Nanosecond Breakdown Characteristics of C₄F₇N and Various Mixtures at Pressures Above 1 Atmosphere in Comparison with SF₆

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This work measures the nanosecond pulsed breakdown performance of ${\mathit{C}}_{\mathbf{4}}{\mathit{F}}_{\mathbf{7}}\mathit{N}$ and compares it to that of ${\mathit{SF}}_{\mathbf{6}}$. The results indicate that ${\mathit{C}}_{\mathbf{4}}{\mathit{F}}_{\mathbf{7}}\mathit{N}$ and its various mixtures exhibit certain advantages in breakdown behavior over simply pure ${\mathit{SF}}_{\mathbf{6}}$ in pulsed spark gaps.

Abstract

This report evaluates the pulsed breakdown performance of $C_4{F}_{7}N$ under a 6.8 kV/ns voltage excitation. The pulsed dielectric strength of $C_4{F}_{7}N$ is compared to $S{F}_6$ in the same experimental setup, and it is found that $C_4{F}_{7}N$ concentrations of 50% or greater are required to achieve a dielectric strength greater than or equal to $S{F}_6$. Pure $C_4{F}_{7}N$ demonstrated higher electric field hold-off for longer time periods and less statistical variance under pulsed conditions when compared to $S{F}_6$. Mixtures of 50%$C_4{F}_{7}N$ with $N_2$ or $C{O}_2$ as buffer gases showed no appreciable difference in pulsed dielectric strength.

1. Introduction

There has been interest in finding alternative gases to $S{F}_6$ for use in high voltage systems [1,2]. $C_4{F}_{7}N$ has been considered as one of the alternatives to $S{F}_6$, and the appeal is two-fold [3]. First, $C_4{F}_{7}N$ has already been demonstrated to have a dielectric strength greater than or equal to $S{F}_6$ in AC or DC electric fields, even when mixed with $C{O}_2$ at fractional concentrations of 15–20% [4,5,6,7,8]. Second, $C_4{F}_{7}N$ has an atmospheric lifetime of 30 years, giving it a much lower global warming potential compared to $S{F}_6$ [9].

When not diluted with a buffer gas, $C_4{F}_{7}N$ has a dielectric strength 2.6 times greater than $S{F}_6$, up to 1000 kPa·mm [10]. Studies on the molecular dynamics of $e^{-}$ + $C_4{F}_{7}N$ collisions have characterized effective ionization rates, excited, ionization, attachment, elastic, and effective cross sections [10,11,12,13,14]. When used as an insulating gas in an electrical breakdown $C_4{F}_{7}N$ has multiple by-products that arise from these different collision types [12,14]. The chemical compatibility of $C_4{F}_{7}N$ and its by-products must be considered in spark gap design. Ethylene propylene diene monomer (EPDM) rubbers, nitrile, and PMMA plastics have shown signs of degradation in $C_4{F}_{7}N$ environments [15,16]. Coating these structures in silicon grease adds a protective barrier that mitigates the degradation caused by $C_4{F}_{7}N$, but this is an ad hoc solution [15]. Silver and aluminum are compatible with $C_4{F}_{7}N$, but after 40 h of exposure at 220 $°$C, $C_4{F}_{7}N$ mixtures demonstrated corrosive effects on copper [17,18]. Various gas adsorbents and desiccants have also been studied for their effectiveness in $C_4{F}_{7}N$ environments [19]. The deleterious effects of $C_4{F}_{7}N$ are circumvented in this setup using two techniques. First, compatible materials are used or coated in a thin layer of grease whenever possible. Second, $C_4{F}_{7}N$ and its mixtures remain in the testing apparatus for no more than 90 min at a time and at room temperature, after which they are evacuated. This setup is designed to minimize the amount of material degradation induced by $C_4{F}_{7}N$.

