Fundamental study of DC and RF breakdown of atmospheric air Free

Radio frequency (RF) breakdown at 3.3 MHz in atmospheric conditions is studied to quantify the power limitations of a tunable electrically small antenna (ESA) design. The ESA has a frequency range of 3–10 MHz and is tuned by altering the capacitance of its parallel plate gap.¹ At 3 MHz and 500 kW power levels, the capacitive gap yields the highest electric field exceeding 20 kV/cm and is most susceptible to breakdown. Paschen's law gives the breakdown voltage between two electrodes as a function of gas pressure and distance, which was found empirically by Paschen's famous 1889 two-sphere experiment.² The presented experimental data fall into the Townsend regime of a self-sustaining discharge at small overvoltages, where it is assumed that for each electron starting at the cathode, at least one electron is generated via secondary emission at the cathode. That is, each avalanche starting at the cathode produces a sufficient number of excited states in the background gas, which eventually leads to spontaneous emission followed by photoemission of electron(s) at the cathode. In its simplest description, one finds

where α is the effective first Townsend coefficient, which is at constant gas density as a function of the electric field, E; d is the gap distance; and γ is the second Townsend coefficient, which has several potential feedback mechanisms lumped into one. For instance, photoemission rather than ion feedback is typically dominant such that the photoemission coefficient from the cathode's metal surface is folded into γ as well. It should be noted that the exact value of γ will vary with the geometry (electrode size), electrode material, electrode surface conditions, etc. As such, a universal Paschen curve based on Eq. (1) may be easily derived and reproduces the well-known Paschen curve shape. However, owing to γ being strongly dependent on the specific experimental conditions, the exact breakdown voltage provided by the Paschen Curve may move up or down by several ten percent. For instance, for atmospheric air, the Paschen minimum will fluctuate from 460 V to 300 V for a typical range in γ from 0.001 to 0.01 calculated from the first Townsend coefficient data published elsewhere.³ 

Thus, while the body of work on DC breakdown is immense, it was necessary to measure DC breakdown values for electrode conditions identical to the RF breakdown conditions such that a direct comparison in breakdown electric fields may be made. The breakdown voltage (in kilovolts),

where p is the gas pressure in Torr and d is the electrode gap distance in centimeters, is described by Lau⁴ and used as a point of comparison for the experimental DC data. This equation assumes a gas temperature of $20 °C$ and is based on a fit to experimental data.^5–7 

Breakdown induced by alternating fields has been observed and measured from power frequencies⁸ up to microwave frequencies.⁹ One of the earliest accounts is Reukema's work on observing RF breakdown between spherical electrodes in ambient air at frequencies from 60 Hz to as high as 425.5 kHz.¹⁰ Reukema makes note of a gradual decrease in breakdown voltage from 20 to 60 kHz and attributes this to the ion mobility.¹¹ Other investigators studying breakdown in this frequency range have come to this conclusion as well.^12,13 As the frequency increases, the heavy ions are no longer swept out of the gap within a half cycle. The accumulating ions create space charge effects that distort the electric field and reduce the breakdown voltage. At approximately 3 MHz, electron mobility begins to have an effect on the breakdown voltage as well, cf. Fig. 1. Some electrons stay in the gap, and during the half-cycle, they are created and decrease the effect of the positive-ion space charge. This, in turn, reduces α and increases the breakdown voltage. While the role of ion mobility and electron mobility in RF breakdown has been discussed,^11,14 steady-state and pulsed RF breakdown in the 1–10 MHz range lacks experimental data and analysis. Note that a discussion of the theory¹⁵ behind RF breakdown and efforts detailing the underlying physical mechanisms may be found elsewhere.^16–18 The focus of this research is to fill in the gaps by examining the measured breakdown fields for megahertz frequencies in atmospheric air.

The obtained megahertz RF breakdown data with a slow-rise time excitation (slowly increasing amplitude over a few second time span) yielded approximately 80% of DC values, which agrees with the results found elsewhere¹¹ and the Monte Carlo simulations shown in Fig. 1, which assumed steady-state conditions.¹⁷ In the following, breakdown fields for different RF rise times will be compared for conditions with and without external ultraviolet (UV) illumination. Furthermore, we will elucidate corona behavior at 3.3 MHz in a strongly inhomogeneous field since it cannot always be expected that the electric field will be uniform in an ESA geometry.¹ 

Bruce profile¹⁹ electrodes made of 360 machinable brass and 304 stainless steel were machined. Also, 1.9 cm diameter spherical electrodes made of 360 machinable brass were prepared. The dimensions of the machined Bruce profile electrodes are shown in Fig. 2.

