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In course of the recent results from Wendelstein 7-X, stellarators are on the brink for assessing their maturity as a fusion reactor. To this end, stellarator specific transport regimes need detailed exploration both with appropriate systematic experimental investigations and models. A way to enhance the efficiency of this process is seen in an systematic evaluation of existing experimental data. We propose appropriate tools developed in information theory for examining large datasets. Information entropy calculations, that have proven to assist the systematic assessment of datasets in many other scientific fields, are used for novelty detection.
Potentially, as a first use-case of this holistic process, this thesis attempts to link and to develop approaches to examine the stellarator specific core-electron-root-confinement (CERC) regime. The specific interest for CERC emerges from the behavior of the radial electric field. While ion-root conditions exhibit negative radial electric fields, CERC’s positive field in the very core of fusion grade plasmas adds an outward thermodynamic force to high-Z impurities and could add to potential actuators to control impurity influx as to be examined for full-metal wall operation in large stellarators. Recently, this feature received revived intent for reactor scale stellarators.
Also, in this work, parameter regions close to the transition from ion-root to CERC are
examined. At lower rotational transform (a characteristic feature of the magnetic field confining fusion grade plasmas), transitions were detected when the plasma current evolved. As in smaller stellarators, it is concluded that low-order rationals and magnetic islands are related to the transitions. This is widely supported by extensive MHD simulations which finally provide indications for the role of zonal flow oscillations. As one of the outcomes, gyrokinetic instabilities are seen interacting for the first time with the neoclassical mechanisms in experiments.
In order to cope with the vast number of highly sampled spatio-temporal plasma data, new
techniques for novelty detection are required. Fundamental prerequisites for the detailed
physics investigations were the feasibility study of entropy-based data analysis techniques, and their adaptation to detect previously unrevealed transition mechanisms. These tools were applied to multivariate bulk plasma emissivity data, which allowed the exploration of large parameter spaces and provided insights in the spatio-temporal dynamics of CERC transitions.
In this manner, this research highlights the feasibility of information flow measure analysis in fusion studies. Applications of different entropy-based complexity measures are explored and this work sheds light on the capabilities, added value and limitations of these techniques. This investigation presents the integration of information flow measures to gain deeper understanding of plasma transport phenomena, by providing an approach to fast systematic data mining suited for real-time analysis. This work paves the way for further development and implementation of information-theoretic methods for plasma data analysis.
In summary, this research highlights the gained insight on CERC transitions, while showcasing the feasibility, added values and limitations of information flow measure analysis for fusion studies, to induce theory based analysis revealing new insights in fundamental, stellarator-specific transport mechanisms.
This thesis describes how the data of the Langmuir probes in the Wendelstein 7-X (W7X) Test Divertor Unit (TDU) were evaluated, checked for consistency with other diagnostics and used to analyse plasma detachment.
Langmuir probes are an electronic diagnostic, and were among the first to be used in plasma physics to determine particle fluxes, potentials, temperatures and densities.
W7X is a large, advanced stellarator, magnetic confinement fusion experiment, operated at the Max-Planck-Institut for Plasma Physics(IPP) in Greifswald, Germany.
Its TDU is an uncooled graphite component, shaped and positioned to intercept the convective heat load of the plasma.
Detachment describes a desirable operation state of strongly reduced loads on this component.
The evaluation of Langmuir probe data relies heavily on models of the sheath, formed at the interface between plasma and a solid surface, to infer plasma parameters from the directly measured quantities.
Multiple such models are analysed, generalised, and adapted to our use case.
A detailed comparison is made to determine the most suitable model, as this choice strongly affects the predicted parameters.
Special attention is paid to uncertainties on the parameters, which are determined using a Bayesian framework.
From the inferred parameters, heat and particle fluxes are calculated.
These are also indirectly measured by two other, camera-based diagnostic systems.
Observations are compared to test the validity of assumptions and calculations in the evaluation of all three diagnostics by checking their results for consistency.
The first comparison, with the infrared emission camera system, shows good agreement with theoretical predictions and reported measurements of the sheath transmission factor, for which we derive and measure a value in W7X.
Parameter dependencies in the quality of this agreement hint at remaining issues.
The second comparison, with the Hydrogen alpha photon flux camera system, shows significant discrepancy with expectations.
These are argued to originate from systematic differences in the measurement locations, which are quantified and related to the magnetic topology.