Pulsed breakdown measurements are performed on a pressurized experimental apparatus that allows for the measurement of breakdown behavior with nanosecond temporal resolution. The $C_4{F}_{7}N$ mixing percentages tested are 50%, 50/50, and 20%, 20/80, with a buffer gas as the remaining percentage. The buffer gases used are $C{O}_2$ and $N_2$. Custom voltage and current diagnostic probes were manufactured and calibrated to handle pulsed excitations with a frequency bandwidth greater than 350 MHz. An electrically triggered Marx generator is used to produce a consistent voltage pulse for statistical comparisons. The experimental apparatus is a 3.8 L chamber with pressures ranging from 101.3 kPa to 456 kPa being tested. All pressures measurements in this report are recorded as absolute pressure.

2. Experimental Setup

The pressure chamber, gray box in Figure 1, is designed for pressures up to 517 kPa. The pressure chamber is pumped down via a roughing pump to below 40 mtorr before being filled with the gas under test.

Inside the chamber is the spark gap with a ground shield across the gap to maintain the coaxial transmission line nature of the cable spools on either side, see Figure 1. The ground shield permits nanosecond temporal resolution across the gap. The cable spools are 2121 high voltage, HV, coaxial transmission line cables and are electrically long to temporally isolate the spark gap from source and load reflections. The one-way electrical delay of the cable spools is 85 ns. The measured impedance of the 2121 HV cable is 59 $\mathsf{\Omega }$. The HV pulse is dissipated using a 50 $\mathsf{\Omega }$ resistive load. The temporal region of interest in the measured gap voltage signal is ≈30 ns. Thus, reflections from the impedance mismatch of the 2121 HV cable and the load arrives well after the spark has finished breaking down.

On either side of the chamber are Rogowski and capacitive voltage divider, CVD, probes to measure transient current and voltage waveforms. The probes are mounted on the high and load side of the chamber; the high side is connected to the Marx generator, and the load side is connected to the load. These probes measure the nanosecond pulses across the gap if breakdown occurs. Voltage and current measurements are denoted with H or L subscripts depending on which side of the chamber they are mounted, see Figure 1. The high voltage pulse is produced using a pressurized Marx generator, which is electrically triggered. The output of the Marx generator is measured with its own CVD probe. The Marx generator is fired in 90 s intervals. To mitigate any effects of material compatibility, all insulating gases were evacuated from the system after 90 min. After the data were taken, the chamber was pumped down to below 30 mtorr and back-filled with lab air or $N_2$.

The gas mixtures are created by filling the chamber with partial pressures of $C_4{F}_{7}N$ and the buffer gas. The gas mixtures tested are 50/50 $C_4{F}_{7}N$ with $N_2$ or $C{O}_2$ as the buffer gas or a 20/80 $C_4{F}_{7}N$ mixture with $N_2$. To create a homogeneous gas mixture, a fan at the base of the chamber is spun via magnetic coupling for ten minutes prior to testing. During this time, the mixing fan is spun at 2000 rpm or greater with an approximate gas flow rate of 337 L/min or greater.

2.1. Test Gap

The spark gap is constructed using 2 hemisphere electrodes, see Figure 2. The ground shield has 4 vent holes with a diameter of 6.3 mm spaced 90$°$ apart around the center of the spark gap. The vent holes in the ground shield permit the gases under test to fill the spark gap while maintaining a coaxial transmission line structure across the gap. The ground shield is coated in a layer of epoxy to prevent the breakdown of the external ground shield instead of across the gap. The electrodes are mounted in PEEK sleeves, see Figure 2, to prevent breakdown from initiating at the junction between the electrode and the 2121 cable. Once the system is fully mounted, the gap distance between the electrodes is 2.2 mm.

CST simulations of the spark gap calculated the capacitance across the gap, $C_{gap}$, to be 1.6 pF, see Figure 2. CST simulation calculated the field enchantment factor of the gap to be 1.315. Thus, the macroscopic electric field is multiplied by 1.315 to determine the peak electric field at breakdown. The macroscopic electric field is the maximum voltage, $V_{max}$, prior to breakdown divided by the gap distance, d.

