# Experimental Characterization of the Capacitively Coupled RF-Plasma Thruster
## 4 Discussion  
The measurements of the plasma potential prove the existence of the electric field in the plasma plume which accelerates ions and decelerates electrons. This is the typical behavior for the ambipolar fields in the plasma. The axial profiles of the plasma potential for three investigated mass flows are shown in Figure 15. There exists a difference in the potential of approximately 10-15 V between the front of the engine and more the distant regions. The decrease of the potential in front of the cut-off seem to be an artefact of the symmetrization procedure. When measured in \"quick\" 1D mode with higher resolution the potential profile does not show such a behavior (opened circles in Figure 15). Also, a small potential well of the order 1 V can be seen between 80 and 100 mmm away from the engine front. There is a jump in the absolute value of the potential between flows 35 and 45, 55 sccm. This just can be correlated to the transition between \(\alpha\) and \(\gamma\) modes of the CCP discharge. This transition is also illustrated by the overall appearance of the discharge in Figure 16.  
Figure 14: Ion energy distribution functions. (**a**)—35 sccm; (**b**)—45 sccm; (**c**)—55 sccm. Figure 13: Measurement results for RPA. (**a**)—35 sccm; (**b**)—45 sccm; (**c**)—55 sccm. Figure 15: Profiles of plasma potential along the axis of the thruster. The IEDF in Figure 14 shows the presence of a low energy peak at approx. 10 eV and a broad higher energy ion group with energies reaching approx. 150 eV. The measured drop of the plasma potential corresponds well to the measured energy of the low energy ions. The range of the high energy ions corresponds to the amplitude of the applied RF voltage of approx. 100 V.  
The amplitude of the low energy peak of the IEDF decreases with increasing distance from the engine cut-off. The only exception from this trend is the IEDF at 55 sccm at 73 cm, see Figure 14c. We believe that the applicability of the RPA was violated in this case. With growing plasma density the Debye length decreases. When it becomes smaller than the aperture of the first screening grid the plasma is able to penetrate the RPA falsifying the IEDF measurements. It seems that at highest mass flow and nearest measurement position this was the case. The electron density profiles show the maximum in front of the thruster and a more or less expressed ring-shaped structure at distances of 50-70 mm from the front of the thruster. The existence of these maxima will be addressed in the next investigations. A possibility exists that these maxima are the artefacts of the symmetrisation procedure. The maximum values of plasma density in front of the thruster reach values of 3 \(\times\) 10\({}^{14}\) m\({}^{3}\) at 35 sccm and 1.5 \(\times\) 10\({}^{15}\) m\({}^{3}\) at 45 and 55 sccm. This is another indicator that the transition between different modes of the CCP discharge taken place when changing the propellant flow from 35 to 45 sccm. The further increase in flow does not lead to significant changes in the plasma density. The obtained values of the plasma parameters allow the estimation of the thruster parameters to be made. They are calculated according Equations (2)-(5) and summarized in Table 1.  
Specific impulse was calculated as:  
\[\text{Isp}=\sqrt{\frac{2\text{E}}{\text{g}^{2}\text{m}_{\text{i}}}} \tag{2}\]  
where E is ion energy, m\({}_{\text{i}}\) is ion mass and g is a standard acceleration due to gravity. Thrust was calculated as:  
\[\text{T}=\frac{\text{I}\sqrt{2\text{Em}_{\text{i}}}}{\text{e}} \tag{3}\]  
where I is ion current, E is ion energy, m\({}_{\text{i}}\) is ion mass, g is a standard acceleration due to gravity and e is elementary charge. Figure 16: Thruster operation (**a**) at 35 sccm propellant flow and (**b**) at 55 sccm propellant flow. Pictures are made with same camera settings.