Langmuir probe observations of individual discharges are analysed to discuss conditions under which detachment occurs, transition into that state and fluctuations observed prior to and during it.
A spatial parametrisation of the data is developed and used to facilitate this.
These observations contribute to the larger aim of understanding particle balance control and fusion plasma edge processes.
An experimental investigation of particle parallel flows has been carried out at Wendelstein 7-X (W7-X), one of the most advanced stellarators in the world. The studies are restricted to the outermost plasma region, the scrape-off layer (SOL), which is shaped to tackle the exhaust problem in vision of future fusion reactors based on plasma magnetic confinement. The aim of the measurements is to set the basis for a physics analysis of the SOL dynamics by obtaining direct information on convective heat transport, together with the assessment of the predominant flow directions of the main plasma ions and of fusion-products or wall-released impurities. In this way, a better comprehension of the interplay between the transport parallel and perpendicular to the SOL field lines can be achieved, contributing to the understanding of the effectiveness of the island divertor configuration.
The chosen instrument for the experimental studies is the Coherence Imaging Spectroscopy (CIS) diagnostic, a camera-based interferometer capable of measuring 2D Doppler particle flows associated with a selected visible line from the plasma. The diagnostic is distinguished by its high time resolution and spatial coverage, allowing the visualisation and measurements of flow velocities for a full module of W7-X simultaneously. A CIS diagnostic has been fully designed for W7-X with an improved level of accuracy achieved thanks to the implementation of a new calibration source, a continuous-wave-emission tunable laser. The laser allowed a full characterization of the diagnostic and a frequent precise calibration, making the CIS system reliable for parallel flow investigations during the operational campaign OP1.2. The validity and importance of the CIS measurements have been further confirmed with dedicated simulation of the SOL plasma parameters by the EMC3-EIRENE code, and by comparisons with other edge diagnostics. The CIS results show the effects related to dynamical changes in the SOL due to impurity gas puffs or the development of a plasma current. Moreover, CIS can be used as a powerful tool to test the limits of the current theoretical models, for example in the case of forward and reversed field experiments.
In der vorliegenden Arbeit wurde die Argon Plasma Quelle „MiniJet-R“ von HHF-Elektronik, Aachen, auf ihre Eignung als medizinischer CAP-Generator und ihre Emission von UVC-Strahlung und NO2 untersucht. Dabei wurde die Emission von UVC-Strahlung auf ihre Abstandsabhängigkeit und ihre Winkelverteilung vermessen. Die UVC-Intensität nimmt im für Entfernungen bis ca. einer Plasmaflammenlänge weniger schnell als 1/r² ab. Erst ab Entfernungen die ca. zwei Plasmaflammenlängen entsprechen nimmt die UVC-Intensität mit 1/r² ab. Die Intensität ist über alle Winkel gleich verteilt, bis eine durch den apparativen Aufbau der Quelle bedingte Abschattung bei Winkeln ab 85° einsetzt. Weiter wurde die Abhängigkeit der UVC-Intensität von den Betriebsparametern Argon Gasdurchfluss und Power Level untersucht. Dabei wurde gezeigt, dass die UVC-Intensität mit steigendem Gasdurchfluss abnimmt. Bei der Charakterisierung der Power Level – Abhängigkeit zeigte sich, dass die UVC-Intensität bei Power Level 3 ein Minimum hat. Zur näheren Bestimmung der UVC-Strahlung des Plasmas wurde das Spektrum des Plasmas von 168nm bis 275nm aufgenommen. Durch den Vergleich des gemessenen Spektrums und eines berechneten NO-Spektrums konnte NO als Hauptquelle der UVC-Strahlung nachgewiesen werden. Mittels Chemilumineszens-Messung konnte außerhalb des Plasmas NO2 als verbleibende Komponente identifiziert werden, während NO nur in vernachlässigbaren Konzentrationen außerhalb des Plasmas nachweisbar war. In weiteren Messungen wurde die NO2-Erzeugung des Plasmas in Abhängigkeit der Betriebsparameter Gasdurchfluss und Powerlevel sowie die NO2-Konzentration in der Raumluft in Abhängigkeit vom Abstand und von der Richtung zum Plasma bestimmt. Dabei wurde nachgewiesen, dass bei ausreichendem Abstand zum Plasma die NO2-Konzentration unterhalb des Arbeitsplatzgrenzwertes liegt. Unter ungünstigen Betriebsbedingungen und in unmittelbarer Umgebung konnten allerdings auch erheblich höhere Konzentrationen festgestellt werden. Die gemessenen UVC-Intensitäten und NO2-Konzentrationen werden mit den geltenden Maximalwerten unter dem Aspekt der Arbeitsplatzsicherheit verglichen. Abschließend erfolgt eine Beurteilung der CAP-Quelle „Minijet-R“ und eine Beschreibung einer idealen CAP-Quelle.
