@phdthesis{Kahnfeld2020,
  author    = {Daniel Kahnfeld},
  title     = {Kinetic and fluid modeling of ion thruster plumes},
  journal    = {Kinetische und fluide Modellierung der Ausstr{\"o}mungsregion von Ionentriebwerken},
  url       = {https://nbn-resolving.org/urn:nbn:de:gbv:9-opus-35429},
  pages     = {173},
  year      = {2020},
  abstract  = {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.},
  language  = {en}
}