## Doctoral Thesis

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Ion thrusters are Electric Propulsion systems used for satellites and space missions. Within
this work, the High Efficient Multistage Plasma Thruster (HEMP-T), patented by the
THALES group, is investigated. It relies on plasma production by magnetised electrons.
Since the confined plasma in the thruster channel is non-Maxwellian, the near-field plume
plasma is as well. Therefore, the Particle-In-Cell method combined with a Monte-Carlo
Collision model (PIC-MCC) is used to model both regions. In order to increase the sim-
ulated near-field plume region, a non-equidistant grid is utilised, motivated by the lower
plasma density in the plume. To minimise artificial self-forces at grid points bordered by
cells of different size a modified method for the electric field calculation was developed in
this thesis. In order to investigate the outer plume region, where electric field and collisions
are negligible, a ray-tracing Monte-Carlo model is used. With these simulation methods,
two main questions are addressed in this work.
What are the basic mechanisms for plasma confinement, plasma-wall-interaction
and thrust generation?
For the HEMP-T the plasma is confined by magnetic fields in the thruster channel, generated
by cylindrical permanent magnets with opposite polarity. Due to different Hall parameters,
electrons are magnetised, while ions are not. Therefore, the dominating electron transport
is parallel to the magnetic field lines. In the narrow cusp regions, the magnetic mirror effect
reduces the electron flux towards the wall and confines the electrons like in a magnetic
bottle. At the anode, propellant gas streams into the thruster channel, which gets ionised
by the electrons creating the plasma. As a result of the electron oscillation between the two
cusp regions, ionisation of the propellant gas is efficient.
The magnetic field configuration of the HEMP-T also influences the plasma potential inside
the thruster channel. Close to the symmetry axis, the mainly axial magnetic field results in
a flat potential. At the inner wall, the field configuration reduces the plasma wall interaction
to only the narrow cusp regions. Here, the floating potential of the dielectric channel wall
and its plasma sheath result in a rather low radial potential drop compared to the applied
anode potential. As a result, the electric potential is rather flat and impinging ions at the
thruster channel wall have energies below the sputter threshold energy of the wall material.
Therefore, no sputtering appears at the dielectric wall. At the thruster exit the confinement
by the magnetic field is weakened and the potential drops with nearly the full anode voltage.
The resulting electric field accelerates the generated ions into the plume and generate the
thrust, but they are also able to sputter surfaces. During terrestrial testing, sputteringat vacuum vessel walls leads to the production of impurities. The amount of back-flux
towards the channel exit is determined by the sputter yield of the vacuum chamber wall. A
large distance between thruster exit and vessel wall reduces the back-flux and smooths the
pattern of deposition inside the thruster channel. Dependent on their material, the evolving
deposited layers can get conductive, modify by this the potential distribution and reduce
the thrust.
For the HEMP-T, ions are mainly generated at high potential close to the applied anode
potential. Therefore, the accelerated ions producing the thrust gain the maximum energy
as observed in experiment. Ions emitted from the thruster into different angles in the
plume contribute mainly to the ion current at angles between 30 ◦ and 90 ◦ . They mainly
originate from ionisation at the thruster exit. The resulting angular distribution of the
ejected ion current is close to the one of the experiment, slightly shifted by about ten
degrees to higher emission angles. In front of the thruster exit, electrons are trapped by
electrostatics forces. This enhanced density allows ionisation and an additional electron
density structure establishes.
What are possible physics based ideas for optimisation of an ion thruster?
An optimised thruster should have a high ionisation rate inside the thruster channel, low
erosion and an ion angular distribution with small contributions at high angles for min-
imised thruster satellite interactions. In experiments, the HEMP-T satisfies already quite
nicely these requests. In the simulations, low erosion inside the thruster channel and angular
ion distributions close to the experimental data are demonstrated. However, the ionisation
efficiency is lower and radial ion losses are larger than in experiment. A possible explanation
of these differences is an underestimated transport perpendicular to the magnetic field lines,
well known for magnetised plasmas.
