**4. Results**

### *4.1. Protrusions with SF6*

The results for the single protrusions in SF6 are shown in Figure 6 for positive and negative polarity. The *E*50 background fields are normalized to the critical field, which eases the interpretations and comparison between different gases. In agreemen<sup>t</sup> with [38], the breakdown values for positive polarity are slightly lower than those at negative polarity. Only for protrusion length of 200 μm or less the differences between the polarities are within the scatter. At such small lengths, many breakdowns also happened away from the protrusions, which were, however, not considered for the determination of *E*50, as mentioned above. The decrease of the normalized *E*50 breakdown field with increasing protrusion length is reasonably described by the prediction for leader breakdown, which occurs significantly below the critical field. Streamer inception and the first electron criterion are fulfilled at lower fields, such that leader breakdown is expected to be the decisive criterion. Only for very small lengths below 250 μm and positive polarity, the first electron criterion might require slightly higher fields than the leader breakdown. This is, however, within the uncertainties of the predictions. We can also observe a higher scatter for positive polarity compared to negative polarity.

Using 20 protrusions—see full symbols in Figure 7—lowers the normalized *E*50 breakdown fields significantly. For comparison, the experimental results and predictions for single protrusions are also shown. The di fference between positive and negative polarity in the figure seems more pronounced than for single protrusions. The experimental breakdown fields are now lower than the predictions for leader breakdown for a single protrusion. The enlargement law predictions from (1) are shown by the black dash-dotted curves and agree for both polarities with the experimental results. Thus, the lowering of the experimental breakdown fields for 20 protrusions is well described by the enlargement law based on the breakdown probability distributions of single protrusions.

**Figure 6.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for SF6 and single protrusion at 0.4 MPa at (**a**) positive and (**b**) negative polarities.

**Figure 7.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for SF6 and 20 protrusions. Not all protrusion lengths could be measured when using multiple protrusions at (**a**) positive and (**b**) negative polarities.

For 100 protrusions this is di fferent at positive polarity—see Figure 8a. There is no further lowering of the breakdown fields when using 100 instead of 20 protrusions and the prediction of the enlargement law (1) is significantly lower than the measurement. There seems to be a lower limit which is not further exceeded when using a larger number of protrusions. This is not the case for negative polarity—see Figure 8b—where we see a good agreemen<sup>t</sup> of the enlargement law predictions with the experimental results for 100 protrusions.

**Figure 8.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for SF6 and 100 protrusions. Not all protrusion lengths could be measured when using multiple protrusions at (**a**) positive and (**b**) negative polarities.

Typical partial discharge images, which were taken at breakdown events, are shown in Figure 9. It can be seen that many discharges happened in parallel, i.e., simultaneously within 10 μs. These discharges could be observed in case of breakdown since the discharge channels are illuminated by the strong light emission from the breakdown spark channel occurring elsewhere in the gap. These images are, therefore, similar to a Shadowgraphs or Schlieren images [48]. The discharge channels have the typical signature of leader channels [35], which confirms the interpretation from leader breakdown predictions, i.e., the breakdown is determined by leader propagation. The negative leader channels (Figure 9c) are thicker and less structured than positive leader channels (Figure 9b); this observation is in agreemen<sup>t</sup> with the expectation from [49].

**Figure 9.** Images of partial discharges and breakdown in SF6 at 0.4 MPa for (**a**) 2 mm length at positive polarity at 130 kV/cm, (**b**) 0.5 mm length at positive polarity at 188 kV/cm and (**c**) 1 mm length at negative polarity at 187 kV/cm. Note the di fferent length scales of the images, which can be judged by the protrusion lengths.

### *4.2. Protrusions with CO2*

Results for single protrusions in CO2 are shown in Figure 10. The figure shows the experimental normalized E50 breakdown values and predictions for first electron, streamer inception and leader breakdown and the background fields for streamer crossing and spark transition of negative streamers. The complete range where streamer crossing and spark transition is expected at negative polarity is indicated by the cyan colored area in the figure. For positive streamers we expect streamer crossing only at the critical field [37], which is, therefore, probably not relevant in the present case, since this needs fields higher than the leader breakdown criterion.

**Figure 10.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for CO2 and single protrusion at 0.6 MPa at (**a**) positive and (**b**) negative polarities.

