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In this thesis we have revisited the formation of the excitonic insulator (EI), which realizes an exciton condensate. In contrast to optically created exciton condensates, the EI forms in thermal equilibrium and is solely driven by the Coulomb attraction between electrons and holes. The EI phase is anticipated to occur near the semimetal-semiconductor (SM-SC) transition at low temperatures. Depending from which side the EI is approached, it forms due to a BCS-type condensation of electron-hole pairs or a Bose-Einstein condensation (BEC) of excitons. The extended Falicov-Kimball model (EFKM) is the minimal model the EI can be described with. This model describes spinless fermions in two dispersive bands (f band and c band), that interact via a local Coulomb repulsion. The EFKM is also used to describe electronic ferroelectricity (EFE). Both phases, the EI and EFE-type ordering, are characterized by a spontaneous f-c hybridization in the EFKM. We have presented the EI phase, the EFE phase, and the orderings they compete with. Moreover, we have determined the ground-state phase diagram of the EFKM. We have focused particularly on the anticipated BCS-BEC crossover within the EI and have analyzed the formation scenarios. The exciton spectrum and the exciton density in the normal phase close to the critical temperature give information about relevant particles and therefore the nature of the transition. We have demonstrated that the whole EI is surrounded by a halo", that is, a phase composed of electrons, holes and excitons. However, on the SM side, only excitons with a finite momentum exist. These excitons appear only in a small number and barely influence the SM-EI transition. This phase transition is driven by critical electron-hole fluctuations, generated by electrons and holes at the Fermi surface. On the SC side, excitons with arbitrary momenta exist. Most notably, we have found the number of zero-momentum excitons to diverge at the SC-EI transition, signaling the BEC of these particles. Within the EI phase, there is a smooth crossover from the BCS regime to the BEC regime. One of the promising candidates to observe the EI experimentally, is the transition-metal dichalcogenide 1T-TiSe2. Strong evidences were found favoring an EI scenario of the charge-density-wave (CDW) formation in this material. However, some aspects point to a lattice instability to drive the CDW transition. We have addressed this issue by analyzing the recently discovered chiral property of the CDW in 1T-TiSe2. We have found that the EI scenario is insufficient to explain a stable, long range chiral charge ordering. Lattice degrees of freedom must be taken into account. In particular, nonlinear electron-phonon coupling and phonon-phonon interaction are crucial. By estimating appropriate model parameters for 1T-TiSe2, we have suggested a combination of excitonic and lattice instability to drive the CDW transition in this material. Experiments in 1T-TiSe2 and other materials suggest that the coupling to the lattice is non-negligible. We have extended therefore the model by an explicit exciton-phonon interaction, and have analyzed crucial effects of this interaction. While the single-particle spectrum is not modified qualitatively, the electron-hole pair spectrum changes significantly. The inclusion of the phonons lead to a massive collective mode in the ordered ground state in contrast to the case for vanishing exciton-phonon coupling, where the mode is acoustic. We have suggested that a gapless collective mode leads to off-diagonal long range order. This questions that the ground state for finite exciton-phonon coupling represents a condensate.
The region surrounding the excitonic insulator phase is a three-component plasma composed of electrons, holes, and excitons. Due to the extended nature of the excitons, their presence influences the surrounding electrons and holes. We analyze this correlation. To this end, we calculate the density of bound electrons, the density of electrons in the correlated state, the momentum-resolved exciton density, and the momentum-resolved density of electron-hole pairs that are correlated but unbound. We find qualitative differences in the electron-hole correlations between the weak-coupling and the strong-coupling regime.
