## 2 Brief Development of Cusped Field Thruster  
The cusped field thruster concept was first put forward by Thales Electron Devices GmbH in Germany, inspired by the focusing method of electron beams though delay lines and multistage depressed collectors (MDC) in travelling wave tubes (TWTs) [29]. It was originally named the High Efficiency Multi-stage Plasma Thruster (HEMPT) [30]. Because of the commonly found electron hall drifting in the thruster, as well as the similar structure with the cylindrical hall thruster, it is usually viewed as a variant of the hall thruster [31]. After several feasibility tests, Thales presented a prototype with thrust of 43 mN in 2002 [32], as shown in Figure 4. Series prototypes of HEMPT3050 and HEMPT30205 [33] have been developed since 2002. Thales greatly improved the performance of the cusped field thruster by optimizing the magnetic topology, channel structure, thermal design and cathode coupling [34]. Typical prototypes are shown in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Prototype**} & \multirow{2}{*}{**Anode Voltage (V)**} & \multirow{2}{*}{**Mass Flow Rate (sccm)**} & \multirow{2}{*}{**Thrust (mN)**} & \multirow{2}{*}{**Specific Impulse (s)**} & \multirow{2}{*}{**Total Efficiency (\%)**} \\  & & & & & & \\ \hline
2002 & DM3a-MS2 & 200–600 & 8 & 5–10 & 500–1200 & 13–20 \\
2003 & DM6 MS1 & 600–1200 & 20 & 30–45 & 1700–2500 & 27–35 \\
2004 & DM7 & 600–1200 & 20 & 36–58 & 2000–3000 & 35–44 \\
2004 & DM8 & 600–1200 & 20 & 33–57 & - & 36–47 \\
2005 & DM9-2 & 600–1200 & 20 & 50–70 & 2500–3000 & 40–50 \\
2005 & DM9-1 & 800–1000 & 20 & 15–70 & 2500–3000 & 36–46 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance of HEMPT3050 series. Figure 4: HEMPT prototypes from Thales. Figure 3: Schematic view of the cusped field thruster concept. The HEMPT prototype was selected as a priority electric propulsion technology by ESA for its prominent advantages [35], and it garnered much attention from international research institutions. As shown in Figure 5, MIT started their research on this thruster in 2007 and named it the divergent cusped field thruster (DCFT) [36]. With the divergent magnet arrangement, DCFT performed the highest anode efficiency of 44.5%, which was comparable to HEMPT 3050 [37]. The thruster has also been developed in Stanford since 2012, named the cylindrical cusped field thruster (CCFT) [38]. A cylindrical channel was employed in CCFT with a chamfered edge at the exit plane, which aims to ensure that electrons traveling along field lines from the cathode have a path to enter the channel with minimal collisions [39]. CCFT achieved an anode efficiency of 21.9% with Kr propellant (while cusped field thruster usually uses Xe propellant for relatively low ionization energy). Research about DCFT and CCFT were majorly investigating the discharge characteristics and physical mechanisms, such as potential distribution, acceleration process, mode transition phenomenon, and oscillation characteristics [40; 41]. The Harbin Institute of Technology (HIT) started research on the cusped field thruster around 2012, including prototype development, experimental investigations and simulation studies. In order to fulfill the requirements of different space missions, HIT developed cusped field thrusters of 20-110 mN level, 10-60 mN level, 1-20 mN level and 0.5-7 mN level, as shown in Figure 6 and Table 3. In particular, the 1-20 mN cusped field thruster was designed for the drag-free flight of the earth's gravity field mission [42]. It achieved a continuously variable thrust from 1 to 20 mN with a resolution of better than 19.5 \(\upmu\)N and thrust stability of \(\pm\)5%. These test results showed that large throttling ability is a common advantage of the cusped field thruster, since thrusters of different levels are able to work stably within a wide range of thrust. This advantage is very competitive for drag-free control flights [43; 44]. Figure 5: (a) DCFT of MIT and (b) CCFT of Stanford.