## 3 Results and Discussion
The standard deviation decreases dramatically at higher  
Figure 8: (**a**): Experimental gap voltage measured in pure \(SF_{6}\) for varying gas pressure. (**b**): Gap voltage of pure C\({}_{4}F_{7}N\) for varying gas pressures. The measured gap voltage for all the shots are temporally offset from one another for clarity. The 279 kPa gap voltage waveform for C\({}_{4}F_{7}N\) begins to level off prior to breakdown due to the maximum output of the [PERSON] generator being reached. Figure 9: The mean peak electric field for pulsed breakdown versus pressure. The black dots are mean values, and the error bars are one standard deviation from the mean. pressures for pure \(C_{4}F_{7}N\). As discussed previously, this is likely due to the rounding off of the gap voltage. The standard deviation of the [PERSON] generator output was 2.7 kV, which translates to an electric field deviation of \(\pm\)16.1 kV/cm. Thus, standard deviations that are more significant are presumed to originate from the gas between the spark gap. \(C_{4}F_{7}N\) overall, whether in pure or mixture form, has a lower standard deviation than \(SF_{6}\). \(SF_{6}\) also has measurable standard deviation in the electric field hold-off in other pulsed breakdown works [28; 29]. In this experimental setup, \(SF_{6}\) also appears to level off in electric field hold-off at higher pressure, which has been seen in other literature [30]. The 50% mixtures of \(C_{4}F_{7}N\) data show a similar performance to \(SF_{6}\). This is in contrast to previous AC and DC testing, which only required 15-20% \(C_{4}F_{7}N\) mixtures to have a similar dielectric strength to \(SF_{6}\)[4; 31; 4; 5; 6; 32]. The 20/80 mixture of \(C_{4}F_{7}N\) and \(N_{2}\) had the lowest hold-off performance versus pressure for a 6.8 kV/ns pulse. Interestingly, the standard deviation of the breakdown is still significantly lower compared to that of the \(SF_{6}\), even approaching that of the [PERSON] generator. At 405 kPa, the 20/80 mixture has the same mean hold-off electric field as 304 kPa \(SF_{6}\) with a standard deviation limited by the [PERSON] generator. E/p versus p-\(\tau_{br}\) graphs, see Figure 10, permit a pulsed breakdown comparison of various insulating gases [33]. However, the results are highly dependent on the dV/dt of the excitation pulse. For this experimental setup, these results apply to a HV pulse whose dV/dt is 6.8 kV/ns. For example, for a 15 ns, 102 kV peak pulse, an engineer may use a 3 mm gap with a 50/50 mixture of \(C_{4}F_{7}N\) with either \(N_{2}\) or \(CO_{2}\) at 152 kPa. \[V_{gap}(t)=V_{H}(t-\Delta t)-V_{L}(t+\Delta t)\ . \tag{2}\]0 E/p versus p-\(\tau_{br}\) of all the gases tested. The error bars are 1 standard deviation from the mean, black dot. Each data set averages 30–35 shots, except for 258 kPa \(C_{4}F_{7}N\), which has only 19 shots. If an engineer wanted to design a spark gap to withstand a 6.8 kV/ns pulse for 15 ns, i.e., a peak voltage of 102 kV, they could use a 3 mm spark gap filled with a 50/50 mixture of \(C_{4}F_{7}N\) and \(CO_{2}\) at 152 kPa. This results in a spark gap with an \(E/p=298.2\) V/(cm \(\cdot\) torr) and a p-\(\tau_{br}=1.71\cdot 10^{-5}\) torr \(\cdot\) s, marked with the yellow diamond. The standard deviation in \(\tau_{br}\), is also represented in the p-\(\tau_{br}\) axis of \[V_{gap}(t)=V_{H}(t-\Delta t)-V_{L}(t+\Delta t)\ . \tag{2}\]1 The time to breakdown will also have a natural standard deviation tied to Marx generator performance. Across the pressure ranges tested, 152 kPa to 456 kPa, this results in a minimum p-\(\tau_{br}\) between 9.12\(\cdot\)10\({}^{-7}\) torr-sec and 2.74\(\cdot\)10\({}^{-6}\) torr-sec. \(SF_{6}\) showed a wider variance compared to \(C_{4}F_{7}N\) and the associated mixtures. Pure \(C_{4}F_{7}N\) has the highest hold-off performance of all the gases tested. Notably, the \(C_{4}F_{7}N\) datasets, mixtures included, exhibited a decrease in standard deviation in \(\tau_{br}\) and peak electric field compared to the \(SF_{6}\) datasets.