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- Plasma , Plasmaphysik , Tokamak , Stellarator , Magnetohydrodynamik , Kinetische Theorie , Simulation , AlfvÃ©n-Welle , Energiereiches Teilchen (1)
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#### Institute

- Institut fÃ¼r Physik (7) (remove)

This dissertation focusses on the numerical modelling of resonant destabilization of AlfvÃ©n eigenmodes by fast ions in fusion plasmas. It especially addresses non-linear simulations of stellarator plasmas in which particle collisions are retained. It is shown that collisions are required for a realistic description of AlfvÃ©n waves in plasmas relevant to nuclear fusion.
We start by carefully verifying the implementation of the collision operators into the electromagnetic version of the gyro-kinetic delta-f particle-in-cell code EUTERPE. After these initial benchmarks are completed successfully, the code is in a position to be applied to realistic tokamak and stellarator scenarios.
Since every collision operator needs to fulfil conservation laws, a momentum-conserving version of the pitch-angle scattering operator is implemented. This is in particular important for neoclassical transport simulations aimed at computing flux-surface variations of the electrostatic potential in stellarators.
Using the simplified CKA-EUTERPE model (employing a fixed-mode-structure approximation), we perform non-linear simulations in tokamaks and stellarators. We show that the non-linear dynamics of fast-ion-driven AlfvÃ©n eigenmodes is significantly influenced by collisions. They have the potential to enhance the saturation level and to affect the frequency chirping of the modes.
It is thus concluded that collisions play an essential role in determining AlfvÃ©n-eigenmode-induced fast-ion transport - an important issue for future fusion devices. In order to address this issue the CKA-EUTERPE model is extended to evolve multiple modes at the same time. First results of this multi-mode version (which enhances the level of realism of the simulations) are shown in the Appendix of the thesis.

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.

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 â—¦ and 90 â—¦ . 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.

Manipulating and utilizing plasmas becomes a more and more important task in various research fields of physics and in industrial developments. Especially in nowadays spacerelevant applications there are different ideas to modify plasmas concerning particular tasks.
One major point of interest is the ability to influence plasmas using magnetic fields. To study the underlying physical effects that were achieved by these magnetic fields for both scenarios Particle-in-Cell simulations were done. Two examples are discussed in this thesis.
The first example originates from an experiment performed by the European Space Agency ESA in collaboration with the German Space Agency DLR. To verify the possibility of heat-flux reduction by magnetic fields onto the thermal protection system of a space vehicle a simplified experiment on earth was developed. Most of the heat that is created during re-entry comes from compression of the air ahead of the hypersonic vehicle, as a result of the basic thermodynamic relation between temperature and pressure. The shock front, which builds up in front of the vehicle deflects most of the heat and prohibits the surface of the space vehicle from direct contact with the maximum flux. State of the art spacecrafts use highly developed materials like ceramics to handle the enormous heat. An attractive approach to reduce costs is to use magnetic fields for heat-flux reduction. This would allow the use of cheaper materials and thus reduce costs for the whole space mission. A partially-ionized Argon beam was used to create a certain heat-flux onto a target. The main finding of the experimental campaign was a large mitigation of heat-flux by applying a dipole-like magnetic field. The Particle-in-Cell method was able to reproduce experimental observations like the heat-flux reduction. An additionally implemented optical diagnostics module allowed to confirm the results of the spectroscopy done during the experiment. The underlying effect that is responsible for the heat-flux reduction was identified as a coupling between the modified plasma and the dominating neutral flux component. The plasma, that is guided towards the target, act as a shield in front of the target surface for arriving neutrals. These neutrals are slowed down by charge-exchange collisions. Furthermore the magnetic field induces an increased turbulent transport that is also needed to reach a reduction in heat-ux. The turbulent transport was also obtained by three-dimensional Direct Simulation Monte Carlo simulations. Unfortunately, such source driven turbulence can not be expected in space, so that a heat flux reduction in real space applications is questionable. Nevertheless, other effects like the induced turbulence by the rotating vehicle can compensate the missing source driven effect.
The second scenario in which a magnetic field is used to modify the heat flux of a plasma is the operation of the pulsed cathodic arc thruster. The same Particle-in-Cell code was used to simulate a typical pulse of this newly developed thruster of Neumann Space Pty Ltd. The typical behavior of the thruster could be reproduced numerically. The thrust is mainly produced by fast electrons. These electrons are accelerated by electric fields as a result of a plasma-beam instability. This plasma-beam instability was verified by a phase space diagnostics for the electrons. To demonstrate the influence of the magnetic field a simulation of the cathodic arc thruster without magnetic field and one with magnetic field were compared. It was shown that the use of a magnetic field leads to a ten times larger thrust by directing the heat ux. The resulting narrow plume is an additional Advantage of the particle guiding magnetic field. This narrowness of the plume reduces the danger of interaction with other components of the space vehicle.
Both scenarios demonstrate the different capabilities for electromagnetic fields to manipulate plasmas and especially the corresponding heat-flux with respect to certain tasks. The possibilities range from reducing the heat-flux onto a target to maximizing the thrust by directing the heat-ux. This thesis demonstrates that simulations are a great tool to support experiments and to deliver an improved physics understanding. They help to identify the basic physics principles in the different systems, because they can deliver information not accessible to experiments.
In particular, a better understanding of the influence of electromagnetic fields on the heat-flux distribution in space-relevant applications was obtained. This can be the basis for further simulation-guided optimization, e.g. for the design of more effective cathodic arc thrusters. Here, the goal is to minimize costs for prototypes by replacing the hardware by virtual prototypes in the simulations. This allows to test basic design ideas in advance and get more highly-optimized designs at a fraction of time and costs.