The importance of ion propulsion devices as an option for in-space propulsion of space
crafts and satellites continues to grow. They are more efficient than conventional chemi-
cal thrusters, which rely on burning their propellant, by ionizing the propellant gas in a
discharge channel and emitting the heavy ions at very high velocities. The ion emission
region of a thruster is called the plume and extends several meters axially and radially
downstream from the exit of a thruster. This region is particularly important for the effi-
ciency of a thruster, because it determines energy and angular distribution of the emitted
ions. It also determines the interaction with the carrier space craft by defining the electric
potential shape and the fluxes and energies of the emitted high energy ions, which are the
key parameters for sputter erosion of satellite components such as solar panels. Developing
new ion thrusters is expensive because of the high number of prototypes and testing cycles
required. Numerical modeling can help to reduce the costs in thruster development, but
the vastly differing length and time scales of the system, particularly the large differences of
scales between the discharge chamber and the plume, make a simulation challenging. Often
both regions are considered to be decoupled and are treated with different models to make
their simulation technically feasible. The coupling between channel and plume plasmas and
its influence on each other is disregarded, because there is no interaction between the two
regions. Therefore, this thesis investigates the physical effects which arise from this cou-
pling as well as models suitable for an integrated simulation of the whole coupled problem
of channel and plume plasmas. For this purpose the High Efficiency Multistage Plasma
Thruster (HEMP-T) ion thruster is considered.
For the discharge channel plasma, a fully kinetic model is required and the Particle-in-Cell
(PIC) method is applied. The PIC method requires very high spatial and temporal resolu-
tions which makes it computationally costly. As a result, only the discharge channel and the
near-field plume close to the channel exit can be simulated. In the channel, the results show
that electrons are magnetized and follow the magnetic field lines. The orientation of the
magnetic field there is mostly parallel to the symmetry axis and the channel walls which re-
sults in a high parallel electron transport and leads to a flat electric potential and a reduced
plasma-wall sheath. Only at the magnetic cusps, which are characteristic of HEMP-Ts the
electrons are guided towards the wall, with ions following due to quasineutrality, where a
classical plasma-wall sheath develops. The ion-wall contact is thus limited to the cusp re-
gion. The small radial drop of the potential towards the wall gives rather low energies of
ions impinging at the wall and minimizes erosion in the HEMP-T.
In the near-field plume, which extends from the thruster exit plane to some centimeters
downstream, the ion emission characteristics is defined. The ratio of radial and axial elec-
tric field components in this region determines the ion emission angle which should be
minimized for maximum thruster efficiency. The plasma discharge in the channel produces
high plasma densities and the subsequent drop from plasma to vacuum potential occurs
further downstream for higher densities. This increases the ratio of radial and axial electric
field components because the plasma expands radially outside of the confinement from the
dielectric discharge channel walls. The potential structure in the near-field plume impacts
also the supply of electrons for the channel discharge because the electrons enter the channel
from the plume. An effect which arises from this coupling is the breathing mode oscilla-
tion. It is an oscillation which is observed in all plasma quantities and is located near the
thruster exit. The oscillation frequency measured in the simulation is in good agreement
with a predator-prey estimate which validates this ansatz. However, the electron tempera-
ture, assumed constant in the predator-prey model, correlates inversely with the oscillation,
i.e. it is minimal at the current maximum and vice versa, which contributes to the observed
oscillations. Because of the oscillation of the plasma number density, the potential drop also
oscillates in the exit region and thus the ratio of radial to axial electric field components,
which results in the oscillation of the mean ion emission angle.
