# Simplified Optimization of the Magnetic Configuration of HEMP-Thrusters
###### Abstract
Additionally, the amount of neutral particles that are not ionized and thus accelerated should be minimized, as these particles can impede the performance of the thruster. Finally, optimizing the overall performance of HEMP thrusters requires careful control of the operating conditions, including the temperature and density of the plasma, the electric fields used to accelerate  
Figure 1: Schematic view of a three-stage HEMP-Thruster. The cylinder is cut horizontally along the cylinder’s axis of symmetry. the plasma, and the magnetic fields used to confine the plasma. These operating conditions should be carefully controlled and monitored to ensure that the thruster is operating within the optimal range for maximum performance. The optimization of ion thrusters is a difficult process and revolves around experimental measurements [4]. Optimizing the performance of HEMP thrusters requires a multi-disciplinary approach that encompasses the design of the ionization chamber, the acceleration stage, and the overall operating conditions. By carefully designing and controlling these aspects of the thruster, it is possible to achieve significant improvements in performance, including higher specific impulse and lower propellant consumption. Since the construction of new designs is expensive, cheaper methods for optimization are sought-after. In [5; 6; 7] a HEMP-Thruster geometry was numerically optimized by a genetic algorithm. Even using simplified power balance models with kinetic corrections requires a lot of computational effort for such an optimization, because the parameter space of such a search is huge. It is beneficial to characterize some traits by other means in order to speed up the costly numerical optimization and to have the ability to improve other properties. This paper presents a fast, analytical approach to finding realistic starting points for the magnetic geometry of HEMP-Thruster design optimization, which can then be used for further refined optimization. This approach to calculating magnetic fields is not only much faster, but also has reduced error compared to numerical approaches, which is particularly important for transport codes where artificial drifts and forces are minimized. First, there is an analytical estimate for the best geometry of a magnetic stage, where the magnetic field should be parallel to the symmetry axis at the center. It will be shown that this estimate is very close to the experimental optimization of two-stage thrusters by trial and error [8; 9]. A similar ratio was also found in the rather complex and time-consuming optimization procedure by genetic algorithms [7]. Secondly, using the analytical solutions further diagnostics can be motivated by physics. Electrons are magnetized and follow the field lines. Therefore, long field lines combined with the confinement by the magnetic mirror effect at the cusps will increase the ionization and thereby the efficiency of the thruster. The different geometries are compared with respect to the field lengths by field line tracing. For the analysis, a weight function reflecting the observed density distribution is used. To obtain a global quality measure for the different magnetic field configurations, a geometric scaling of the single field lines is applied. The mirror effect at the end of the cylindrical magnets determines the electron confinement by limiting the losses and is responsible for enhanced ionization.