In the present thesis, a systematic study of beam driven Alfvén eigenmodes in high-density and low-temperature plasmas of the W7-AS stellarator is performed. The device went out of operation in 2002 and the study is based on stored experimental data. Alfvén instabilities can roughly be divided into ideal MHD Alfvén eigenmodes and those existing due to kinetic effects. The spectrum of ideal MHD Alfvén waves in toroidal fusion devices consists of a continuum of stable waves that are strongly localized. Weakly damped, discrete eigenmodes can exist in gaps of the continuous spectrum which are formed by plasma inhomogeneities and the coupling of Alfvén continua. This allows an identification of ideal MHD Alfvén eigenmodes in terms of their frequency and mode numbers. Kinetic effects can modify this spectrum and cause additional types of eigenmodes, the kinetic Alfvén eigenmodes (KAE) and energetic particle modes (EPM). The goal of this thesis is twofold: (I) identification and description of fast particle driven Alfvén instabilities in W7-AS, and (II) study of energetic particle losses induced by Alfvén instabilities. The reconstruction of the ideal MHD plasma equilibrium for each discharge with sufficient accuracy is the very foundation of all subsequent steps. This is achieved, based on measured plasma parameter profiles that are further refined by validating them to the measurements of other, independent plasma diagnostics. The applied scheme is inspired by an approach of Integrated Data Analysis (IDA) to combine different diagnostic data and provide combined uncertainties. After mode number analysis and eigenmode identification, the theoretically expected, linear growth rate of the instability is calculated where possible, and the various contributions of the fast particle drive to the instability of the mode are identified. Alfvénic activity recorded by the Mirnov diagnostic is analyzed, which consists of a set of spatially distributed coils that measure magnetic fluctuations. On W7-AS, the probes are arranged in three poloidal arrays at different toroidal positions. The spacing between the probes is non-equidistant. In addition, the signals of one probe array are digitized with a different sample rate. These characteristics prohibit the straight-forward use of standard tools available for harmonic analysis. Instead, a new tool has been developed and thoroughly tested. It is a multi-dimensional extension of the Lomb periodogram, able to provide reliable time-resolved frequency and mode number spectra in the case of uneven datapoint spacing. Numerical studies of this periodogram show a good performance with respect to mode number resolution given the low number of available probes, and robustness against perturbations of the signal. Only two of the probe arrays can be used for the analysis of eigenmodes with frequencies >70 kHz, such that for high-frequency phenomena insufficient information about the mode numbers is available. A total of 133 different Alfvén eigenmodes is studied in discharges from different experimental campaigns. A restriction to discharges from various high-beta campaigns with neutral beam heating is required to allow for a realistic reconstruction of plasma equilibrium and velocity distribution functions of energetic particles. The discharges are characterized by high density, ne = 5 x 1019 m-3 to 2.5 x 1020 m-3 at relatively low temperatures of Te = Ti = 150 ... 600 eV. Alfvén eigenmodes often appear transiently in the startup phase of these discharges, where density and heating power are being ramped up. Occasionally, Alfvén eigenmodes are seen in the stationary, high-beta phase in the presence of considerable neutral beam heating. Most of the Alfvén eigenmodes are successfully classified as ideal MHD eigenmodes. 19 global, 47 toroidicity-induced and 8 ellipticity-induced Alfvén eigenmodes (GAEs, TAEs, and EAEs, respectively) are unambiguously identified by their mode numbers and frequencies. Excellent agreement between experimentally observed mode number spectra and theoretically calculated eigenmode structure is shown for a TAE example. Additional 13 events are found to have frequencies inside the EAE gap and could possibly be EAEs. Evidence for high-frequency Alfvén eigenmodes (mirror- and helicity-induced Alfvén eigenmodes) is seen, but can not be proven rigorously due to uncertain mode numbers and the complexity of the Alfvén continuum. The remaining 41 Alfvén eigenmodes can not be classified to be one of the above cases. Reasons are either high frequencies, mode numbers obscured by far-field effects, or mode numbers that could not be related to ideal MHD Alfvén eigenmodes. A selection of these shows indications of strong non-linear wave-particle interactions and are assumed to be EPMs. Kinetic Alfvén eigenmodes are not expected to exist in the experimental conditions that were studied. The radially resolved velocity distribution function is used to describe the parameter regimes in which the modes are observed in terms of the dimensionless parameters vb/vA (beam velocity normalized to the Alfvén velocity) and ßfast/ßth, where beta is the ratio of plasma pressure to magnetic pressure. The first parameter describes through which of the possible resonance velocities particles can interact with the eigenmode. A peculiarity of the fast particle dynamics in fusion devices is that they can resonantly interact with Alfvén eigenmodes through sideband resonances even if v < vA. The second parameter describes the energy content of the destabilizing fast particle population compared to the potentially stabilizing thermal plasma component. These parameters contain relevant information about the instability of an eigenmode and such diagrams are given for all observed modes. In addition to that, the expected linear growth rate of gap modes is calculated based on a theoretical model that extends the ideal MHD by a perturbative, drift-kinetic description of the energy exchange between waves and circulating particles, neglecting the effects of trapped particles. For the discharges under consideration the thermal electron speed is comparable to vA and the electrons provide a significant Landau damping contribution. Due to strong density gradients near the plasma boundary in most of the discharges, the thermal ions can provide a small drive via the spatial inhomogeneity which does not overcome the electron damping, however. The drive by spatial inhomogeneity of thermal ions requires a certain propagation direction of the mode and is equally stabilizing for opposite mode numbers. The fast particles also contribute to the growth rate via spatial inhomogeneity, velocity gradients and velocity anisotropy terms are negligible in W7-AS. Most of the observed GAE or EAE modes have negative mode numbers, which correspond to a propagation direction for which the spatial inhomogeneity of thermal and beam ions is predicted to be stabilizing. A fast particle drive of these modes is not confirmed, whereas the TAEs are found to be strongly destabilized by neutral beam injection. The distribution of plasma parameters for discharges showing TAEs in terms of the dimensionless stability parameters suggests an instability threshold that is qualitatively confirmed by an exploration of the parameter space with the theoretical model. Wave-induced, resonant losses of energetic ions scale linearly with the wave amplitude. To identify them, correlations between ion loss probe signals and wave amplitudes are searched, where correlation times in the order of the slowing-down time of energetic particles are expected. Significant correlations can be established only exceptionally for 3 of the identified ideal MHD Alfvén eigenmodes. Those Alfvén eigenmodes, however, which are assumed to be EPMs frequently show severe losses of energetic ions that are visible in the time traces of the plasma energy as well.