The machined electrode surface is smoothed through multiple sanding steps with decreasing grit size. After sanding with 2000 grit, the brass and stainless steel electrodes are polished with TC6 Emery E5 and the Jewelers Rouge JR1 compound, respectively, followed by the white Rouge WR1 compound. The residual compound is cleaned off with a Kimwipe soaked in an acetone solution. Typically, after about 30 discharges, the electrodes are polished and cleaned using the same technique described above to remove surface contaminants that may be introduced through successive breakdown tests. Average breakdown voltages for a fixed gap size were compared for fresh and before repolishing electrodes and found to be within a few percent of each other. This is not surprising since the energy in a single discharge is quite small.

The electrode gap is fed directly with a high potential tester where the voltage is increased slowly (few seconds) up to ∼40 kV or until breakdown occurs, see Fig. 3. A commercial high voltage probe is used to measure the DC voltage across the gap.

For DC experiments, air breakdown is observed for gap distances from 1 to 10 mm and is measured six times per 1 mm increment.

The same electrode setup is used where the high potential tester is replaced with a custom RF high voltage source. An inductively fed highly resonant LC tank circuit was developed that enabled generating tens of kilovolts at megahertz frequencies, see Fig. 4 for the basic schematic. The RF source itself consists of a series of amplifiers that produce a maximum of 1500 W output with the RF source signal path depicted in Fig. 5.

The physical implementation of L2 yielded a rather large structure, see Fig. 6, owing to the otherwise dominating resistive losses in smaller coils. That is, the large secondary coil of the circuit (L2) is of a square design (diameter approximately equal to the length) to minimize loss and maximize the quality factor, Q.

Malleable copper tubing (approximately 9.5 mm in diameter) was used to fabricate both coils. The combination of the copper's low resistivity along with the large conductor surface yielded the desired low Ohmic resistance at megahertz frequencies. The dimensions of the large coil are 25.4 cm × 24.1 cm with a turn count of 14. The primary coil (L1) is approximately 3.6 cm × 12.7 cm with a turn count of 3. A vacuum capacitor is connected in parallel with the gap to tune the circuit to the desired resonant frequency, and throughout the experiments, a frequency of 3.3 MHz was selected. The resonant frequency of the circuit is verified using a network analyzer. The high Q of the circuit requires a low coupling coefficient k ∼ 0.1. As a result of these conditions, the placement of L1 with respect to L2 is critical within 0.5 mm. Any positional shift exceeding 0.5 mm will noticeably alter Q such that the much-reduced voltage will no longer affect air breakdown in the gap.

Properly tuned, the high Q, inductively fed LC tank circuit generates sufficiently high voltages, up to 30 kV (60 kV peak to peak) with ∼400 W drive, to break down the gap. Carefully tuning the mutual inductance yields a coupling coefficient such that the LC tank circuit appears as a 50 Ω load to the driving source.

The RF amplitude is monitored through a custom-built capacitive voltage divider, see Fig. 7. A parallel plate capacitor of approximately 2 nF was constructed and connected in series with the tuning capacitor to produce the voltage divider consisting of C2 and C3. The capacitor C3 was fabricated from two 10 cm diameter brass plates separated by 0.051 mm Kapton film. It is imperative that the brass plate surfaces are carefully cleaned; otherwise, residual particles tend to puncture the Kapton film and short-circuit the capacitor. The RF amplitude is measured at the node Vout and fed to the oscilloscope through a 100:1 probe.

The RF circuit is fed using three different excitation methods at 3.3 MHz.

The first excitation type features a slow-rise envelope with ∼5 mV/μs voltage rise, which is obtained by gradually reducing the attenuation over several seconds until the gap breaks down, cf. Fig. 5. It is worth noting that DC breakdown values are obtained by increasing the voltage on a similar time scale (seconds) until air breakdown occurs.

The second excitation method is fast-rise, where a 5000 cycle pulsed signal is switched on as fast as the setup will allow it, resulting in a voltage rise of 200 V/μs, which is substantially faster than the slow-rise (Fig. 8). Amplifier 3 is not used in this mode, cf. Fig. 5.

