## 3 Low Power Cusped Field Thruster Development at HIT
### Cusped Field Thruster Downscaling in HIT  
Aiming to fulfill the microthruster requirements of the Tianqin project, the space-borne gravitational wave detection mission in China [65], HIT started the cusped field thruster downscaling work in 2015. Experiments and simulations were carried out to study the thruster geometry, variable cross-section design and channel materials. Some of the important results are as follows. Experimental investigations on the reduction of channel diameter show that the channel diameter significantly affects thruster operation parameter space and low mass flow performance. It is apparent that in low mass flow conditions, a larger diameter leads to lower mass flux density and, as a result, less electron-neutral collision possibility. As a result, the ignition anode voltage increases as the channel diameter increases. Additionally, it becomes impossible to ignite in low mass flow conditions, as Figure 14 shows. The mass flux difference also leads to the performance difference of thrusters. A large throttling ability of more than three orders of magnitudes is achieved in thrusters with different channel diameters, but the highest specific impulse is limited in small-diameter ones, as Figure 15 shows. Performance limitation is found in small diameter thrusters, which is rather similar to the traditional annular hall thrusters [66]. However, they still  
Figure 14: Ignition anode voltages of thrusters with different channel diameters (24 mm, 12 mm and 6 mm) and the same channel length (60 mm). Figure 12: Experimental results of the two conduction routes in the cusped field thruster. Figure 13: Simulation and experimental results of the two ionization regions characteristics. show higher performance in low mass flow conditions when it comes to the same mass flow rate. As a result, diameter reduction is necessary for cusped field thruster downscaling. Studies on channel length were conducted to find out the appropriate geometry for the cusped field thruster. Experimental results show that a long channel leads to significant plume divergence and a reduction in overall efficiency, but a thruster with a too-short channel performs low propellant utilization due to ionization region reduction [67]. It can be seen from the simulation results that the long channel results in higher ion loss on the wall downstream from the channel, as shown in Figure 16. In respect to a typical cusped field thruster with a certain channel diameter, there should be an optimal channel length with the best equilibrium of ion energy efficiency and propellant utilization [68]. Figure 15: Thrust and specific operation spaces of thrusters with different diameters. (**a,b**) 6 mm, (**c,d**) 12 mm and (**e,f**) 24 mm. Three frequently used dielectric wall materials, boron nitride, alumina and quartz, were applied on the cusped field thruster to find out the effects. Similar to the traditional annular hall thruster, the cusped field thruster discharge characteristics are significantly affected by the secondary electron emission (SEE) coefficient [69]. The temperature cooling-down effects are extremely strong for a high-SEE wall material, which weakens the electron-neutral collision discharge [70]. On the other hand, low-SEE wall material leads to more original-electron loss on the wall, which is also unfavorable for the ionization process. Currently, the boron nitride with SEE around 1 in typical working conditions is still the preferred wall material for cusped field thrusters [71]. The variable expanding channel is applied on the cusped field thruster with positive results, as Figure 17 shows. It is found that the expanding configuration contributes to a wider operation range of anode power and mass flow rate. Ignition voltage is noticeably lower for thrusters with larger channel expanding angles, which could be explained as an improvement on original electron conduction benefited from the exit magnetic field weakening.