The collisionless tearing mode is investigated by means of the delta-f PIC code EUTERPE solving the gyrokinetic equation. In this thesis the first simulations of electromagnetic non-ideal MHD modes in a slab geometry with EUTERPE are presented. Linear simulations are carried out in the cases of vanishing and finite temperature gradients. Both cases are benchmarked using a shooting method showing that EUTERPE simulates the linearly unstable tearing mode to a very high accuracy. In the case of finite diamagnetic effects and values of the linear stability parameter Delta of order unity analytic predictions of the linear dispersion relation are compared with simulation results. The comparison validates the analytic results in this parameter range. Nonlinear single-mode simulations are performed in the small- to medium-Delta range measuring the dependency of the saturated island half width on the equilibrium current width. The results are compared with an analytic prediction obtained with a kinetic electromagnetic model. In this thesis the first simulation results in the regime of fast nonlinear reconnection~(medium- to high-Delta range) are presented using the standard gyrokinetic equation. In this regime a nonlinear critical threshold has been found dividing the saturated mode from the super-exponential phase for medium-Delta values. This critical threshold has been proven to occur in two slab equilibria frequently used for reconnection scenarios. Either changing the width of the equilibrium current or the wave number of the most unstable mode makes the threshold apparent. Extensive parameter studies including the variation of the domain extensions as well as the equilibrium current width are dedicated to a comprehensive overview of the critical threshold in a wide range of parameters. Additionally, a second critical threshold for high-Delta equilibria has been observed. A detailed comparison between a compressible gyrofluid code and EUTERPE is carried out. The two models are compared with each other in the linear regime by measuring growth rates over wave numbers of the most unstable mode for two setups of parameters. Analytical scaling predictions of the dispersion relation relevant to the low-Delta regime are discussed. Employing nonlinear simulations of both codes the saturated island half width and oscillation frequency of the magnetic islands are compared in the small-Delta range. Both models agree very well in the limit of marginal instability and differ slightly with decreasing wave vector. Recently, the full polarisation response in the quasi-neutrality equation was implemented in EUTERPE using the Padé approximation of the full gyrokinetic polarisation term. Linear simulation results including finite ratios of ion to electron temperature are benchmarked with the dispersion relation obtained from a hybrid model. Finite temperature effects influence the saturated island width slightly with increasing ion to electron temperature ratio which has been verified by both models.
