# Simplified Optimization of the Magnetic Configuration of HEMP-Thrusters
###### Abstract  
One type of ion thruster that has gained attention in recent years is the High Efficiency Multistage Plasma (HEMP) thruster. Optimizing the performance of these thrusters can be challenging due to the complexity of the underlying physics. Since the construction of new designs is expensive, cheaper methods for optimization, e.g., numerical optimization, are being sought. This paper presents a fast, analytical approach to finding realistic starting points for the magnetic geometry design of HEMP thrusters. First, a ratio of length to radius is presented, where the magnetic field is especially parallel at the center of the magnetic ring. This result is confirmed with the open-source library magpylib. Its speed and accuracy qualify this tool for further optimization processes. Here, we present some simple performance indicators, which may be beneficial to characterize the magnetic field structure for further optimization. ion thruster; optimization; magnetic field +
Footnote †: journal: Applied  
1  
charged exit stream of xenon ions keeps the satellite from charging up with a positive charge. The positive potential at the anode leads to a plasma building up in the thruster channel. With sufficient electric conductivity of the plasma, the potential drop is moved from the anode to the thruster exit, where the plasma density decreases. This creates an electric field in front of the thruster exit that accelerates the electrons toward the thruster. There, the electrons follow the magnetic field lines provided by the permanent magnets. The resulting gyro radius of the electrons is much smaller than the channel radius, resulting in the magnetization of the electrons. Due to the magnetic field structure, they remain trapped in the thruster channel. The confinement of the electrons leads to high ionization rates. Because of the magnetization of the electrons and the magnetic field line structure between the cusps, the electron transport parallel to the symmetry axis is strong inside the channel. In contrast, the ions are not magnetized due to their large mass and the magnetic field strength typical for such thrusters (\(\approx\)200 mT), and drift with low energies through the thruster, following the distribution of the electrons. At the exit, they are accelerated by the electric field resulting from the potential drop. They are emitted with high emission velocities, thus generating thrust. This mode of operation, with high ionization efficiency, high exit velocity of the ions, and minimal erosion, makes the HEMP-Thruster a very attractive electric propulsion device. It can generate thrust in a wide range from 1 \(\upmu\)N to 100 mN. The flexibility to provide thrust over a wide range and its long lifetime due to minimal erosion make the HEMP-Thruster a favorable concept for long-duration space missions [2]. More information on HEMP thrusters can be found in [3]. One advantage of the HEMP-Thruster is that it is relatively simple to operate, as it does not require the use of high-voltage grids or other complex systems. This makes it more reliable and easier to maintain than other types of ion thrusters. However, the HEMP-Thruster requires a lot of power to operate, and the cost of the permanent magnets can be high. Optimizing the performance of these thrusters can be challenging due to the complexity of the underlying physics and the need for precise control of the ionized gases. A key aspect of optimization is the design of the ionization chamber, where the neutral propellant is ionized into plasma. This chamber should be designed to maximize the ionization rate while minimizing the amount of energy required to ionize the propellant. Another important aspect is the design of the acceleration stage, where the ions are accelerated to generate thrust. This stage should be designed to maximize the acceleration of the plasma particles while minimizing the amount of energy required to accelerate the ions.