A successful example for an optimisation using numerical simulations is the reduction of
back-flux of sputtered impurities during terrestrial experiments by an improved set-up of
the vacuum vessel. The implementation of baffles reduces the back-flux towards the thruster
exit and therefore deposition inside the channel. These improvements were successfully im-
plemented in the experiment and showed a reduction of artefacts during long time measure-
ments. This leads to a stable performance, as it is expected in space.

In this thesis, size-sensitive phenomena of three-dimensional dust crystals emerged in a low temperature plasma are presented. Depending on the number of particles in the system phase transitions, collective vortex motions and large-scaled expansions can be observed. To investigate these fascinating effects an advanced experimental setup as well as new evaluation methods have been developed. This thesis will present these new techniques and the gained insights.

Achieving commercial production of electricity by magnetic confinement fusion requires improvements in energy and particle confinement. In order to better understand and optimise confinement, numerical simulations of plasma phenomena are useful. One particularly challenging regime is that in which long wavelength MHD phenomena interact with kinetic phenomena. In such a regime, global electromagnetic gyrokinetic simulations are necessary. In this regime, computational requirements have been excessive for Eulerian methods, while Particle-in-Cell (PIC) methods have been particularly badly affected by the "cancellation problem", a numerical problem resulting from the structure of the electromagnetic gyrokinetic equations. A number of researchers have been working on mitigating this problem with some significant successes. Another alternative to mitigating the problem is to move to a hybrid system of fluid and gyrokinetic equations. At the expense of reducing the physical content of the numerical model, particularly electron kinetic physics, it is possible in this way to perform global electromagnetic PIC simulations retaining ion gyrokinetic effects but eliminating the cancellation problem. The focus of this work has been the implementation of two such hybrid models into the gyrokinetic code EUTERPE. The two models treat electrons and the entire bulk plasma respectively as a fluid. Both models are additionally capable of considering the self-consistent interaction of an energetic ion species, described gyrokinetically, with the perturbed fields. These two models have been successfully benchmarked in linear growth rate and frequency against other codes for a Toroidal Alfvén Eigenmode (TAE) case. The m=1 internal kink mode, which is particularly challenging in terms of the fully gyrokinetic cancellation problem, has also been successfully benchmarked using the hybrid models with the MHD eigenvalue code CKA. Non-linear simulations in this TAE case have been performed confirming the analytical prediction of a quadratic relationship between the linear growth rate of the TAE and the saturated amplitude of the TAE for a range of moderate values of the linear growth rate. At higher linear growth rate, a slower scaling of saturated amplitude with linear growth rate is observed. This analysis has been extended to include the non-linear wave-wave coupling between multiple TAE modes. It has been shown that wave-wave coupling results in a significant reduction in the saturated amplitude. It has been demonstrated that both plasma elongation and ion kinetic effects can exert a stabilising influence on the internal kink mode. A population of energetic particles can also exert a stabilising influence at low normalised pressure. At high normalised fast particle pressure the stabilised kink mode has been shown to give way to the m=1 EPM, which has been simulated both linearly and non-linearly (the "fishbone" mode). The first self-consistent simulations of global modes in the magnetic geometry of the optimised stellarator Wendelstein 7-X have been performed both linearly and non-linearly. Limitations have been encountered in performing simulations in 3D geometry. A hypothesis for the cause of these problems is outlined and ideas for mitigation are briefly described. In addition to the hybrid model simulations, some of the first utilisations of a new scheme for mitigating the cancellation problem in the fully gyrokinetic regime have been carried out in the framework of this thesis. This scheme, which was developed separately, is concisely described in this work. The new scheme has been benchmarked with existing gyrokinetic and hybrid results. The linear Wendelstein 7-X simulations and linear and single mode non-linear TAE simulations have been repeated with the new model. It is shown that bulk plasma kinetics can suppress the growth rate of global modes in Wendelstein 7-X. The results of fully gyrokinetic TAE simulations, the first to have been performed to our knowledge, are shown to be in close agreement with those results obtained using hybrid models. In the TAE case, the hybrid models are an order of magnitude less computationally demanding than the new gyrokinetic scheme, which is in turn at least an order of magnitude less computationally demanding than the previous gyrokinetic scheme.

