## 3 Low Power Cusped Field Thruster Development at HIT
### Configuration and Physical Mechanism Studies on Low Power Cusped Field Thruster  
In order to find out the operation mechanism, the component effects and the optimization methods of the cusped field thruster, a series of experimental investigations and simulation studies were carried out at HIT. The magnets geometry, magnetic topology, variable cross-section channel, and other thruster components were studied. A Particle-In-Cell simulation was used to illustrate the plasma characteristics in the discharge channel and the plume region, aiming to analyze the inner physical mechanism of the thruster. The study on magnet length and ratios showed that a higher downstream magnet ratio leads to a separatrix more parallel to the exit plane, and, as a result, a more focused plume [52; 53] and better total performance. In contrast, a higher ratio of middle stage magnet leads to enhanced ion loss to the channel wall [54]. The main ionization region in the cusped field thruster is downstream from the last cusp, which is decided by the downstream magnet length, as Figure 8 shows [55]. Extension of the ionization region promotes the ionization process by increasing the electron-neutral collision probability. Magnetic field strength has significant effects on the cusped field thruster. It was found that increasing magnetic field strength in the channel led to radial cross-field electron current reduction and ionization shrinking, and, as a result, propellant utilization degradation [56]. Although in a thruster with a stronger magnetic field, the more effective confinement of electrons leads to higher current utilization, the reduction in propellant usage ultimately results in a decrease in overall performance. In the simulation results, it  
Figure 8: Experimental investigation results (thrust) of different (**a**) magnet length and (**b**) ratio. can be seen that the electrons tend to gather around the channel axis as the magnetic field increases [57] (Figure 9b). Studies on magnetic topology show that the shape of the last magnetic separatrix influences the plume divergence significantly [58]. As for the cusped field thruster, the main potential drop is typically near the channel exit [29], which makes the channel exit the main acceleration region. The thermalized potential theory indicates that while the thruster operates, electric potential contour lines should approximately coincide with the magnetic field lines as the electrons move along magnetic field lines [59]. Plume divergency reduction is achieved through optimization of magnet arrangement, which makes the last magnetic separatrix approximately parallel to the channel exit, as shown in Figure 10.  
Variable cross-section was studied through spacers set on different locations in the channel, as shown in Figure 11. It was found that an appropriate-width spacer placed downstream from the cusps in the channel contributed to better total performance. A PIC simulation shows that high electron density in this region makes it a dominant ionization region. With the atom density increment caused by the spacers, enhancement of ionization occurred in this region [60]. Further physics mechanisms of the cusped field thruster operation were also studied, including the electron transmission, the ionization and acceleration process, the electric field formation [61] and the mode transition phenomenon. As shown in Figure 12, two major electron transmission routes with different impedances are experimentally found in the cusped field thruster: the inner route along the axis and the outer route touching the channel wall [62]. At the same time, two significant ionization regions are also found: the dominant ionization region and the additional exit ionization region [63], as shown in Figure 13. In low anode voltage conditions, the inner conduction route plays the dominant role, which makes a relatively high anode current with a high electron current. In these conditions, ionization in the exit region is strong, which leads to a divergent plume and low ion energy efficiency.