Regarding suitable models for a combined simulation of channel and plume plasmas, the
PIC model for channel and near-field plume is explicitly coupled to a hybrid fluid-PIC
model for the plume. The latter treats the electrons as a fluid, hence increasing the effective
spatial and temporal resolutions which can be applied in the plume simulations at the cost
of reduced accuracy of the electron model. Plasma densities decrease by two orders of
magnitude two meters downstream from the channel exit. The explicitly coupled kinetic
and hybrid PIC models are well suited for the computation of a HEMP-T and its plume
expansion, but they disregard the coupling of channel and plume plasmas for which other
methods are necessary. For this purpose a new approach is presented with a proof-of-
principle validation. The limited spatial resolution in the plume can be overcome with the
mesh-coarsening method, which increases the resolution in regions of low plasma density
without numerical artifacts. Sub-cycling for the electrons in the plume can then be used
to increase the temporal resolution in the plume. The combination of both methods, called
the sub-cycling mesh-coarsening (SMC) algorithm in the scope of this work, promises high
savings in computational cost which can make a combined simulation of plume and channel
plasmas feasible.
With this thesis, studies which form the bedrock for the long term goal of first wall heat load control and optimization for the advanced stellarator Wendelstein 7-X are developed, described and put into context. It is laid out how reconstruction of features of the edge magnetic field from plasma facing component heat loads is an important first step and can successfully be achieved by artificial neural networks. A detailed study of plasma facing component heat load distribution, potential overloads and overload mitigation possibilities is made in first order approximation of the impact of the main plasma dynamic effects.
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.
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.
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.
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.
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.
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.
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.
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.
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 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.
Die vorliegende Arbeit liefert Beiträge zur optischen und elektrischen Charakterisierung des dynamischen Verhaltens von Plasmaspezies in Atmosphärendruck-Plasmen insbesondere mit Hinsicht auf den Einsatz in der Plasmamedizin. Dabei wurde ein breites Spektrum verschiedener Diagnostiken angewandt, um die Zugänglichkeit zur Bestimmung weiterer Plasmaparameter an Atmosphärendruck zu prüfen. Diese Arbeit stellt eine neue Methode zur Bestimmung der Ionendichte bei Atmosphärendruck- Bedingungen vor, bei der elektrische Oszillationen ausgewertet werden, deren Ursprung ionenakustische Wellen im Plasma sind. Weiterhin wurden neben relativen optischen Messungen wie der phasenaufgelösten optischen Fotografie (PROI) und der Kreuz- Korrelations-Spektroskopie (CCS) auch absolute optische Messungen mit der interferometrischen Hakenmethode und dem Pockels-Effekt durchgeführt. Anhand von elektrischen Messungen wurde ferner gezeigt, dass mit einer Strom- und Spannungs-Charakteristik der Einfluss von Aufbauparametern, wie der Kapillarposition oder dem Gasfluss, auf das Plasma untersucht werden kann. Gegenstand der Untersuchungen waren verschiedene Plasmaquellen, die für eine Nutzung in der Plasmamedizin entwickelt wurden. Sowohl die elektrischen Messungen des Parametereinflusses als auch die Bestimmung der Ionendichte erfolgten an der selbstpulsenden transienten Funkenentladung in Argon an offener Atmosphäre. Der geringe Filamentdurchmesser und der dennoch hohe Entladungsstrom ermöglichen die Detektion der ionenakustischen Instabilität. Darüber hinaus wurde diese erratisch zündende Entladung räumlich und zeitlich aufgelöst mit der CCS spektroskopisch untersucht. Dabei wird insbesondere die Selbst-Triggerung der CCS ausgenutzt, um einen Zeitbezug trotz des großen Entladungsjitter zu erhalten. Für die PROI wurden die räumlich und zeitlich stabilen Entladungsanordnungen der Nadel-Platte-Geometrie und des Kapillarjets in Helium gewählt. Die Anordnungen wurden mit einer periodischen Sinusspannung betrieben und wiesen Entladungsspalte von d = 5 - 15 mm auf. Eine besondere Anforderung der Messung mit dem Pockels-Effekt ist zu der räumlichen und zeitlichen Stabilität eine dielektrische Gegenelektrode, welche bei der Anordnung des Kapillarjets möglich war. Bei der Anwendung der interferometrischen Hakenmethode kam neben einem Erdgas-Sauerstoff-Mischgasbrenner sowohl eine Mikrowellen-Entladung (Plexc) als auch ein MHz-Plasmajet (kINPen) zur Anwendung. Die Bedeutung der elektrischen Messungen, besonders der Strom- und Spannungscharakteristik