Scaling laws in thruster physics

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.