Methodik hat ermöglicht, ein effektives, vereinfachtes Buncher-System für die Injektion in HF-Beschleuniger wie RFQs, Zyklotrons, DTLs usw. zu entwerfen, welches kleine Ausgangsemittanzen und beträchtliche Strahltransmissionen erzielt. Um einen mono-energetischen und kontinuierlichen Strahl aus einer Ionenquelle für den Einschuss in eine Hochfrequenz-Beschleunigerstruktur anzupassen, wird eine Energiemodulation benötigt, die im weiteren Verlauf (Driftstrecke) zur Längsfokussierung des Strahls führt. Durch eine Sägezahnwellenform wird die ideale Energiemodulation aufgrund der linearen Abhängigkeit zwischen der Energie der Teilchen und ihren relativen Phasen erreicht. Dies ist jedoch technologisch nicht möglich, da Teilchenbeschleuniger Spannungsniveaus im Bereich kV bis 100 kV benötigen. Dagegen ist für eine solche Zielsetzung eine räumliche Trennung der sinusförmigen Anregung mit der Grundfrequenz und höheren Harmonischen möglich.
Daher wurde in dieser Arbeit ein verbesserter harmonischer Buncher, der sogenannte „Double Drift Harmonic Buncher - DDHB“ entwickelt, welcher zahlreiche Vorteile hat. Eine geringe longitudinale Emittanz sowie finanzielle Aspekte sprechen für diesen Lösungsansatz. Die Hauptelemente eines DDHB Systems sind zwei Kavitäten, die durch eine Driftlänge L1 getrennt sind, wobei der erste Resonator mit der Grundfrequenz bei -90° synchroner Phase und angelegter Spannung V1 und der zweite Resonator bei der zweiten harmonischen Frequenz mit +90 synchroner Phase und angelegter Spannung V2 betrieben werden. Schließlich ist eine zweite Drift L2 am Ende des Arrays für eine longitudinale Strahlfokussierung am Hauptbeschleunigereingang erforderlich. Somit erfüllt ein solcher Aufbau das angestrebte Ziel einer hohen Einfangseffizienz und einer kleinen longitudinalen Emittanz durch Anpassen der vier Designparameter V1, L1, V2 und L2.
Das Verständnis der Fokussierung, ausgehend von einem Gleichstromstrahl, einschließlich der Raumladungskräfte, ist einer der wesentlichen Bestandteile der Strahlphysik. Viele kommerzielle Codes bieten Simulationsmöglichkeiten in diesem Anwendungsbereich. Ihre Ansätze bleiben jedoch dem Anwender meist verborgen, oder es fehlen wichtige Details zur genauen Abbildung des vorliegenden Konzepts. Daher bestand eine Hauptaufgabe dieser Arbeit darin, einen speziellen Multi-Particle-Tracking-Beam-Dynamics-Code (BCDC) zu entwickeln, bei dem der Raumladungseffekt während des Bunch-Vorgangs, ausgehend von einem DC-Strahl berechnet wird. Der BCDC - Code enthält elementare Routinen wie Drift und Beschleunigungsspalt oder magnetische Linse für die transversale Strahlfokussierung und Raumladungsberechnungen unter Berücksichtigung der Auswirkungen der nächsten Nachbar-Bunche (NNB). Der Raumladungsalgorithmus in BCDC basiert auf einer direkten Coulomb- Gitter-Gitter-Wechselwirkung und Berechnungen des elektrischen Feldes durch Lokalisierung der Ladungsdichte auf einem kartesischen Gitter. Um Genauigkeit zu erreichen, werden die Feldberechnungen in Längsrichtung symmetrisch um das zentrale Bucket (βλ-Größe) erweitert, so dass das Simulationsfeld dreimal so groß ist. Die zentrale Teilchenverteilung wird dann nach jedem Schritt in die benachbarten Buckets kopiert. Anschließend werden die resultierenden Felder im Hauptgitterfeld neu berechnet, indem die elektrischen Felder im Hauptgitterfeld mit denen aus den benachbarten Regionen überlagert werden. Ohne diese Methode würde z. B. ein kontinuierlicher Strahl, welcher jedoch in der Simulation nur innerhalb einer Zelle der Länge βλ definiert ist, zu einer resultierenden Raumladungsfeldkomponente Ez an beiden Rändern der Zelle führen. Ein solches unphysikalisches Ergebnis konnte durch die Anwendung der NNB-Technik bereits weitgehend eliminiert werden. Zusätzlich zum NNB-Feature verfügt das BCDC über eine weitere Besonderheit nämlich die sogenannte Raumladungskompensation (SCC). Aufgrund der Ionisierung des Restgases kommt es entlang des Niederenergiestrahltransports zu einer teilweisen Raumladungskompensation, und zwar am und hinter dem Bunchersystem mit unterschiedlichen Prozentsätzen. Eines der Hauptziele des DDHB-Konzepts besteht darin, es für Hochstromstrahlanwendungen zu entwickeln. Dabei ermöglicht die teilweise Raumladungskompensation, dass das Design in der Praxis höhere Stromniveaus erreicht. Dadurch ist das BCDC-Programm ein leistungsstarkes Werkzeug für Simulationen in künftigen, stromstarken Projekten. Proof-of-Principle-Designs wurden in dieser Arbeit entwickelt.