This thesis is devoted to experiments on three-dimensional dust clouds which are confined in low temperature plasmas. Such ensembles of highly electrically charged micrometer-sized particles reveal fascinating physics, such as self-excited density waves and vortices. At the same time, these systems are challenging for experimental approaches due to their three-dimensional character. In this thesis, new optical diagnostics for dusty plasmas have been developed and, in combination with existing techniques, have been used to study these 3D dusty plasmas on different size and time scales.

Im ersten Teil der Arbeit wird der erfolgreiche Aufbau einer Diagnostik zur quantitativen Bestimmung von Oberflächenladungsdichten beschrieben. Das Messprinzip bedient sich des elektro-optischen Pockelseffekts eines BSO-Kristalls, der in der Entladungszelle als Dielektrikum eingesetzt ist. Diese Methode arbeitet zeitlich und lateral aufgelöst, was die Untersuchung der Dynamik von Oberflächenladungen auf drei verschiedenen Zeitskalen ermöglicht. Die erste Zeitskala liegt in der Größenordnung von einigen 100 ns. Damit kann erstmals die Deposition von elektrischer Ladung auf einer dielektrischen Oberfläche während eines Entladungsdurchbruchs beobachtet werden. Die Deposition beginnt im Zentrum eines zuvor deponierten Ladungsspots. Die Polarität der neudeponierten Ladung ist der des ursprünglichen Ladungsspots entgegengesetzt. Die Folge ist, dass die absolute Ladungsdichte im Zentrum im Verlauf einiger hundert Nanosekunden kleiner wird als in den Randbereichen. Der Umladungsprozess wird so lange fortgesetzt, bis das elektrische Feld der neu deponierten Ladungen dem äußeren Feld so stark entgegenwirkt, dass die Spannung zur Aufrechterhaltung der Entladung unterschritten wird und die Entladung erlischt. Die zweite untersuchte Zeitskala liegt in der Größenordnung der Periodendauer der externen Spannung. Im Nulldurchgang der Spannung liegen zeitlich stationäre Ladungsdichteverteilungen auf dem Dielektrikum vor. Die Geometrie eines mittleren Ladungsspots wird in Abhängigkeit der anliegenden Spannungen und des Gasdrucks untersucht. Einerseits ist der Spotradius abhängig von den Ionisationsprozessen im Volumen, weil die Dichte der Raumladungen die Stärke des Elektronenfokus in das Innere der Entladung steuert. Andererseits wird die Spotbildung durch eine laterale Drift von Ladungsträgern kurz vor der Oberfläche aufgrund des elektrischen Feldes deponierter Ladungsträger beeinflusst. Die dritte untersuchte Zeitskala liegt in einer Größenordnung von Sekunden. Im Fall einer initial homogenen Oberflächenladungsverteilung nimmt die mittlere Ladungsdichte in einer Größenordnung von Sekunden monoton ab. Dieser Prozess stellt einen Ladungsabbau dar, dessen zeitliches Verhalten durch zwei überlagerte Exponentialfunktionen beschreiben ließ. Dadurch werden zwei Ladungsträgerpopulationen im BSO angenommen, die verschieden abgebaut werden. Im Fall einer initial inhomogenen Ladungsdichteverteilung wird ein Transport elektrischer Ladung auf der BSO-Oberfläche in einer Größenordnung von Sekunden beobachtet. Es wird weiterhin erstmals die durch einen Atmosphärendruck-Plasmajet deponierten Ladungen auf BSO zeitaufgelöst gemessen. Die zeitliche Entwicklung der Oberflächenladungen kann mit der Messung des elektrischen Stroms an einer der Ringelektroden des Jets korreliert werden. Dadurch wird geschlossen, dass der Ladungsaustauch nicht direkt durch einen Bullet verursacht wird. Er erzeugt stattdessen einen elektrisch leitfähigen Kanal zwischen der Düse des Jets zur BSO-Oberfläche. Infolgedessen kann Ladung, die sich auf der Innenseite der Jetkapillare befindet, auf den BSO-Kristall transportiert werden. Im zweiten Teil der Arbeit werden Kenngrößen entwickelt, die den Ordnungszustand einer aus Einzelobjekten zusammengesetzten Entladungsstruktur quantitativ beschreiben. Die Kenngrößen werten dabei die laterale Leuchtdichteverteilung der