## 3 Torsional Thrust Balance Assembly and Calibration
### Influence of the Wire Voltage  
The steady-state calibration was performed under the condition that the thruster power supply wire was off, so the influence of the electrostatic force generated by the wire was not considered. However, the thruster will be applied with a high voltage (positive or negative) through the power supply wire during thrust measurement, and the resulting electrostatic force exerting on the torsional arm may cause the actual measured displacement to be different from that which only the thrust causes. If this uncorrected displacement is applied to calculate the thrust, it must introduce error. Figure 18 shows the torsional thrust balance response to an electrostatic force applied by the electrostatic comb under the conditions that the wire is powered or not. It can be seen from the figure that the arm displacement with the wire powered is offset \(\Delta x_{o}\) relative to that when the wire is off, resulting in the displacement reading \(\Delta x_{r}\) relative to the arm initial position being smaller than its actual deflection displacement \(\Delta x_{r}+\Delta x_{o}\), which will cause the measured thrust to be less than the actual thrust of the thruster. It can be inferred from Equation (13) that the thrust exerting on the arm has a good linear relationship with the response displacement. Therefore, the actual deflection displacement of the arm during thrust measurement can be equivalent to the superposition of displacements caused by the electrostatic force of the wire and the thrust separately. Therefore, the arm displacement during thrust measurement can be compensated if the influence of the wire voltage on arm displacement is clear. To quantitate the influence of the wire voltage on the arm displacement, we applied a triangular voltage wave with a peek-to-peek of 5 kV to the wire, with or without thrust exerting on the arm. The thrust was simulated by the electrostatic comb powered with 780 V equivalent to 31.96 \(\mu\)N. Figure 19 shows the voltage waveform and the corresponding arm displacement after intrinsic drift was compensated. It can be seen from the figure that in the first three quarter cycles of the voltage waveform, the arm displacement curves under the condition of with and without simulated thrust are in good agreement. This means that the electrostatic force generated by the wire and the thrust of the thruster are  
Figure 17: Power spectrum density of 0.001–25 Hz frequency band. decoupled. However, the displacement curves greatly deviate from each other in the last quarter cycle, and the displacement at \(-2.5\) kV is slightly larger than that at \(2.5\) kV. In fact, electrostatic force is only related to the voltage amplitude and has nothing to do with the polarity. The reason for the above deviations may be that the intrinsic drift rate increases in that time range. We ignored the wire voltage polarity and averaged the displacements at the same voltage amplitude with or without the simulated thrust. The resulting arm displacement as a function of wire voltage is shown in Figure 20; the error bars in the figure are the standard deviation of the mean value. We applied a 2 kV voltage to the wire and measured the arm displacement when an equivalent thrust of \(\sim\)3 uN and \(\sim\)30 uN was applied. Figure 21 shows the arm displacement; the values in black text are displacement deviations with or without wire voltage at the same thrust. We found that by averaging the deviations, compared with the displacement  
Figure 19: Wire voltage profile and the corresponding arm displacement. Figure 20: Arm displacement as a function of wire voltage. Figure 18: The influence of wire voltage on arm displacement reading. without wire voltage, the actual displacement reading deviation caused by the wire voltage is \(-1.9\)\(\upmu\)m \(\pm\) 0.07 \(\upmu\)m (\(\sim\)0.9 \(\upmu\)N) and \(-2.3\)\(\upmu\)m \(\pm\) 0.08 \(\upmu\)m (\(\sim\)1.1 \(\upmu\)N), respectively.