Optomechanical (om) systems are characterized by their nonlinear light-matter interaction. This is responsible for unique dynamic properties and allows the detection of a variety of classical and quantum mechanical phenomena on a microscopic as well as on a macroscopic scale. In this work we have studied the dynamic behavior of two laser-driven om systems, the single om cell ("cavity optomechanics / membrane-in-the-middle setup") and a two-dimensional hexagonal array of these cells ("om graphene"). The first case was motivated by the possibility to detect the transition from quantum mechanics to classical mechanics directly on the basis of the dynamic behavior. For this we focus on multistability effects of the optical and mechanical degrees of freedom, that are modeled by harmonic oscillators. Our description is based on the quantum optical master equation, which takes into account the environmental interaction assuming a vanishing temperature. As a consequence of decoherence, the dynamics occur near the semiclassical limit, i.e. it is characterized by quantum fluctuations. The quantum-to-classical transition is realized formally by rescaling the equations of motion. In the classical limit, quantum fluctuations disappear and the mean field equations were evaluated by analytical and numerical methods. We found that classical multistability is characterized by stationary signatures on the route to chaos, as well as by the coexistence of single-periodic orbits for the mechanical degree of freedom. The latter point was extensively evaluated by means of a self-consistent approach. For the dynamics in the quantum regime quantum fluctuations cannot be neglected. For this purpose, the master equation was solved by means of a numerical implementation of the Quantum State Diffusion (QSD) method. Based on Wigner and autocorrelation functions, we were able to show that quantum multistability is a dynamic effect: chaotic dynamics is suppressed and there is a time-dependent distribution of the phase space volume on classical simple-periodic orbits. The results can be interpreted within a semiclassical picture, which makes use of the single QSD quantum trajectory. Accordingly, the quantum-classical transition is explained as a time-scale effect, which is determined by tunneling probabilities in an effective mean-field potential. The subject of the second part of the work is the transport of low-energy Dirac quasiparticles in om graphene, propagating as light and sound waves. For this purpose, we investigated the scattering of a plane light wave by laser-induced photon-phonon coupling planar and circular barriers. The starting point is the om Dirac equation, which results from the continuum approximation of the Hamiltonian description of the two-dimensional array near the semiclassical limit. This work was motivated by the rich and interesting relativistic transport and tunneling phenomena found for electrons in graphene, which now appear in a new way. The reason is the presence of the new spin degree of freedom, which distinguishes the optical and mechanical excitations. In this spin space, the om interaction can be understood as a potential, which in our analysis consists of a time-independent and a time-dependent sinusoidal part. For the first case of a static barrier, the transport is elastic and is characterized by stationary scattering signatures. After solving the scattering problem via continuity conditions we were able to identify different scattering regimes depending on scattering parameters. In addition to relativistic phenomena such as Klein tunneling, simple parameter variation allows to use the barrier as a resonant light-sound interconverter and angle-dependent emitter. For the oscillating barrier, the transport is inelastic and is characterized by dynamic scattering signatures. To solve the time-periodic scattering problem, we have applied the Floquet theory for an effective two-level system. As a result of the barrier oscillation, photons and phonons can get and give away energy portions in the form of integer multiples of the oscillation frequency. The interference of short (classical) and long-wave (quantum) components leads to mixing of the scattering regimes. This allows to use the barrier as a time-periodic light-sound interconverter with interesting radiation characteristics. In addition, we have argued that the oscillating barrier provides the necessary energetic conditions for detecting zitterbewegung.
The stratospheric aerosol layer plays an important role in the radiative balance of Earth primarily through scattering of solar radiation. The magnitude of this effect depends critically on the size distribution of the aerosol. The aerosol layer is in large part fed by volcanic eruptions strong enough to inject gaseous sulfur species into the stratosphere. The evolution of the stratospheric aerosol size after volcanic eruptions is currently one of the biggest uncertainties in stratospheric aerosol science. We retrieved aerosol particle size information from satellite solar occultation measurements from the Stratospheric Aerosol and Gas Experiment III mounted on the International Space Station (SAGE III/ISS) using a robust spectral method. We show that, surprisingly, some volcanic eruptions can lead to a decrease in average aerosol size, like the 2018 Ambae and the 2021 La Soufrière eruptions. In 2019 an intriguing contrast is observed, where the Raikoke eruption (48∘ N, 153∘ E) in 2019 led to the more expected stratospheric aerosol size increase, while the Ulawun eruptions (5∘ S, 151∘ E), which followed shortly after, again resulted in a reduction in the values of the median radius and absolute distribution width in the lowermost stratosphere. In addition, the Raikoke and Ulawun eruptions were simulated with the aerosol climate model MAECHAM5-HAM. In these model runs, the evolution of the extinction coefficient as well as of the effective radius could be reproduced well for the first 3 months of volcanic activity. However, the long lifetime of the very small aerosol sizes of many months observed in the satellite retrieval data could not be reproduced.