einer Entladung, wurde an dem Parametereinfluss der Kapillarposition einer erratisch zündenden transienten Funkenentladung vorgestellt. Es konnte gezeigt werden, dass der Zeitunterschied zwischen dem Stromsignal eines Vorstreamers und der Hauptentladung durch das Einbringen einer Kapillare in den Entladungsspalt deutlich verringert wird. Insbesondere der Beitrag der lokalen elektrischen Feldstärkeerhöhung an der Kapillarkante und der Diffusionsanteil der Umgebungsluft wurden als Ursachen, durch Vergleich einer Feldsimulation mit der Beobachtung der Vorphase an der Kapillarkante in den CCS-Messungen, diskutiert. Anschließend konnte gezeigt werden, dass der Leistungseintrag in die Vorphase durch die Platzierung der Kapillare deutlich reduziert werden kann. Ein wesentliches Ergebnis dieser Arbeit ist die Beobachtung von ionenakustischen Wellen als Oszillationen im Abklingen des Stromsignals einer erratisch zündenden transienten Funkenentladung. Hierzu war es nötig, elektrische Störungen zu erkennen und zu eliminieren. Es konnte ein Erdschleifen-freier Aufbau realisiert werden. In diesem Aufbau zeigt sich, dass die Signale der ionenakustischen Welle ausschließlich in einem bestimmten Gasflussbereich beobachtet werden. Die gemessene Frequenz der Oszillationen wurde als Ionenplasmafrequenz f_{pl ,i} identifiziert und enthält daher Angaben zu den Ionendichten im Bereich von n_{Ar_2^+} = 3•10^{14} cm^{-3} bis 1•10^{12} cm^{-3}. Nach einer Abschätzung der zu erwartenden Elektronendichte, die der gemessenen Ionendichte sehr nahe kommt, wurde die Dispersionsrelation für die vorhandenen Entladungsbedingungen aufgestellt und gelöst. Dabei zeigt sich eine starke zeitliche Dämpfung über die Ionen-Neutralteilchenstöße sowie eine räumliche Verstärkung für die Ionenplasmafrequenz. Aus der Dämpfung der Oszillationsamplituden konnte die Ionen- Neutralteilchen-Stoßfrequenz nu_i = 3•10^7 Hz ermittelt werden. Weiterhin ergibt sich aus der Lösung der Dispersionsrelation ein Existenzbereich für die ionenakustischen Wellen in Abhängigkeit von der Ionendichte und der elektrischen Feldstärke.
Diese Dissertation beschäftigt sich mit der Erzeugung von edelmetallfreien Katalysatoren für die Sauerstoffreduktion in Brennstoffzellen. Dabei wird ein neuartiger, dualer Plasmaprozess entwickelt, aufgebaut und die so-erzeugten Schichten mit verschiedenen elektrochemischen (CV, RDE und RRDE) und strukturanalytischen Methoden (SEM, EDX, IR, XPS, Leitfähigkeit, XRD, NEXAFS, EXAFS und TEM) untersucht. Auf diese Weise ist es erstmalig gelungen edelmetallfreie Katalysatoren mit einem Plasmaprozess herzustellen, ohne dass eine zusätzliche Pyrolyse benötigt wird. Die katalytische Aktivität der Schichten ist außerdem deutlich höher als die von rein chemisch hergestellten Metall–Polypyrrol-Schichten.
The confinement of energy has always been a challenge in magnetic confinement fusion devices. Due to their toroidal shape there exist regions of high and low magnetic field, so that the particles are divided into two classes - trapped ones that are periodically reflected in regions of high magnetic field with a characteristic frequency, and passing particles, whose parallel velocity is high enough that they largely follow a magnetic field line around the torus without being reflected. The radial drift that a particle experiences due to the field inhomogeneity depends strongly on its position, and the net drift therefore depends on the path taken by the particle. While the radial drift is close to zero for passing particles, trapped particles experience a finite radial net drift and are therefore lost in classical stellarators. These losses are described by the so-called neoclassical transport theory. Recent optimised stellarator geometries, however, in which the trapped particles precess around the torus poloidally and do not experience any net drift, promise to reduce the neoclassical transport down to the level of tokamaks. In these optimised stellarators, the neoclassical transport becomes small enough so that turbulent transport may limit the confinement instead. The turbulence is driven by small-scale-instabilities, which tap the free energy of density or temperature gradients in the plasma. Some of these instabilities are driven by the trapped particles and therefore depend strongly on the magnetic geometry, so the question arises how the optimisation affects the stability. In this thesis, collisionless electrostatic microinstabilities are studied both analytically and numerically. Magnetic configurations where the action integral of trapped-particle bounce motion, J, only depends on the radial position in the plasma and where its maximum is in the plasma centre, so-called maximum-J configurations, are of special interest. This condition can be achieved approximately in quasi-isodynamic stellarators, for example Wendelstein 7-X. In such configurations the precessional drift of the trapped particles is in the opposite direction from the direction of propagation of drift waves. Instabilities that are driven by