Fundamental investigation of unipolar and RF corona in atmospheric air Free

Radio frequency (RF) corona at 3.3 MHz in atmospheric air is studied to evaluate the power limitations of an electrically small antenna (ESA) design.¹ As is with all high-power RF systems, the formation of corona is a limiting factor to radiated output due to the corona-driven power loss and noise generation.² The ESA relevant to this study operates at a 3–10 MHz frequency range and is tuned by adjusting the gap distance of its parallel plate gap.^1,3 At 3 MHz and 500 kW power levels, the capacitive gap yields the highest electric field (greater than 20 kV/cm) and is susceptible to breakdown or corona formation. Based on the measured breakdown voltage data in previous work, the power in the gap of the ESA for a 10 cm gap minimum was calculated at 845 kW (∼26 kV/cm), whereas the ESA operation limit is set at 500 kW.⁴ Measured RF corona voltage data also elucidated the limits of protrusion dimensions in the ESA for corona formation. For instance, a protrusion with 0.05 mm radius should not be any taller than 0.07 mm in the ESA geometry at 500 kW.⁴ The focus of this paper is to quantify the corona onset and further investigate the mechanisms involved at 3.3 MHz. For non-uniform fields, the generation of charge carriers varies across the gap distance. Electron multiplication is determined by the integral of the effective ionization coefficient, α_e, along the path $∫αedx$⁠. The breakdown criterion for non-uniform fields, or the corona inception voltage, takes the form

where d is the gap distance and gamma is Townsend's second ionization coefficient which encompasses various secondary processes that govern the feedback mechanism of the discharge and exhibits some electrode material dependence. The corona onset voltage depends on many factors, which include electrode gap distance, emitter radius, the type of excitation being applied to the electrode geometry, the type of gas, and the gas pressure. For those studying corona onset, it is desirable to calculate the electric field in a non-uniform geometry. Various equations for calculating the electric field in non-uniform geometries are reported in literature.⁵ For geometries more closely related to the needle-plane gap, Mason presents an analytical solution of the field stress at the tip of a paraboloid-plane gap,⁶ and Kosmahl provides an analytical solution for the field along the centerline of an ellipsoidal cone under a homogeneous field.⁷ For complex geometries in which an analytical solution is not feasible, the typical approach to solve for the electric field is to do so computationally via software, such as COMSOL Multiphysics or ANSYS Maxwell. It is noted that the electric field for the needle-plane geometry discussed in this paper is solved computationally using COMSOL Multiphysics.

When discussing corona under static fields, it is useful to make a distinction between the positive and negative needle corona. This simply refers to the polarity of the needle electrode in reference to the plane electrode, which leads to different manifestations or modes of corona. The detailed modes of corona are not discussed here since they are well studied and reported elsewhere.^8–10 Instead, a brief qualitative discussion of the development of positive and negative needle corona is covered here. In a negative needle configuration, a free electron—possibly originating from field emission of microprotrusions on the tip surface or from field-detached electrons from ion clusters in the vicinity of the needle^5,11—will accelerate away from the negative needle and collide with neutral molecules, resulting in either ionizations or excitations. Secondary electrons generated from multiple ionization events lead to the development of electron avalanches, in which these electrons travel into the low field region in the gap and become attached to neutral gas molecules or atoms, forming negative ions. Positive ions left behind from the electron avalanche form a space charge as they move toward the negative needle, which further enhances the field near the needle electrode tip. This enhanced field at the tip promotes the field emission from the micro protrusions, providing a potential feedback mechanism to maintain a self-sustaining discharge for negative corona. Similarly, photoemission at the needle electrode resulting from photons released from the excited molecules that relax to the ground state provides a feedback path for a sustained discharge. It is noted that photoemission at the needle electrode is the dominant mechanism involved in supplying new electrons for sustaining a discharge in negative needle corona.⁹ 