Adding amplifier 3 into the chain yields the third excitation method, resulting in higher power output into the LC oscillator with ∼414 V/μs rise.

The obtained DC breakdown data reveal the expected decrease in the breakdown field with increasing gap size, see Fig. 9. It is compared with Lau's equation⁴ and AC breakdown measurements made by Gossel and Leu²⁰ and Ritz.⁶ 

Breakdown fields measured using the smaller diameter spherical electrodes were substantially higher and yielded a higher standard deviation, specifically for the smaller gaps overall. This is believed to be a consequence of the smaller size and shape of the electrode as the electrode area is known to play a crucial role in the overall feedback mechanism.²¹ It is simply less probable for a photon emitted from excited gas molecules in the gap to find the cathode for the photoemission of an electron if the cathode is physically small.

The measured breakdown fields using the Bruce profile electrodes aligned reasonably with Lau's equation and the measured data from Ritz. Both Bruce stainless steel and brass are close to the curve generated by Eq. (2) for gaps above 2 mm in size. Differences may be explained by impurities that reside within the material and its susceptibility to form an oxide layer which will again affect the feedback mechanism and thus the breakdown voltage. At 1 cm, the measured breakdown voltage was approximately 28.3 kV for the Bruce profile and brass spherical electrode configurations, which is close to the often-cited ∼30 kV/cm breakdown field for atmospheric air. The tendency for stainless steel to exhibit higher breakdown voltages than those obtained with other materials (brass) is consistent with what is reported elsewhere.⁷ 

Using Eq. (1) and the experimental breakdown fields, cf. Fig. 9, the second Townsend coefficient, γ, is calculated for the DC breakdown voltages for both stainless steel and brass Bruce profile electrodes, see Fig. 10.

The first Townsend ionization coefficient, α, used for the calculations was taken from Sarma and Janischewskyj,³ which are the best fit of measurements by Harrison and Geballe,²² Masch,²³ and Sanders.²⁴ The attachment coefficient, η, was also taken from Sarma and Janischewskyj³ and was the best fit of measurements by Harrison and Geballe.²² The resulting equations for α/p and η/p (cm⁻¹ · Torr⁻¹) as functions of the reduced electric field, E/p, are repeated here. The effective ionization coefficient is calculated by subtracting η from α for a range of 25–60 V · cm⁻¹ Torr⁻¹. At high E/p, electron attachment becomes negligible compared to the number of ionizations. Following the procedure described by Sarma and Janischewskyj,³ the equation found by the ionization data^23,24 beyond 60 V · cm⁻¹ Torr⁻¹ is used without the contribution of attachment. The equations for α/p are valid for E/p from 25 to 240 V · cm⁻¹ Torr⁻¹, and η/p is valid from 25 to 60 V · cm⁻¹ Torr⁻¹

Note that the choice of Eqs. (3) and (4) is based on an extensive literature survey; they are believed to provide the most reliable α values in empirical equation form. In general, one notes significant inconsistencies in the reported values for the air ionization coefficient, α, which will have a large impact on the calculated γ due to the exponential dependence in (1). Thus, the values of γ shown in Fig. 10 have to be taken with caution. Nevertheless, the derived values for γ using the brass Bruce profile DC breakdown measurements fall within the 0.01–0.001 regime, which is listed by Nasser.¹¹ Contrarily, the calculated γ using stainless steel Bruce profile DC breakdown measurements is much lower and drops drastically at gaps <3 mm. It would suggest that the DC breakdown measured in smaller gaps using stainless steel Bruce profile electrodes no longer follows the pure Townsend mechanism and that surface rather than volume effects take over. It is noted that Gossel and Leu²⁰ also measured higher AC breakdown voltages using stainless steel electrodes in small gaps, cf. Fig. 9, which supports the finding that breakdown using stainless steel electrodes occurs at comparatively higher fields.