Entladungsemisssion, u.a. auf Basis der Tripel-Korrelationsfunktion. Dabei werden zwei separate Bifurkationsspannungen zwischen einer hexagonalen und einer ungeordneten Anordnung beobachtet: Bei der Verringerung der Spannung wird zunächst der Bifurkationspunkt der azimutalen Ordnung durchlaufen und anschließend der Bifurkationspunkt der radialen Ordnung. Die Systeme gehen jeweils in einen Zustand geringerer Ordnung über. Die Ursache des Ordnungsverlusts ist das zunehmende Fehlen von Entladungsspots, was im Mittel zu einer geringeren Wechselwirkung der Spots untereinander führt und das System an Freiheitsgraden gewinnt. Im dritten Teil dieser Arbeit wird erstmals ein Ansatz verfolgt, der die Steuerung lateral strukturierter Entladungen ermöglicht. Dafür wurde ein Aufbau konstruiert, bei dem ein gekühlter Halbleiter als Dielektrikum in der Entladungszelle dient. Dessen externe Beleuchtung führt bei einer anliegenden Spannung zu einer Änderung des Spannungsteilerverhältnisses der kapazitiven Elemente und schließlich zu einer lokalen Erhöhung der Spannung über dem Entladungsraum. Die Größe und Leuchtintensität der durch die Beleuchtung gezündeten Entladung ist stark abhängig von der beleuchteten Fläche, der Leistungsdichte der Beleuchtung und der anliegenden Spannung.

In the last decade a new domain has developed in plasma physics: plasma medicine. Despite the successes that have already been achieved in this exciting new field, the interaction of plasmas with “biological materials” is not yet fully understood. Further investigations in particular with respect to the properties of the applied plasmas sources are therefore essential in order to decode this complex interaction process. Currently, a great variety of different discharge types are used in plasma medical investigation which are generally are operated in noble gases like helium and argon or with dry air. In the present work, the main focuses is on the diagnostics of reactive oxygen and nitrogen species (RONS) resulting from the plasma chemistry of an argon radio-frequency (RF) atmospheric pressure plasma jet (APPJ) and its interaction with the ambient atmosphere. To conduct this study, a commercially available plasma device, so-called kinpen is used due to its technical development maturity and its accessibility on the market. As a method of choice, diagnostic techniques are based on optical spectroscopy known to be a reliable tool to investigate plasmas. Consequently, three complementary optical laser diagnostics, namely quantum cascade laser absorption spectroscopy (QCLAS), laser induced fluorescence (LIF) and planar single shot LIF (PLIF), have been successfully applied to the plasma jet itself or its effluent. All of these diagnostics offer a high species selectivity and an excellent spatial and temporal resolution. They are used in this work for i) the characterization of the plasma chemical dynamics with respect to the generation of biological active RONS – in particular for the case of N2 and O2 admixtures. ii) the measurement of the NO density profile in the plasma effluent iii) the investigation of the flow characteristics of the neutral gas component (laminar vs. turbulent) and its influence on the plasma chemistry. Numerical analysis have been carried out in collaboration with PLASMANT (University of Antwerp) via kinetic simulations of the entire plasma chemistry. Expectingly, atomic oxygen (O) and nitric oxide (NO) turn out to be precursors of ozone (O3) and nitric dioxide (NO2). However, it was intriguing to unveil that atomic oxygen and nitrogen metastable (N2(A)) play together a key part --as intermediate species-- in the generation of more stable RONS, e.g. NO. The absolute density of NO space resolved was measured by LIF and absolutely calibrated molecular beam mass spectrometer. LIF was used to determine relative density of OH radical in the plasma plume. 2D-LIF was used to investigate the gas flow pattern with OH as a flow tracer. The results are discussed in details and show different operating mode of the jet, e.g. laminar or turbulent and that the plasma influences these regimes. The first detection and relative measurement by LIF of nitrogen metastable (N2(A)) produced by an argon APPJ is also shortly reported in this work. The outcome of this thesis will bring new insights in the field of argon APPJs chemistry and its interaction with the ambient atmosphere which can be valuable to support plasma modelling and to consider for the applications in plasma medicine.