For protrusion lengths below 1.5 mm with positive polarity, the breakdown happens at or slightly above the critical background field—see Figure 10a. The leader BD predictions do not explain this. Probably this can be explained by the first electron criterion (red dashed curve). At or above the critical field, avalanches can start everywhere in the gap, which is in agreemen<sup>t</sup> with the experiment. Many breakdowns did not occur at the protrusion but in other locations of the gap in this case. There was also a larger scatter in the breakdown fields, which is reflected in the error bars of the experimental breakdown values, especially at negative polarity.

At negative polarity, experimental *E*50 values are close to the leader breakdown predictions for protrusions larger than 1 mm—see Figure 10b. An additional possibility for breakdown at negative polarity might be streamer crossing and transition to spark. Therefore, at negative polarity both mechanisms might be decisive for breakdown. From the partial discharge images—see Figure 11—this could not be decided unambiguously. For smaller protrusions, breakdown occurs at the critical field. As for positive polarity, breakdowns often occurred at the plate electrodes and not at the protrusion for smaller protrusion lengths.

Using 20 protrusions, see Figure 12, the measured breakdown fields decrease at both polarities compared to the results from the single protrusion experiments. For positive polarity, this is in agreemen<sup>t</sup> with the prediction from the enlargement law (1)—see Figure 12a. Note that predictions for the enlargement law were not possible for small protrusion lengths due to the limited amount of data and large uncertainties of the breakdown probability distributions. The measured breakdown values are for the positive polarity at the first electron prediction for single protrusions but still higher than the leader breakdown predictions. For negative polarity, a lowering of E50 values is observed mainly below 1 mm protrusion length—see Figure 12b. The measured breakdown fields below 0.5-mm protrusion length coincide with the first electron and streamer inception prediction. Interestingly, for protrusion lengths of 1 mm and more, no significant decrease of the E50 values for 20 protrusions compared to single protrusions is observed. The breakdown fields are at the expected spark transition level, which is assumed to be independent of protrusion length.

**Figure 11.** Images of partial discharges and breakdown in CO2 at 0.6 MPa for (**a**) positive polarity at 115 kV/cm with 100-μm protrusions and (**b**) negative polarity at 139 kV/cm with 200-μm protrusions.

**Figure 12.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for CO2 and 20 protrusions at (**a**) positive and (**b**) negative polarities.

As mentioned in Section 2.1, also a smaller spacing of 2 mm between the protrusions was tested with 20 protrusions for CO2. These results were not significantly different from the usual spacing of 4 mm—see Figure 12. Only a small reduction of less than 6% in field maximum was expected from the comparison of electric field calculations when using the smaller spacing (not shown in Figure 12), which is similar to the experimental uncertainties.

For 100 protrusions and positive polarity—see Figure 13a—the measured breakdown fields drop to the leader breakdown predictions for protrusions of 0.5 mm length and more. This is not predicted by the enlargement law, which results only in a moderate reduction. For smaller protrusions, the breakdown fields are still significantly higher than the leader breakdown prediction, probably due to the lack of a first electron. For larger protrusions of 1 mm and more, the positive breakdown fields are now similar or even lower than the negative ones, as would be expected from the leader breakdown criterion.

**Figure 13.** Normalized breakdown fields *E*50/*Ecr* vs. protrusion length *L* for CO2 and 100 protrusions at (**a**) positive and (**b**) negative polarities. Not all protrusion lengths could be measured when using multiple protrusions.

For 100 protrusions and negative polarity—see Figure 13b—the breakdown values drop significantly only for small protrusions below 0.5 mm lengths, compared to the previous case of 20 protrusions. For 250 μm and below, they are probably determined by streamer inception. Above 250 μm protrusion length, there is only a small drop of breakdown fields with increasing protrusion length. It seems that a saturation is reached, which is probably not due to the first electron criterion, but due to streamer crossing followed by spark transition. The enlargement law predictions are now significantly lower than the measurements.

Images of partial discharges and breakdown in CO2 are shown in Figure 11. Local channel illuminations indicated local channel heating could be clearly observed, which might be during leader propagation but also for a streamer to spark transition. Similarly to SF6, discharges occurred simultaneously in the time window of 10 μs. Weak density variations in the non-luminous regions indicate some channel heating also in these regions. Interestingly, breakdowns from the bottom plate electrode could also be observed.

