# Thrust Measurements on the High Efficient and Reliable Vacuum Arc Thruster (HERVAT)
## 3 Experimental Results
### PPU and Arc Energies  
The electric measurements of characteristic current and voltage pulses measured throughout the experiments show a highly reliable operation of the PPU (zero failures during all operation modes). Thus, the thruster could be reliably triggered and operated in the main discharge mode for more than \(1\times 10^{7}\) pulses. In Figure 6, typical traces for the thruster operation in the \"trigger-less\" mode with and without magnetic field produced by the additional electromagnetic nozzle are shown. The measurements were obtained from an average over 100 pulses. Here, the anode currents and the PPU output voltage are illustrated. It is evident that the use of a magnetic nozzle increases the pulse length to 550 us and the arc voltage to 55 V, while the pulse length is only 250 us with the arc burning at 35 V in the absence of a magnetic field. This effect is well-known and described in [7; 8; 15]. In the presence of the magnetic field, the maximum arc current drops from 150 A to 50 A as a result of the additional coil resistance and the effect of the magnetic nozzle on the vacuum arc [16].  
Figure 6: Current and voltage traces for \(C_{1}=198.2\) μF without (**left**) and with magnetic nozzle (**right**).  
In both graphs in Figure 6, it can be observed that the voltage value remains at the level of the arc voltage, after the arc has extinguished. This indicates that the capacitors are not fully discharged. This needs to be considered in the calculation of the effective energy per pulse \(E_{pulse,eff}\), which is needed for the determination of TTPR. The energy dissipated from the capacitors into the arc discharge is then given by  
\[E_{pulse,eff}=E_{HV}+E_{\text{C1,}eff}+E_{\text{C2,}eff}. \tag{2}\]  
The energy input from the high voltage pulse is determined by the high voltage generator circuit. In the current setup it was \(E_{HV}\) = 53 mJ. The released energy from the capacitor \(E_{C_{i},eff}\), depends on the initial charging voltage \(U_{C_{i},initial}\) and the final voltage \(U_{C_{i},end}\) remaining in that capacitor after the extinguishing of the arc:  
\[E_{\text{C1,}eff}=\frac{1}{2}\cdot C_{i}\cdot(U_{\text{C}_{i},initial}^{2}-U_{ \text{C}_{i},end}^{2}). \tag{3}\]  
Energy losses due to the parasite resistance, inductance and capacitance of the wires from the PPU to the thruster are not taken into account for this work.  
The energy dissipated into the arc \(E_{ar,eff}\) was obtained by integration of the measured arc currents \(I_{arc}\) and voltages \(U_{arc}\) over duration of a single pulse using the following relation  
\[E_{arc,eff}=\int_{0}^{t_{pulse}}I_{arc}(t)\cdot U_{arc}dt. \tag{4}\]  
with \(t_{pulse}\) the time for which the current level of the arc falls below 1 A. With these data, the TTPR using the PPU effective energy outputs and the energy dissipated into the arc were calculated and compared. The results are summarised in Table 1. The ratio of the energy stored in the PPU to the energy dissipated in the arc clearly shows the increase of the efficiency with the presence of the magnetic field. The efficiency of 0.9177 was calculated for \(C_{1}\) = 436.9 \(\upmu\)F.