This thesis describes the implementation and first on-line application of a multi-reflection time-of-flight (MR-ToF) mass analyzer for high-resolution mass separation at the ISOLTRAP mass spectrometer at ISOLDE/CERN. On the one hand, the major objective was to improve ISOLTRAPs mass-measurement capabilities with respect to the ratio of delivered contaminating ions to ions of interest. On the other hand, the time necessary to purify wanted from unwanted species should be reduced as much as possible to enable access to even more exotic nuclei. The device has been set up, optimized and tested at the University of Greifswald before its move to ISOLTRAP. The achieved performance comprises mass resolving powers of up to 200000 reached at observation times of 30ms and a contamination suppression of about four orders of magnitude by use of a Bradbury-Nielsen gate. With the characteristics, it outperforms clearly the so far state-of-the-art purification method of a gas-filled Penning trap. To improve the utilization of the MR-ToF mass analyzer, the in-trap lift method has been developed. It simplifies the application and optimization of the device, which is a crucial time factor in an on-line experiment. The device was the first of its kind successfully applied to radioactive ion beams for a mass analysis, for a mass separation (in combination with the Bradbury-Nielsen gate) as a preparatory step for a subsequent Penning-trap mass measurement and as a high-precision mass spectrometer of its own. The later was recently used for the first mass measurement of the neutron-rich calcium isotopes 53Ca and 54Ca. The so-far achieved mass-resolving power of 200000 belongs to the highest reported for time-of-flight mass analyzers at all. The first successful application of the MR-ToF system as the only mass separator at ISOLTRAP resulted in the mass measurement of 82Zn. The new mass value has been compared to mass extrapolations of the most recent Hartree-Fock-Bogoliubov (HFB) mass models, HFB-19 to HFB-21, of the BRUSLIB collaboration. The mass of the nuclide is of high interest for the compositions and depth profile of the outer crust of neutron stars. In the classical model of the outer crust of a cold, non-accrediting and non-rotating neutron star, the sequence of nuclides found within this parts is determined mainly by the binding energy of exotic nuclides. The crustal compositions determined with the three HFB mass models differed with respect to the appearance of a layer of 82Zn, originating from different mass extrapolations of this mass. With the new experimental data, the extrapolations could be evaluated. It was found that the HFB-21 mass value differs less from the experimental data than the ones from HFB-19 and 20. Therefore, in the classical model, 82Zn does not appear anymore in the outer crust. Due to its high resolution and very fast measurement time, the MR-ToF mass analyzer will be an important instruments for future activities at ISOLTRAP, at the ISOLDE facility in general, and at other radioactive ion-beam facilities.
Abstract
The presented experimental system is a barrier discharge system with plane parallel electrodes. The lateral surface charge distribution being deposited on the dielectric layer during each breakdown is observed optically using the well known electro-optic effect (Pockels effect). The temporal resolution of the surface charge measurement has been increased to 200 ns, and so for the first time it is possible to resolve the charge transfer to the dielectric surface in a single breakdown. In the present measurements, a patterned glow-like barrier discharge is investigated. It is found that the charge reversal in a single discharge spot (microdischarge) starts in the centre and then grows outwards. These experimental findings verify previously unconfirmed predictions from earlier numerical calculations and thereby contribute to a better understanding of the interaction between the plasma and the electrical charge on the electrodes.
Abstract
The surface charge distribution deposited by the effluent of a dielectric barrier discharge driven atmospheric pressure plasma jet on a dielectric surface has been studied. For the first time, the deposition of charge was observed phase resolved. It takes place in either one or two events in each half cycle of the driving voltage. The charge transfer could also be detected in the electrode current of the jet. The periodic change of surface charge polarity has been found to correspond well with the appearance of ionized channels left behind by guided streamers (bullets) that have been identified in similar experimental situations. The distribution of negative surface charge turned out to be significantly broader than for positive charge. With increasing distance of the jet nozzle from the target surface, the charge transfer decreases until finally the effluent loses contact and the charge transfer stops.
Behavior of a porous particle in a radiofrequency plasma under pulsed argon ion beam bombardment
(2010)
The behavior of a single porous particle with a diameter of 250 μm levitating in a radiofrequency (RF) plasma under pulsed argon ion beam bombardment was investigated. The motion of the particle under the action of the ion beam was observed to be an oscillatory motion. The Fourier-analyzed motion is dominated by the excitation frequency of the pulsed ion beam and odd higher harmonics, which peak near the resonance frequency. The appearance of even harmonics is explained by a variation of the particles's charge depending on its position in the plasma sheath. The Fourier analysis also allows a discussion of neutral and ion forces. The particle's charge was derived and compared with theoretical estimates based on the orbital motion-limited (OML) model using also a numerical simulation of the RF discharge. The derived particle's charge is about 7–15 times larger than predicted by the theoretical models. This difference is attributed to the porous structure of the particle.