## 3 Results and Discussion
### Experimental Measurements
#### 3.1.2 Plasma Parameters  
The values of electron density profiles measured with the Langmuir probe are shown in Figure 10. The measurements are located within the range of \(2\times 10^{12}\) to \(2\times 10^{15}\,\mathrm{m}^{-3}\). Missing data points in the center of the beam arise due to the limited range of the measurement device, which was not able to compensate for the sudden increase in the voltage range. The ionic parts of the VCC could not be collected in these radial positions.  
The values of \(8\times 10^{14}\) to \(1\times 10^{15}\,\mathrm{m}^{-3}\), which were taken in the closest position to the symmetry axis, correspond to the density of the ions estimated from the beam current \(l_{\mathrm{beam}}\) and energy \(E_{\mathrm{kin}}\) according to  
\[n_{\mathrm{beam}}=\frac{l_{\mathrm{beam}}}{e\pi R^{2}u}\qquad u=\sqrt{\frac{2 E_{\mathrm{kin}}}{m_{\mathrm{Xe}^{+}}}}\,, \tag{9}\]  
where \(R\) is the beam radius, and \(u\) is the velocity of beam ions. For a beam current of \(17\,\mathrm{mA}\) and energy of \(1\,\mathrm{keV}\), a number density of \(n_{\mathrm{beam}}=4\times 10^{15}\,\mathrm{m}^{-3}\) is obtained. Similar broadening of the radial profile with increasing axial distance as in the case of plasma potential is observed. Obtaining the mean electron energy requires additional efforts. For  
Figure 9: Comparison of radial plasma potential profiles at \(\Delta x=10\,\mathrm{mm}\) for noncompensated and partially compensated (\(1\,\mathrm{mA}\) electron source) beams.  
its determination, the information about both the plasma and floating potentials in the same spatial position is needed. The probes in the current setup are placed axially aligned so that two radial scans have to be made for identifying the electron temperature: one with the emissive probe and one with the Langmuir probe, both axially adjusted. Only for selected spatial positions can the \(T_{e}\) measurements be made. Figure 11 highlights the data needed for the determination of the electron energy and its corresponding values at an axial distance of \(\Delta x=50\,\mathrm{mm}\).  
The data in Figure 11 reveal that the potential jump has an influence on the determination of the electron temperature. The plasma potential measured with the emissive probe has a broader profile than the floating potential measured with the Langmuir probe. This is due to the fact that between both measurements, the probe holder should be moved 40 mm away from the thruster. The divergence of the ion beam results in a slightly different width of the disturbance introduced by the probe system in the axial positions separated  
Figure 11: Comparison of plasma and floating potentials at \(\Delta x=50\,\mathrm{mm}\). Electron temperature measurements in partially compensated environment.  
Figure 10: Radial profiles of electron number density at different axial positions.  
by 40 mm. The electron temperature depends on the absolute value of the plasma and floating potentials, and this slight difference results in severe uncertainty about electron temperature determination _inside_ the beam. Thus, the electron temperature can be reliably determined with our setup only outside of the ion beam. The reliably measured values lie within a range of 1.5 to 5 eV. The measured value of 8 eV at \(r=-25\) mm is questionable due to the reasons stated above. For the correct determination of \(T_{e}\) inside the ion beam, the plasma and floating potentials should be measured under identical disturbances. One possibility for such measurement lies in using a two-probe arrangement, with the probes entering the beam successively. The second probe enters the beam after the first one has already left it. If the distance between emissive and Langmuir probes is bigger than the beam diameter, then each probe will introduce the same disturbance and the values of plasma and floating potentials can be used for the determination of electron temperature. This measurement lies within the scope of future work.