the trapped particles usually rely on a resonance between these two frequencies. Here it is shown analytically by analysing the electrostatic energy transfer between the particles and the instability that, thanks to the absence of the resonance, a particle species draws energy from the mode if the frequency of the mode is well below the charateristic bounce frequency. Due to the low electron mass and the fast bounce motion, electrons are almost always found to be stabilising. Most of the trapped-particle instabilities are therefore predicted to be absent in maximum- J configurations in large parts of parameter space. Analytical theory thus predicts enhanced linear stability of trapped-particle modes in quasi-isodynamic stellarators compared with tokamaks. Moreover, since the electrons are expected to be stabilising, or at least less destabilising, for all instabilities whose frequency lies below the trapped-electron bounce frequency, other modes might benefit from the enhanced stability as well. In reality, however, stellarators are never perfectly quasi-isodynamic, and the question thus arises whether they still benefit from enhanced stability. Here the stability properties of Wendelstein 7-X and a more quasi-isodynamic configuration, QIPC, are investigated numerically and compared with another, non-quasiisodynamic stellarator, the National Compact Stellarator Experiment (NCSX) and a typical tokamak. In gyrokinetic simulations, performed with the gyrokinetic code GENE in the electrostatic and collisionless approximation, several microinstabilities, driven by the density as well as both ion and electron temperature gradients, are studied. Wendelstein 7-X and QIPC exhibit significantly reduced growth rates for all simulations that include kinetic electrons, and the latter are indeed found to be stabilising when the electrostatic energy transfer is analysed. In contrast, if only the ions are treated kinetically but the electrons are taken to be in thermodynamic equilibrium, no such stabilising effect is observed. These results suggest that imperfectly optimised stellarators can retain most of the stabilising properties predicted for perfect maximum-J configurations. Quasi-isodynamic stellarators, in addition to having reduced neoclassical transport, might therefore also show reduced turbulent transport, at least in certain regions of parameter space.
There is a wide variety of Alfvén waves in tokamak and stellarator plasmas. While most of them are damped, some of the global eigenmodes can be driven unstable when they interact with energetic particles. By coupling the MHD code CKA with the gyrokinetic code EUTERPE, a hybrid kinetic-MHD model is created to describe this wave–particle interaction in stellarator geometry. In this thesis, the CKA-EUTERPE code package is presented. This numerical tool can be used for linear perturbative stability analysis of Alfvén waves in the presence of energetic particles. The equations for the hybrid model are based on the gyrokinetic equations. The fast particles are described with linearized gyrokinetic equations. The reduced MHD equations are derived by taking velocity moments of the gyrokinetic equations. An equation for describing the Alfvén waves is derived by combining the reduced MHD equations. The Alfvén wave equation can retain kinetic corrections. Considering the energy transfer between the particles and the waves, the stability of the waves can be calculated. Numerically, the Alfvén waves are calculated using the CKA code. The equations are solved as an eigenvalue problem to determine the frequency spectrum and the mode structure of the waves. The results of the MHD model are in good agreement with other sophisticated MHD codes. CKA results are shown for a JET and a W7-AS example. The linear version of the EUTERPE code is used to study the motion of energetic particles in the wavefield with fixed spatial structure, and harmonic oscillations in time. In EUTERPE, the gyrokinetic equations are discretized with a PIC scheme using the delta-f method, and both full orbit width and finite Larmor radius effects are included. The code is modified to be able to use the wavefield calculated externally by CKA. Different slowing-down distribution functions are also implemented. The work done by the electric field on the particles is measured to calculate the energy transfer between the particles and the wave and from that the growth rate is determined. The advantage of this approach is that the full magnetic geometry is retained without any limiting assumptions on guiding center orbits. Extensive benchmarks have been performed to test the new CKA-EUTERPE code. Three tokamak benchmarks are presented, where the stability of TAE modes are studied as a function of fast particle energy, or in one case as a function of the fast particle charge. The benchmarks show good agreement with other codes. Stellarator calculations were performed for Wendelstein 7-AS and the results demonstrate that the finite orbit width effects tend to be strongly stabilizing.