Overall, the presented DC breakdown measurements using different electrode material configurations revealed the breakdown amplitudes being primarily affected by the choice of cathode material, see Fig. 11. That is, configurations where the cathode material is brass yield lower breakdown voltages with a noticeably higher standard deviation than its steel counterpart. The overall effect of the cathode material is expected since the second Townsend coefficient, γ, will vary between different electrodes. The effect is statistically significant and easily repeatable. Covering the extremes in Fig. 11 at 31.16 and 29.3 kV/cm, respectively, (standard deviation included) and following Eq. (1) with the first Townsend coefficient data from Sarma and Janischewskyj³ and Raju,²⁵ a variation of γ from 0.02 (brass) to 0.002 (stainless) suffices to explain the observed spread in breakdown fields in Fig. 11. That is, while the γ value spread covers one order of magnitude, the accompanying spread in the breakdown field is considerably smaller at a ∼6% span. The reason for this disparity may be found in Eq. (1) that has γ as a linear factor, whereas the electric field dependent α appears to be exponential. Further research beyond the scope of this work would be needed to capture quantitatively γ values in model calculations.

Having established a baseline for the DC measurements through comparison with the literature, we relate the experimental data with the results from the RF breakdown measurements with Bruce profile electrodes at 5 mm gap distance, see Fig. 12. Slow-rise RF excitation (four left-most data points in the figure) yielded results similar to the sparse literature on the topic²⁶ and recent simulations at 3.3 MHz.¹⁷ The RF breakdown voltages with the same slow-rise as DC breakdown yielded approximately 83% of DC breakdown field amplitude. It is fair to assume that slowly increasing the voltage on the gap gave sufficient time for an ion cloud to form and electrons to enter the gap.¹¹ 

RF breakdown produced by fast-rise excitation resulted in a value of about 90% of the DC breakdown fields. The even faster-rise excitation using stainless steel Bruce profile electrodes yielded breakdown voltages that were noticeably higher (120% of DC) with substantially a larger deviation (over 640 V) than its DC counterpart (∼61 V).

Such behavior is expected to be due to the faster rise of the electric field induced in the electrode gap. That is, for a given gas and pressure, it has been shown previously that the breakdown field is a monotonically falling function of the breakdown delay time for unipolar, cf. Fig. 14 in Ref. 27, and microwave, gigahertz, cf. Fig. 5 in Ref. 28, excitation. Since the rise time of the presented data is on the order of the delay time (breakdown occurs during or close to the rising edge of the pulse), it is obvious that the breakdown voltage (field times gap distance) is also a monotonically falling function of the rise time. Or, in other words, the breakdown voltage increases when the rise time is shortened. Apparently, this is true for the megahertz RF exciting electric fields as well.

Considering the high standard deviation of RF breakdown seen with Bruce profile steel electrodes fed with faster-rise excitation, there was interest in seeing whether the statistics could be improved by seeding electrons in the gap during the experiment. To accomplish this task, the approach of inducing photoemission from the electrodes by illuminating the gap with a UV light source producing a sufficiently low wavelength—high photon energy—was taken.

In order for a photon to release an electron from the electrodes via photoemission, the photon energy needs to be larger than the work function of the material. One finds elsewhere²⁹ that Type 304 stainless steel has a work function of approximately 4.34 eV, which translates into a photon wavelength of 280 nm or below.

A Xenon flash lamp was used as the deep UV source for this experiment, which produced a spectrum reaching into the photoemission regime, see Fig. 13.

Besides a broad background, peaks in the deep UV spectrum were measured at 246.57 and 259.73 nm, which are well below the threshold wavelength of 282 nm, making the 5 J Xenon flash lamp a suitable source.

A calcium-fluoride plano–convex lens is utilized to produce a focused image of the lamp onto the electrode gap. It is noted that CaF₂ has better transmission characteristics in the deep UV range compared to fused silica or similar materials.

With UV application, the resulting breakdown field for the faster-rise application was much lower with substantially a less standard deviation than without UV application, see the right two data points in Fig. 14. It is fair to argue that the statistical time lag of breakdown is largely eliminated due to the existence of the photoemitted electrons in the gap at the moment when the pulse is applied. Furthermore, the gap breaks earlier on the rising edge of the applied voltage amplitude, and one observes that the faster-UV breakdown voltage is still higher compared to the slower rise time cases. Thus, one may conclude that the “faster-rise” rise time, ∼80 μs, is of the order of the formative time of the RF breakdown.