This work study a monolayer of branched poly(ethyleneimine (PEI) adsorbed onto oppositely charged surfaces with iron chelates or iron ions in the absorption solution. The conformation of adsorbed PEI is explored in the dependence of the composition of the adsorption solution by measuring the surface forces using atomic force microscopy (AFM) with the colloidal probe (CP) at different ionic strengths (INaCl) in surrounding aqueous solution. The surface coverage of these layers is investigated using X-ray reflectivity.
PEI solutions show different pH values with iron chelates (pH = 3), iron ions (pH = 4.67) or pure water (pH = 9.3) at room temperature. Low surface coverage of PEI at pH = 3 adjusted by monovalent ions was also observed. However, adsorbing PEI with iron ions or iron chelates and washing with pure water shifts the pH, leading to an adsorbed PEI layer with high coverage. In our observation, the influence of iron ions and iron chelates on the surface coverage of PEI film is stronger than the pH effect. PEI adsorbed from a pure water solution shows flat conformation. Surface force measurements with CP show that PEI adsorbed from solutions containing iron chelates or iron ions cause almost identical steric forces. The thickness of the brush L is determined as a function of the ionic INaCl in the measuring solution. It scales as a polyelectrolyte brush.
The maximum number density of gold nanoparticles (AuNPs) adsorbed onto the PEI brushes was identical and larger than on flatly adsorbed PEI. On the PEI layer with the larger surface coverage, the AuNPs aggregate; on the PEI layer with the lower surface coverage they do not aggregate. Taken together, these results contribute to understanding the mechanisms determining surface coverage and conformation of PEI and demonstrate the possibility of controlling surface properties, which is highly desirable for potential future applications.
In this thesis, we also investigate the top layer (PSS and PDADMA) of polyelectrolyte multilayer (PEM) films. PEM films were prepared by sequential adsorption of oppositely charged PEs on solid substrates. PEM films consist of polydiallyldimethylammonium (PDADMA) as polycation and the polystyrene sulfonate (PSS) as polyanion. PDADMA has a smaller linear charge density than PSS. For this system, two different growth regimes are known: parabolic and linear. I studied the top layer (PSS and PDADMA) conformation of PEM films and how the structure of this top layer is affected by increasing the number of PDADMA/PSS layer pairs N and the addition of salt to the surrounding solution.
The INaCl was changed during the force-distance measurements. PSS terminated films always show electrostatic forces at INaCl < 0.1 M and flat conformation. The surface charge density is always negative at INaCl < 0.1 M. The surface charge of the PSS top layer starts to turn from negative to positive at N â‰¥ 14. At N between 13 and 15, adsorbed PSS cannot compensate all the excess PDADMA charge. This leads to an accumulation of the positive extrinsic sites within the PSS terminated film beyond a specific N. At INaCl â‰ˆ 0.1 M, an exponential decaying force was measured. This is an indication of unusual long-ranged hydration force (decay length Î»-1 â‰ˆ 0.2-0.5 nm), and PSS terminated film shows zwitterionic or neutral surface. At INaCl > 0.1 M, a non-electrostatic action occurs and the PSS terminated film reswells in solution.
PDADMA terminated surface consisting of few layers show a flat conformation and the electrostatic forces were measured. For N â‰¥ 9 and INaCl â‰¤ 0.1 M, steric forces were measured. The force-distance profiles are well-explained by Alexander and de Gennes theory. PDADMA chains show a maximum L that is around 40-45 % of the contour length. For INaCl â‰ˆ 0.1 M, and N > 9, a flat, neutral or zwitterionic surface is found (Î»-1 â‰ˆ 0.3-0.9 nm). For N = 9 and INaCl > 0.1 M, a strong screening of electrostatic interaction and attractive forces are observed. For N > 9 and INaCl > 0.1 M, the ion adsorption into the PE chains leads to an increase in the monomer size and as a result, the L increases and PDADMA brushes reswell again into the solution.
These data show that by varying N and INaCl, different surface forces can be obtained: Electrostatic forces (flat chains) both positive and negative, steric forces (brush), hydration force (flat, neutral or zwitterionic surface), and effects not yet explained (reswelling brush).

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.