2.2. Electrical Diagnostics

The diagnostic probes used are coaxially mounted capacitive voltage dividers, CVD, and Rogowski probes, see Figure 3. The Rogowski coils and CVDs are designed, manufactured, and calibrated at the Texas Tech University Center for Pulsed Power and Power Electronics. These diagnostics permit the passive measurement of large amplitude voltage (10’s–100’s kV) and current (1 kA–100’s kA) transients over a wide frequency range [20,21,22,23,24,25].

An RF design rule of thumb stipulates that a signal 10% to 90% risetime, ${\tau }_{10/90}$, has a frequency bandwidth, $f_{BW}$, equivalent to $f_{BW}=0.35/{\tau }_{10/90}$ [21]. Thus, a risetime of 1 ns requires a frequency bandwidth of 350 MHz. The CVD and Rogowski probes’ transfer function, H, was measured using a vector network analyzer, VNA, and calculated using Equation (1) [23]. The CVD and Rogowski probes are calibrated on a 100-m-long spool of 2121 cable. The 2121 cable has a characteristic impedance of 59 $\mathsf{\Omega }$ and is terminated with a matched load when used for calibration.

$$H={\displaystyle \frac{S_{21}}{1-S_{11}}}.$$

(1)

The transfer function of the high-side probes is shown in Figure 4. The CVD probe follows a slope of 20 dB per decade until it levels off. The transition region of the CVD is the −3 dB point of the transfer function. Before the −3 dB point, CVD operates in a derivative mode. After the −3 dB point, the CVD is self-integrating [21]. Fourier transform signal corrections permit the CVD to have a bandwidth of 2.5 GHz, resulting in a minimum possible resolution of 140 ps, see Figure 4. The Rogowski probe transfer function has a valley around 850 MHz, which limits the bandwidth, see Figure 4. The bandwidth used in data processing is 600 MHz, resulting in a minimum possible resolution of 583 ps for the Rogowski probes. All the other CVD and Rogowski probes on the setup had similar transfer functions and bandwidths.

The transfer function of the diagnostic probes is used to calculate the input signal measured by the probes using discrete Fourier transform analysis. The oscilloscopes are in a Faraday cage some distance from the pressure chamber to reduce noise. All probes are connected to the oscilloscopes via 12.2-m RG223 cables. To account for the high-frequency losses of these cable lengths, the cable transfer function was measured on the VNA in situ, similar to other works [22,26].

2.3. Marx Generator Output

To isolate the effects of the gas within the spark gap, the consistency of the high-voltage pulse source is measured. An 8-stage Marx generator is used to generate the high voltage, HV, pulse in this setup. The Marx generator is charged to −38 kV and is arranged in an inverting configuration so the output pulse is positive. The Marx generator is pressurized to 304 kPa of lab air and is electrically triggered using a trigatron in the first stage electrode [27]. The output is captured using a CVD, as depicted in Figure 1.

The output voltage waveform of the Marx generator is shown in Figure 5. The maximum output voltage, risetime, and dV/dt are calculated for every shot. The Marx generator produces a 83.5 kV, 10 ns rise time excitation (6.8 kV/ns). The standard deviations in amplitude and risetime were observed to be 3% and 8%, respectively. However, due to losses in the 2121 HV cable spool, what reaches the cable is very similar in shape to the Marx generator output waveform but 10 kV lower in amplitude. All datasets in the report have similar Marx generator outputs. Based on the statistical deviation of the Marx generator, the breakdown electric field may vary anywhere between 3.3–16.1 kV/cm.

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 $\mathsf{\Delta }t$ to account for the electrical delay caused by the pressure chamber feedthroughs. The $\mathsf{\Delta }t$ 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.

$$V_{gap}\left(t\right)=V_H(t-\mathsf{\Delta }t)-V_L(t+\mathsf{\Delta }t).$$

(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 $S{F}_6$ and $C_4{F}_{7}N$ are given in Figure 8. As pressure increases, the voltage across the gap increases to 123 kV for $S{F}_6$ and 145 kV for $C_4{F}_{7}N$. Notably, the gap voltage measured in $S{F}_6$ 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. $S{F}_6$ 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 Marx generators voltage output reaching its maximum.

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.

