## 3 Results and Discussion  
An example of a measured breakdown event in 203 kPa of 100% C\({}_{4}\)F\({}_{7}\)N is shown in Figure 6. Breakdown occurs when the gap voltage, \(V_{gap}\), begins to collapse and is calculated according to Equation (2). \(V_{gap}\) is the differential voltage of the spark gap using the CVD probes. The signals \(V_{H}\) and \(V_{L}\) are temporally shifted by \(\Delta t\) to account for the electrical delay caused by the pressure chamber feedthroughs. The \(\Delta t\) used in the calculation is 0.5 ns. \(V_{H}\) is the input voltage on the high side of the setup. \(V_{L}\) is the voltage traveling down the load cable spools. \(I_{H}\) and \(I_{L}\) are the current measurements via the Rogowski probes. \(I_{H}\) captures the charging of the transmission line downstream from the Rogowski coil prior to breakdown. \(V_{H}\) measures the voltage increase at the spark gap. Once breakdown occurs \(V_{H}\) and \(V_{L}\) approach approximately the same voltage. The Rogowski measurements \(I_{H}\) and \(I_{L}\) help verify that no alternate breakdown paths formed. An alternate breakdown path is defined as an electrical breakdown not strictly across the two gap electrodes. \[V_{gap}(t)=V_{H}(t-\Delta t)-V_{L}(t+\Delta t)\ . \tag{2}\]  
The nanosecond breakdown characteristics are primarily summarized by the maximum voltage across the gap, \(V_{max}\), the time from voltage application to breakdown, \(\tau_{br}\), and the gap voltage collapse. The time to breakdown for this work is defined as the time it takes for \(V_{gap}\) to increase from 5 kV to its peak, see Figure 7.  
The measured \(V_{gap}\) for \(SF_{6}\) and \(C_{4}F_{7}N\) are given in Figure 8. As pressure increases, the voltage across the gap increases to 123 kV for \(SF_{6}\) and 145 kV for \(C_{4}F_{7}N\). Notably, the gap voltage measured in \(SF_{6}\) showed a sharp oscillation in the falling edge, a feature that was not observed in \(C_{4}F_{7}N\). LTSpice simulations revealed this to be caused by fall times of the gap voltage. \(SF_{6}\) breaks down faster and has a shorter fall time than C\({}_{4}\)F\({}_{7}N\), producing an oscillation in the gap voltage waveform because of the small impedance mismatches produced by the high voltage feedthroughs when transitioning from the DS-2121 cable to inside the pressure chamber. A noteworthy feature of the C\({}_{4}\)F\({}_{7}N\) data is the rounding off of the gap voltage at higher pressures such as 258 kPa, see Figure 8b, due to the [PERSON] generators voltage output reaching its maximum. Figure 5: A sample waveform of the [PERSON] generator output voltage. Three different attributes of the output waveform are measured to verify shot consistency; the risetime, the dV/dt, and the maximum voltage. The mean peak electric field versus pressure is plotted in Figure 9. The error bars represent 1 standard deviation across 30 shots for each dataset. The \(C_{4}F_{7}N\) dataset consists of 19 shots. Figure 6: The experimentally measured waveforms \(V_{H}\), \(V_{L}\), \(I_{H}\), \(I_{L}\) from their respective CVD and Rogowski probes. The subscript \(H\) denotes that the waveform is measured on the side of the spark gap connected to the Marx generator output. The subscript \(L\) denotes that the waveforms are measured on the load side of the setup. The data is from a pure \(C_{4}F_{7}N\) shot at 203 kPa. The gap voltage, \(V_{gap}\), is calculated according to Equation (2) with a \(\Delta t\) of 0.5 ns to account for the delay of the chamber feedthroughs. Figure 7: The gap voltage from a shot taken in pure \(C_{4}F_{7}N\) at 203 kPa. The time to breakdown, \(\tau_{br}\), is measured from 5 kV to the maximum voltage, \(V_{max}\); the falling edge is when the insulating gas begins to form a plasma conducting channel between the electrodes. The 100% C\({}_{4}F_{7}N\) data had the highest pulsed electric field hold-off of all the gases tested for 6.8 kV/ns signal.