It is instructive to compare the measured RF breakdown data with breakdown data obtained previously at microwave frequencies in the gigahertz regime. Moving from megahertz to gigahertz, it is obvious that for sufficiently high frequencies, neither the electrons nor ions will travel significant distances that would cause a substantial number density loss to electrode surfaces (diffusion over long timescales excluded). One finds that the effective electric field, $Ee$⁠, which may be used to calculate average drift velocities, equals the rms electric field amplitude if the electron collision frequency, $νc$⁠, is much higher than the microwave frequency, ω.³⁰ For atmospheric air, the electron collision frequency is estimated to be around 3 THz.³⁰ Thus, it is safe to argue that for microwave frequencies as high as 30 GHz, the effective electric field is simply the rms field amplitude. In the first order, the effective field may be directly compared to the unipolar electric field amplitude causing air breakdown. Thus, as a first rough estimate, one may argue that the rf-field amplitude leading to breakdown in air at gigahertz frequencies needs to be a factor square root of two higher than unipolar breakdown. This is not quite the case as shall be discussed in the following, presumably owing to the much-reduced electron loss due to the lack of significant charge carrier drift in the microwave field.

To observe microwave breakdown, ionization needs to outweigh the electron losses such as diffusion, recombination, and attachment. At atmospheric conditions, the breakdown process is attachment controlled, and it was estimated (again for $νc≫ω$⁠) that the breakdown field at gigahertz frequencies equals E/p = 30 (V/cm Torr) for air in the case of very long microwave pulses.³⁰ This electric field amplitude is corroborated by the experimental data of Gould and Roberts³¹ which reveals 33 (V/cm Torr) breakdown fields for microsecond pulses. That is, the breakdown rms electric field in the gigahertz regime is estimated to be ∼25 kV/cm rms in atmospheric air. This value may be compared to Fig. 12, which yields, when normalized to DC breakdown (30.5 kV/cm amplitude), a factor of 0.85, 1.0, and 1.16, for slow-rise 3.3 MHz, DC, and gigahertz breakdown, respectively, or when rms values are compared: 0.6, 1.0, and 0.82, respectively. Note that the provided absolute breakdown field amplitudes constitute somewhat of a minimum breakdown threshold. That is, for shorter pulses, the formative time lag of breakdown needs to be considered.^32,33

In general, the breakdown field amplitude is a monotonically decreasing function of the pulse application time or breakdown delay time (note that no breakdown will occur if the pulse duration is shorter than the breakdown delay). For instance, one finds that reducing the pulse duration from 1 ms to 100 ns results in a 30%–50% increase in electric field breakdown amplitude for atmospheric breakdown conditions at 2.8 GHz.^32,34 Similar is observed for unipolar pulse conditions.^27,35 Of course, many experiments have a finite rise time, and breakdown may in the extreme case occur on the rising edge of the pulse. Thus, a certain caution is generally recommended when quantitatively comparing breakdown data from different sources. Relatively speaking, however, the presented data reveal that 3 MHz fields exhibit a distinctly lower breakdown threshold than 3 GHz fields (∼25% lower in atmospheric air).

Since corona losses are always a concern in any high power RF transmission systems such as the megahertz ESA,³⁶ RF and DC corona measurements in atmospheric conditions were also recorded. A 10 cm diameter stainless-steel Bruce profile electrode paired with a tungsten needle is set at 2 cm gap distance for both DC and RF measurements. The tungsten needle dimensions are as follows: 47.6 mm tapered length, 250 μm tip radius, and 6.36 mm base width. The same setup for RF slow-rise is implemented for RF corona. The electrode configuration is flipped to examine DC corona formed with a positive (anode) and a negative (cathode) tungsten needle, respectively. A high potential tester is connected to the anode electrode to generate DC corona. Corona is said to be detected as soon as the digital current meter of the high potential tester would indicate current flow, which was at 0.1 μA and 1 μA, for positive and negative polarities, respectively.

The minimum corona current was detected for the negative needle at ∼5 kV and produced visible glow at 8 kV, see Fig. 15. The current draw increases in a positive nonlinear trend. At the maximum point, it is drawing nearly 200 μA. The negative needle emits electrons easily due to field emission on the tip of the needle.

DC corona measurements with a positive needle convey similar trends as the negative needle DC corona. The same current amplitude, ∼1 μA, is reached at ∼6 kV, which is approximately 1 kV higher than in the negative needle corona case. Visible glow began at 15 kV, which is 7 kV higher than negative needle corona. However, the current draw with respect to voltage is much less. Similarly, the V/I maximum for positive needle corona is over 6 times larger than negative needle corona. This difference in current draw and V/I measurements is a result of the electron source. Since the Bruce profile electrode in a positive needle configuration has a relatively flat surface, it is not a very efficient electron source. Instead, the electrons present in the air surrounding the electrodes, which are less than what the negative needle emits, are drawn toward the positive needle.