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. The standard deviation decreases dramatically at higher 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 Marx generator output was 2.7 kV, which translates to an electric field deviation of ±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 $S{F}_6$. $S{F}_6$ also has measurable standard deviation in the electric field hold-off in other pulsed breakdown works [28,29]. In this experimental setup, $S{F}_6$ 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 $S{F}_6$. 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 $S{F}_6$ [4,5,6,31,32]. 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 $S{F}_6$, even approaching that of the Marx generator. At 405 kPa, the 20/80 mixture has the same mean hold-off electric field as 304 kPa $S{F}_6$ with a standard deviation limited by the Marx 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 $C{O}_2$ at 152 kPa.

The standard deviation in ${\tau }_{br}$ is also represented in the p$·{\tau }_{br}$ axis of Figure 10. 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·${10}^{-7}$ torr·sec and 2.74·${10}^{-6}$ torr·sec. $S{F}_6$ 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 $S{F}_6$ datasets.

4. Conclusions

This paper reported the experimental characterization and comparison of the nanosecond pulsed breakdown behavior of $S{F}_6$, $C_4{F}_{7}N$, and $C_4{F}_{7}N$-based mixtures. $C_4{F}_{7}N$ outperforms $S{F}_6$ in high voltage pulsed hold-off conditions experiencing a 6.8 kV/ns pulse. The 20/80 mixtures of $C_4{F}_{7}N$ with $N_2$ did not match or exceed $S{F}_6$ performance in peak pulsed electric field hold-off, as shown in the previous DC and AC results [4,5,6,31,32]. Insulating gases, such as $S{F}_6$, in spark gaps show a wide variance in dielectric strength under pulsed electric fields [28,29,30]. The 50/50 mixtures of $C_4{F}_{7}N$ with $C{O}_2$ and $N_2$ as buffer approached the performance of $S{F}_6$. $C_4{F}_{7}N$ consistently showed less variation in breakdown characteristics, whether in pure or mixture form, compared to $S{F}_6$. The measured variation in breakdown performance of $C_4{F}_{7}N$ at 253 kPa and 258 kPa can be attributed to the variance in the output pulse of the Marx generator. In future, larger datasets with a more consistent HV excitation source may be able to isolate the statistical variation in these pressure regimes. Notably, $C_4{F}_{7}N$ has a lower vapor pressure and higher boiling point than $S{F}_6$; 294 kPa and −4.7 $°$C compared to 2108 kPa and −63.9 $°$C [3,34]. Thus, mixture and buffer gases are appealing to permit $C_4{F}_{7}N$ to operate across large pressure and temperature regimes.

Other works have shown that $C_4{F}_{7}N$ has many decomposition products, such as $CN$ and $C{F}_3$, which occur with electron attachment or once the gas is fully ionized [3,9,12,35]. $S{F}_6$ tends to avoid these issues as long as impurities such as oxygen and water are kept low [36]. There are also long-term pulsed performance concerns of $C_4{F}_{7}N$, and its voltage holds off over time; some systems measured a 14% reduction in the dielectric strength of $C_4{F}_{7}N$ and $C{O}_2$ mixtures after just 9 months [16]. $C_4{F}_{7}N$ has a range of incompatible materials to be considered when designing HV systems [15,16,17,19]. These designs may have an increase in manufacturing costs, affect operational lifetimes, and require more research and design. Future research in development, deployment, cost, and environmental impact of $C_4{F}_{7}N$ devices is still required for large-scale industrial applications.

Thus, $C_4{F}_{7}N$ is not a simple drop-in replacement for $S{F}_6$ as more design considerations must be taken into account, such as lifetime, material compatibility, operating temperature and pressure regimes, and buffer gases. Under pulsed conditions, with relatively low shot numbers, $C_4{F}_{7}N$ may be a suitable replacement for $S{F}_6$ but requires mixing ratios of 50% or more. Pure $C_4{F}_{7}N$ also has a dielectric strength greater than $S{F}_6$ under pulsed conditions, permitting the design of more compact pulsed power systems. There is an ongoing search for alternatives to $S{F}_6$ as an insulating gas.