Magnetic reconnection is a ubiquitous phenomenon observed in a wide range of magnetized plasmas from magnetic confinement fusion devices to space plasmas in the magnetotail. The process enables the release of accumulated magnetic energy by rapid changes in magnetic topology, heating the plasma in the vicinity of the reconnection site, generating fast particles and allowing a wealth of instabilities to grow. This thesis reports on the results from a newly constructed linear, cylindrical and modular guide field reconnection experiment with highly reproducible events, VINETA.II. A detailed analysis of the reconnecting current sheet properties on a macroscopic and microscopic scale in time and space is presented. In the experiment, four parallel axial wires create a figure-eight in-plane magnetic field with an X-line along the central axis, as well as an axial inductive field that drives magnetic reconnection. Particle-in-cell simulations show that the axial current is limited by sheaths at the boundaries and that electrostatic fields along the device axis always set up in response to the induced electric field. Current sheet formation requires an additional electron current source, realized as a plasma gun, which discharges into a homogeneous background plasma created by a rf antenna. The evolution of the plasma current is found to be dominantly set by its electrical circuit. The current response to the applied electric field is mainly inductive, which in turn strongly influences the reconnection rate. The three-dimensional distribution of the current sheet is determined by the magnetic mapping of the plasma gun along the sheared magnetic field lines, as well as by radial cross-field expansion. This expansion is due to a lack of equilibrium in the in-plane force balance. Resistive diffusion of the magnetic field by E=η j is found to be by far insufficient to account for the high reconnection rate E=-dΨ/dt at the X-line, indicating the presence of large electrostatic fields which do not contribute to dissipative reconnection. High-frequency magnetic fluctuations are observed throughout the current sheet which are compared to qualitatively similar observations in the Magnetic Reconnection Experiment (MRX, Princeton). The turbulent fluctuation spectra in both experiments display a spectral kink near the lower hybrid frequency, indicating the presence of lower hybrid type instabilities. In contrast to the expected perpendicular propagation of mainly electrostatic waves, an electromagnetic wave is found in VINETA.II that propagates along the guide field and matches the whistler wave dispersion. Good correlation is observed between the local axial current density and the fluctuation amplitude across the azimuthal plane. Instabilities driven by parallel drifts can be excluded due to the large required drift velocities or low resulting phase velocities that are not observed. It is instead suggested that a perpendicular, electrostatic lower hybrid mode indeed exists that resonantly excites a parallel, electromagnetic whistler wave through linear mode conversion. The resulting fluctuations are found to be intrinsic to the localized current sheet and are independent of the slower reconnection dynamics. Their amplitude is small compared to the in-plane fields, and have a negligible contribution to anomalous resistivity through momentum transport in the present parameter regime.

