# The Helical Resonator: A Scheme for Radio Frequency Plasma Generation
## 7 Experimental Results
The results of the measurements are shown in Figure 13 for resonator 2 and in Figure 14 for resonator 3. In both cases, the addition of the probe causes a downshift in frequency of the resonance pattern, both for the case without the shield (top row) and for the shielded case (bottom row). Again, the curves for the shielded case appear sharper, indication of a lower dissipation. The fitting procedure adopted is the following: at first, the curves without HV probe were fitted as described above. Subsequently, the curves obtained with the HV probe attached to the resonator open end were fitted, using expression (59), but keeping the values of \(Z_{c}\) and \(f_{0}\) fixed to those resulting to the previous fit, and adjusting only \(\alpha H\) and the new parameter \(\tau_{L}\). While, in principle one would think that also \(\alpha H\) should be kept constant--and this was tried at the beginning--it was realized that it was not the case, possibly due to novel radiation sources stemming from the new layout. The results shown in Figure 13 for resonator 2 demonstrate that the model for the loaded resonator is actually very good. Indeed, the quality of the fit appears to be even better than for the resonator in standard conditions, suggesting that also in this case, some parasitic capacitance should be taken into account. Only the phases for the unshielded case show some discrepancy, mainly due to the experimental curves in the regions away from the resonance being somehow higher than the expected \(\pi/2\) value. This is likely due to some instrumental error, which is not unlikely, given that the Pocket VNA is a low-cost instrument. Similar considerations apply also to the curves depicted in Figure 14, which refer to resonator 3. Figure 13: **Top**: plot of the modulus **(left)** and phase (**right)**, normalized to \(\pi\), of the input impedance of resonator 2, both in standard configuration and with the HV probe attached to the open end. The dashed curves are the fits obtained as described in the text. **Bottom**: same as above, but with the addition of a conducting shield around the resonator. The results of the fits for the two resonators are summarized in Table 1. It can be seen that a characteristic impedance of about 1 k\(\Omega\) was found for both resonators, which was then reduced to one quarter and to a half, respectively, when the shield was placed. The strong reduction in dissipation in the shielded case was confirmed. It is, however, to be noticed that also the placement of the HV probe on the high voltage end led to a reduction in dissipation, something which is not yet fully understood but which may depend on the radiation pattern. It is remarkable to observe that in the case of resonator 3, both measurements with the HV probe, with and without shield, led to a load capacitance of around 4 pF, not dissimilar to the nominal value of 3 pF. In the case of resonator 2, two slightly higher, and different, values of 5 and 7 pF were found. It is, however, to be noticed that the quality of contacts and other issues, such as the proximity of the work bench surface, may add parasitic capacitance. It is nevertheless remarkable that the correct order of magnitude could be obtained. Concerning the comparison with the predictions of the propagation model of Section 3, for resonator 2 in the unshielded configuration, the model overestimates the characteristic impedance by a factor 2.8 and the velocity factor by a factor 2.6, while in the shielded case, the overestimate is by a factor 1.9. For resonator 3 in the unshielded configuration, there is an overestimation of the characteristic impedance by a factor of 1.6 and of the velocity factor by a factor of 2.2, whereas in the shielded case, the velocity factor is overestimated by a factor 1.9. Overall, these results confirm that the propagation model needs to be somehow updated to better match the experimental results.