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Institute
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.
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.
Modern space missions depend more and more on electric propulsion devices for in-space
flights. The superior efficiency by ionizing the feedgas and propelling them using electric
fields with regard to conventional chemical thrusters makes them a great alternative. To
find optimized thruster designs is of high importance for industrial applications. Building
new prototypes is very expensive and takes a lot of time. A cheaper alternative is to rely
on computer simulations to get a deeper understanding of the underlying physics. In order
to gain a realistic simulation the whole system has to be taken into account including the
channel and the plume region. Because numerical models have to resolve the smallest time
and spatial scales, simulations take up an unfeasible amount of time. Usually a self-similarity
scaling scheme is used to greatly speed up these simulations. Until now the limits of this
method have not been thoroughly discussed. Therefore, this thesis investigates the limits
and the influence of the self-similarity scheme on simulations of ion thrusters. The aim
is to validate the self-similarity scaling and to look for application oriented tools to use
for thruster design optimization. As a test system the High-Efficiency-Multistage-Plasma
thruster (HEMP-T) is considered.
To simulate the HEMP-T a fully kinetic method is necessary. For low-temperature plasmas,
as found in the HEMP-T, the Particle-in-Cell (PIC) method has proven to be the best
choice. Unfortunately, PIC requires high spatial and temporal resolution and is hence
computationally costly. This limits the size of the devices PIC is able to simulate as well
as limiting the exploration of a wider design space of different thrusters. The whole system
is physically described using the Boltzmann and Maxwell equations. Using these system
of equations invariants can be derived. In the past, these invariants were used to derive a
self-similarity scaling law, maintaining the exact solution for the plasma volume, which is
applicable to ion thrusters and other plasmas. With the aid of the self-similarity scaling
scheme the computation cost can be reduced drastically. The drawback of the geometrical
scaling of the system is, that the plasma density and therefore the Debye length does not
scale. This expands the length at which charge separation occurs in respect to the system
size. In this thesis the limits of this scaling are investigated and the influence of the scaling
at higher scaling factors is studied. The specific HEMP-T design chosen for these studies is
the DP1.
Because the application of scaling laws is limited by the increasing influence of charge separation with increased scaling, PIC simulations still are computationally costly. Another approach to explore a wider design space is given using Multi-Objective-Design-Optimization
(MDO). MDO uses different tools to generate optimized thruster designs in a comparatively
short amount of time. This new approach is validated using the PIC method. During this
validation the drawback of the MDO surfaces. The MDO calculations are not self-consistent
and are based on empirical values of old thruster designs as input parameters, which not
necessarily match the new optimized thruster design. By simulating the optimized thruster
design with PIC and recalculate the former input parameters, a more realistic thruster design is achieved. This process can be repeated iteratively. The combination of self-consistent
PIC simulations with the performance of MDO is a great way to generate optimized thruster
designs in a comparatively short amount of time. The proof of concept of such a combination
is the pinnacle of this thesis.