### *4.3. Electrodes with Surface Roughness*

The results from the electrodes with surface roughness are shown in Figures 14 and 15 for SF6 and CO2, respectively. Note that for the *E*50 evaluation the electric field at the surface of the electrodes was used, since the fields are weakly non-uniform in the case of the small surface. Again, the *E*50 breakdown field is normalized to the critical field. For comparison calculations for first electron, streamer inception and breakdown are shown for a single protrusion in the figures. Increasing the area in SF6 at positive polarity led to a significant lowering of the *E*50 breakdown fields at positive, but negligible decrease at negative polarity—see Figure 14a. This can be understood by the streamer inception and first electron criterion. At positive polarity, the experimental breakdown field drops roughly to the predicted streamer inception field for large areas. This can probably be explained by a su fficiently high number of sites for discharge inception for large electrode areas, i.e., there is a high likelihood for a first electron at a small surface protrusion. Then, the streamer inception becomes a su fficient breakdown criterion. For small areas a first electron is probably lacking, and the breakdown field becomes even higher than the critical field. In the predictions for a single protrusion a first electron is only available at the critical field, i.e., probably these predictions are still too optimistic. The prediction from the enlargement law (solid arrow) for increasing area reproduces qualitatively the decrease of breakdown field with increasing surface area. However, it predicts for large areas the breakdown at the critical field and not at the streamer inception field. Using (1) to predict the breakdown field scaling from large to small area would quite underestimate the measured breakdown field (dashed arrow). Thus, at positive polarity, the enlargement law predictions do not agree well with the experiments.

**Figure 14.** Normalized breakdown fields *E*50/*Ecr* vs. effective surface area in SF6 at 0.4 MPa at (**a**) positive and (**b**) negative polarities. Calculations for first electron, streamer inception and breakdown at a single hemispherical protrusion of 20 μm height are shown for comparison.

At negative polarity, this is di fferent—see Figure 14b. Here, the predictions in both directions, i.e., from small to large electrode, or vice versa, give the correct breakdown fields. Note that the experimental breakdown field is in this case again approximately at the predicted streamer inception field. This is plausible, since at negative polarity there is no lack of a first electron (see dashed line in Figure 14b) and breakdown occurs for small and large electrode roughly at similar fields, which is at streamer inception. Note that streamer inception is independent of polarity, i.e., for large areas, the breakdown fields are similar for both polarities.

**Figure 15.** Normalized breakdown fields *E*50/*Ecr* vs. effective surface area in CO2 at 0.6 MPa at (**a**) positive and (**b**) negative polarities. Calculations for first electron, streamer inception and breakdown at a single hemispherical protrusion of 20 μm height are shown for comparison.

In CO2, the observations are similar—see Figure 15. At positive polarity (Figure 15a), experimental breakdown fields drop for large electrodes to close to the critical field, which is slightly higher than the predicted streamer inception and breakdown field. This discrepancy is probably still within the accuracy of the predictions. Only for small area and positive polarity there is probably again a lack of a first electron which leads to an increase of E50 in the experiments. Note that this lack of first electron is not predicted by the model. Due to the strongly non-linear field dependence of (4), at the critical field, a first electron is always predicted. Probably the model is not su fficiently precise for CO2 and small protrusions. At negative polarity in CO2 (Figure 15b), there is a slightly more pronounced area e ffect than for SF6. Again, the breakdown happens for large areas close to the critical field, which is only slightly above the first electron criterion prediction—see dashed horizontal line in Figure 15b. Thus, there is possibly also a lack of first electron for small areas at negative polarity, which is, however, much less pronounced than at positive polarity. The discrepancies can be probably explained by the simplicity of the model for the first electron.

Images of partial discharges and breakdown are shown in Figures 16 and 17 for both gases used. For CO2, there are again discharges from the plate electrode, similarly to the protrusion results—see Figure 16. Arrested discharges could also be observed at breakdown for SF6—see Figure 17. This shows that there is a competition between various discharge channels.

**Figure 16.** Images of partial discharges and breakdown in CO2 at the small surface. (**a**) Positive polarity at a surface field of 322 kV/cm and (**b**) Negative polarity at 235 kV/cm surface field.

**Figure 17.** Images of partial discharges in SF6 at 0.4 MPa, negative polarity at a surface field of 375 kV/cm. The picture is edited with different brightness on the two halves to better show the structures of the partial discharge.
