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Kinetic modeling and infrared spectroscopy of charge carriers across the plasma-wall interface
(2022)
In this thesis, charge transport at the plasma-wall interface is investigated theoretically, on a semiclassical, microscopic level. Based on the Boltzmann and Poisson equations a set of equations is derived and numerically solved to model charge carriers both within a semiconducting wall and a gaseous plasma in front of it. While the plasma is considered collision-free, within the solid, phonon collisions, as well as recombination processes between conduction band electrons and valence band holes are considered. This results, for the first time, in a self-consistent modeling of both the gaseous electron-ion plasma and the electron-hole plasma in the solid on the same footing. Utilizing specific approximations for different physical scenarios, numerical solutions are presented both for the floating and the electronically contacted (biased) interface. In the latter case, the current voltage characteristic is calculated and shown to heavily depend on the charge kinetics within the wall.
Furthermore, we present optical methods to measure the wall charge noninvasively. These utilize the influence of the deposited surplus charges on the optical reflection coefficient of the surface. By calculating the optical response of these charges, we show that the magnitude of the surface charge can be inferred from the change in the reflectivity of the surface caused by the presence of the plasma. While nonlocal effects are considered, it is shown analytically and numerically that these can be neglected at the scales of the considered physical systems.
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.
In this work, we theoretically investigate both aspects of charge-transferring atom-surface collisions: local-moment-type correlations and emission of secondary electrons from surfaces. Ideally, one chooses an approach that keeps as many electronic and lattice degrees of freedom at an ab-initio level as possible. In practice, however, this sophistication is hard to maintain. In this work, we do not aim to perform a description from first principles which could utilize density functional theory or quantum-chemical techniques. Instead, we keep only the most important degrees of freedom of the scattering process and use effective models for them. These are basically the Anderson-impurity model leading to time-dependent Anderson-Newns Hamiltonians and Gadzuk’s semiempirical approach to describe the projectile-target interaction from classical image shifts. In direct comparison with the description from first principles, the semiempirical approach offers a flexible basis for the modeling of a great variety of projectile-target combinations. The addition of further effective models to increase the general quality of the results is possible since the approach is very modular. The clear physical interpretation of each effective model, as well as the requirement for only a few and generally available parameters are further advantages of this approach. Rewritten in terms of Coleman’s pseudo-particle operators, the model is then numerically analyzed. This is done within a non-crossing approximation for the hybridization self-energies which are utilized by contour-ordered Green functions for each relevant electronic state of the projectile.
In this doctoral thesis, algorithms are presented that are designed for the investigation in the mesopause region between the upper Mesosphere and Lower Thermosphere (MLT). The photochemical models are proposed and applied to represent the oxygen airglow and the oxygen photochemistry in the MLT. Atomic oxygen, O, in the ground state, O(3P), is of special interest because it is a reactive trace gas actively contributing to the Earth’s airglow. The retrievals of O(3P) concentrations, [O(3P)], are based on the nightglow time series of the green line emission measured remotely as in the first part of this thesis and the individual profiles of multiple nightglow emissions of O and molecular oxygen (O2) measured in situ as in the second part of this thesis. To process the complete spectral time series measured by using the satellite-borne instrument SCIAMACHY (SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY), an intricate set of algorithms is developed and applied with the regularized total least squares minimization approach to estimate a set of the optimal regularization parameters and to retrieve a corresponding set of vertical Volume Emission Rate (VER) profiles. Furthermore, these algorithms take emissions of another origin and the Earth's shape into account. Considering not identified states of O2, the established photochemical models are adjusted resulting in two model modifications. Both model modifications are employed to retrieve the [O(3P)] time series on the basis of the VER time series in the MLT. The model input parameters vary in the atmosphere that motivated to propose these two model modifications and to employ available sources of the input parameters. One semi-empirical model, one general circulation model and the satellite-borne instrument SABER (Sounding of the Atmosphere using Broadband Emission Radiometry) are employed as sources of the reference [O(3P)] and input parameters time series. The SABER instrument employed as a source of the input parameters is preferred according to the comparison of the retrieved and reference [O(3P)] time series. Studying the impact of the 11-year solar cycle on O(3P) in the MLT, an algorithm is developed and applied with the Levenberg-Marquardt algorithm to estimate the optimal fit parameters step-wise. The results of the O(3P) sensitivity analysis obtained with respect to the solar activity forcing at the 11 year and 27 day time scales and the lunar gravitational forcing agree with the reference model simulations. The hypothesis regarding vertical shifts between different of Meinel bands at least partly caused by the hydroxyl radical (OH*) quenching with O(3P) is confirmed experimentally. Based on the conclusion drawn in the first part of this thesis that the data sets’ self-consistency is high as for the averaged SABER and SCIAMACHY measurements, a comprehensive set of available data with a higher level of the data sets’ self-consistency is employed in the second part of this thesis. Multiple airglow emissions measured in situ during four campaigns are employed to propose the Multiple Airglow Chemistry (MAC) model. Processed emissions are the Herzberg I, Chamberlain, Atmospheric and Infrared Atmospheric band emissions of O2 and the green line emission of O. Considering all widely known and additionally complemented reactions, the MAC model is proposed to represent the oxygen airglow and the oxygen photochemistry in the MLT. The presented MAC model is based on the hypothesis of Slanger et al. (2004) stating that higher excited states of O2 are coupled with each other through vibronic de-excitation caused by collisions among molecules of this group of O2 states in the MLT. This hypothesis is modified excluding the singlet Herzberg state of O2 from the group of O2 states considered by Slanger et al. (2004). The MAC calculations are carried out sequentially starting with higher excited O2 states to provide the retrieved output concentrations of these O2 states as the input concentrations to the next calculation steps. The final step is only based on concentrations of all species, whereas each of the earlier steps is based on a corresponding VER profile besides of the input concentrations. The oxygen photochemistry in the MLT is represented by all species considered at the final step that makes it possible to adopt the MAC reactions in a general circulation model. Four modifications of the MAC model, i.e. including or excluding the triplet Herzberg states of O2 and including or excluding ozone and odd hydrogen (hydrogen, OH* and hydroperoxy radical), lead to negligible differences in the retrieved [O(3P)] profiles. Based on the MAC calculations verified and validated on the basis of the four rocket campaigns, one of the effective modifications of the MAC model (excluding the triplet Herzberg states of O2, ozone and odd hydrogen) is further reduced to the most effective modification. This implies that for the [O(3P)] retrieval only the O2 Atmospheric band emission, temperature and concentrations of molecular nitrogen (N2) and O2 are sufficient to apply. Calculations carried out by using the most effective modification of the MAC model are verified and validated on the basis of self-consistent in situ measurements obtained simultaneously. The MAC model enables identifying precursors of (1) the three lowest O2 valence states and (2) the second excited O state responsible for (1) the Atmospheric and Infrared Atmospheric band emissions of O2 and (2) the green line emission of O, respectively. Particularly, the singlet Herzberg state of O2 is identified as the major precursor of the second excited O state resulting in the green line emission. In focus of potential further research is an extension of the MAC model with vibrationally excited states of O2 and ionized species.