To capture the onset of corona at 3.3 MHz, a digital watt meter is connected at the output of the amplifier chain to measure the forward power being delivered to the load. Peak RF voltage with respect to forward power is recorded, see Fig. 16, and a change in the slope is an indication that the LC circuit is loaded down by corona. The distinct slope change point “D” coincides with the visual onset of corona on the tungsten needle electrode. Observing the prior, smaller slope change, one might argue that weak corona is forming at 21 W rms input power (5 kV) already. Either way, the corona onset voltage for 3.3 MHz seems nearly the same as the DC onset value, cf. point “A” in Fig. 15. However, it is roughly estimated that the RF corona draws, at the measured onset, about one order of magnitude higher current than the DC corona. That is, the 1%–2% drop from the linearly interpolated voltage seen before visible corona onset (cf. point “D” in Fig. 16) could be reproduced by introducing such RF current flowing in parallel with the capacitance $Ceff$ of the lumped element model (cf. Fig. 4).

The input power is stepped up by 0.1 dBm increments after corona onset until breakdown occurs, point “E” in Fig. 16. Again, the voltage drops drastically (off-scale in the figure) due to the sharp rise in current draw as a result of the plasma arc from breakdown. At 2 cm gap distance (needle tip to plane), the onset voltage for corona is approximately 5.1 kV and sustains down to 4 kV. Below 4 kV, the corona on the tungsten needle extinguishes. Based on these conditions, a 2 cm gap requires approximately 23 W rms with the presented LC circuit to ignite corona. The macroscopic field at this point is about 2.55 kV/cm, which translates into roughly 85 kV/cm at the needle tip with an approximate field enhancement factor, β ∼ 33.3, obtained from an electrostatics simulation.

Relating these results to the electrically small antenna¹ suggests that care must be taken in fabricating such an antenna as any sharp corners or protrusions need to be minimized. To avoid corona in the antenna and allow a 20 kV/cm macrofield at full power (∼500 kW), a protrusion of, for instance, 0.05 mm radius should be no taller than 0.07 mm. This suggests that surface smoothness should be considered when selecting construction materials particularly for the high electric field tuning capacitor gap.¹ Thus, to avoid corona losses, the use of smooth, large radius, tapered capacitively loaded loop edges with low field enhancement is recommended. Besides the corona losses, it is worth noting that the antenna operated at 500 kW will require a gap size between the antenna petals of 10 cm (Ref. 1), and thus, an absolute voltage of 200 kV peak will need to be supported. This assumes that the breakdown electric field remains reasonably constant for larger gap sizes for the RF case. It is noted that 50 kW operation with a 3 cm gap and 60 kV potential difference is more likely to be practical.

DC breakdown fields measured in stainless steel and brass Bruce profile electrodes followed reasonably close with the results reported elsewhere,^4,6 providing a reliable baseline for comparisons to RF breakdown. Varying anode and cathode materials in DC breakdown experiments confirmed the cathode being a dominant factor in the overall feedback mechanism. Configurations with brass cathodes yielded lower breakdown voltage and a higher standard deviation than stainless steel cathode configurations, independent of the anode material. Compared to 3.3 MHz excitation, slow-rise excited RF breakdown fields (∼80% of DC) matched the sparse literature and simulation results. The fast rise (⁠$≥≃$ 200 V/μs) RF breakdown data extend the literature for the 3 MHz regime, and as a result of fast-rising fields stressing the electrode gap, breakdown amplitudes higher than DC were observed. UV application to the electrode gap lowered the standard deviation and breakdown amplitudes, especially in the faster rise time cases. The RF corona was studied to find practical limits in an ESA with regard to surface smoothness—protrusions—and the maximum electric field. Based on the presented measurement data, an estimated limit for the ESA with a 10 cm minimum gap at 3.3 MHz would be 845 kW with a gap voltage of ∼260 kV (26 kV/cm). At 500 kW, the resulting ESA electric field of ∼20 kV/cm may be safe for operation. The presented experimental quantification of RF breakdown in the megahertz regime will enable reliable operation of capacitively loaded ESAs in possible future ionospheric research in the equatorial region.

This material is based upon work supported by the Air Force Office of Scientific Research under Award No. FA9550-14-1-0019. One of us, IA, would like to thank the Los Alamos National Laboratory for their support.