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.

The present thesis deals with dynamic structures that form during the expansion of plasma into an environment of much lower plasma density. The electron expansion, driven by their pressure, occurs on a much faster time scale than the ion expansion, owed to their mobility. The high inertia of the ions causes the generation of an ambipolar electric field that decelerates the escaping electrons while accelerating the ions. The ambipolar boundary propagates outwards and forms a plasma density front. For a small density differences, the propagation of the front can be described with the linear ansatz for ion acoustic waves. For a large density differences, experiments have shown that the propagation velocity of such a front is still related to the ion sound velocity. However, the reported proportionality factors are scattered over a wide range of values, depending on the considered initial and boundary conditions. In this thesis, the dynamics during plasma expansion are studied with the use of experiments and a versatile particle-in-cell simulation. The experimental investigations are performed in the linear helicon device Piglet. The experiment features a fast valve, which is used to shape the neutral gas density profile. During the pulsed rf-discharges, plasma is generated in the source region and expands collisionless into the expansion chamber. The computer simulation is tailored very close to the experiment and provides a deeper insight in the particle kinetics. The experimental results show the existence of a propagating ion front. Its velocity is typically supersonic and depends on the density ratio of the two plasmas. The ion front features a strong electric field. The front can have similar properties to a double layer is not necessarily a double layer by definition. The computer simulation reveals that the propagating electric field repels the downstream ambient ions. These ions form a stream with velocities up to twice as high as the front velocity. The observed ion density peak is due to the accumulation of the repelled ions and is located at their turning point. The ion front formation depends strongly on the initial ion density profile and is part of a wave-breaking phenomenon. The observed front is followed by a plateau of little plasma density variation. This could be confirmed for the expansion experiment by a comparison with virtual diagnostics in the computer simulation. The plateau has a plasma density determined by the ratio between the high and low plasma density. It consists of streaming ions that have been accelerated in the edge of the main plasma. The presented results confirm and extend findings obtained by independent numerical models and simulations.

Magnetic reconnection is a fundamental plasma process where a change in field line connectivity occurs in a current sheet at the boundary between regions of opposing magnetic fields. In this process, energy stored in the magnetic field is converted into kinetic and thermal energy, which provides a source of plasma heating and energetic particles. Magnetic reconnection plays a key role in many space and laboratory plasma phenomena, e.g. solar flares, Earth’s magnetopause dynamics and instabilities in tokamaks. A new linear device (VINETAII) has been designed for the study of the fundamental physical processes involved in magnetic reconnection. The plasma parameters are such that magnetic reconnection occurs in a collision-dominated regime. A plasma gun creates a localized current sheet, and magnetic reconnection is driven by modulating the plasma current and the magnetic field structure. The plasma current is shown to flow in response to a combination of an externally induced electric field and electrostatic fields in the plasma, and is highly affected by axial sheath boundary conditions. Further, the current is changed by an additional axial magnetic field (guide field), and the current sheet geometry was demonstrated to be set by a combination of magnetic mapping and cross-field plasma diffusion. With increasing distance from the plasma gun, magnetic mapping results in an increase of the current sheet length and a decrease of the width. The control parameter is the ratio of the guide field to the reconnection magnetic field strength. Cross-field plasma diffusion leads to a radial expansion of the current sheet at low guide fields. Plasma currents are also observed in the azimuthal plane and were found to originate from a combination of the field-aligned current component and the diamagnetic current generated by steep in-plane pressure gradients in combination with the guide field. The reconnection rate, defined via the inductive electric field, is shown to be directly linked to the time-derivative of the plasma current. The reconnection rate decreases with increasing ratio of the guide field to the reconnection magnetic field strength, which is attributed to the plasma current dependency on axial boundary conditions and the plasma gun discharge. The above outlined results offer insights into the complex interaction between magnetic fields, electric fields, and the localized current flows during reconnection.