In the positive needle case, the plane electrode is not a good source for field emitted electrons due to its flat geometry and thus small geometrical field enhancement. Hence, initiating electrons must originate through a path other than metallic field emission from the surface. The initiating electrons involved in the positive corona have been speculated to originate from field detachment of negative ions in the surrounding gas,⁵ while others report that the initial electron that starts the ionization process originates from background radiation.^12,13 Both are connected; the negative ion density results from the accumulation of charge generation in the gaseous volume due to cosmic radiation balanced by ion recombination. The initiating electron that is released into the gap will accelerate toward the positive needle leading to the development of electron avalanches. The electrons from the electron avalanches are neutralized upon reaching the positive needle surface. Positive ions remaining from the electron avalanche will drift toward the plane electrode, liberating electrons from the flat cathode upon impact. High-energy photons are emitted from the ionization region surrounding the positive needle electrode as a result of electron–ion recombination. The emitted photons induce volume photoionization outside of the ionization region, liberating electrons that will form new avalanches and support a self-sustaining positive corona discharge.^14–16 Additionally, photons not attenuated by air within the gap initiate photoemission at the cathode, contributing to the feedback.

The mechanisms contributing to corona formation under an alternating field are dependent on the frequency being applied. At power frequencies (60 Hz), the field reversals in the needle-plane gap are too slow to inhibit the movement of ions across the gap. That is, at frequencies between 15 and 500 Hz, the critical distance at which charge is retained in the gap from one to the next half-wave is approximately 1.2 m for ions in atmospheric air in uniform fields.⁹ Therefore, ions easily drift across the gap within one half-cycle in smaller, cm-sized gaps, and the corona will form very similar to DC conditions at such frequencies. Both mechanisms involved in positive and negative needle corona manifest simultaneously under the low-frequency alternating field. As the applied voltage is increased beyond the onset level, the needle-plane gap will prefer to breakdown during the positive half cycle due to the breakdown voltage for the positive needle being lower than the negative needle.⁹ As the frequency is increased, the onset voltage of the corona begins to decrease. It will decrease 3%–5% at 10⁵ Hz (Ref. 9) and approximately 15% at 10⁶ Hz.¹⁷ At these high frequencies, the electrons and ions do not move across the gap in one half-period as they would in static fields or low frequencies. Rather, they will oscillate in the gap, accumulating and giving rise to noticeably higher currents. When the applied voltage level is further raised, the gap will break down at substantially lower voltages than what is reported for low-frequency corona. Between 50 Hz and 75 kHz in a needle-plane geometry, the breakdown voltage drops by 55%,¹⁷ which is much lower than the maximum drop of approximately 20% observed in homogeneous fields⁴ in the same frequency regime.

The breadth of literature available on DC coronas is enormous. Nasser et al. studied sustained positive streamers in atmospheric air and quantified the critical field need for propagation.¹⁸ Phelps and Griffiths found the critical field required for sustained positive streamers varies with 1.5 times the pressure for dry air as well as a strong linear dependence to the water vapor partial pressure.¹⁹ Ashikev et al. and Goossens et al. studied the transitions of negative corona in ambient air.^20–22 Benocci and Mauri measured IV characteristics and photocurrents of positive and negative corona in a pure helium environment.²³ Ferriera et al. used a stationary solver to calculate time-averaged current and voltage values for a needle-plane geometry in atmospheric air, attaining good agreement with measured values.²⁴ One may look to the literature referenced therein²⁴ to find a more in-depth discussion of the physical mechanisms and development of DC corona.^9,13,25–28

RF corona, while not as heavily reported as DC corona, has been studied by several researchers in various works. Sato and Haydon observed the onset and development of 10 MHz corona in a needle-plane geometry over a pressure range of 80 to 650 Torr.²⁹ Sakiyama and Graves studied and provided evidence of two different discharge modes and the transition mechanism of RF corona at atmospheric pressure.³⁰ Their work is centered on 13.56 MHz corona in a needle-plane geometry (referred to as the plasma needle), which is relevant to biomedical applications. Others have studied the optical emission spectrum³¹ and physical discharge characteristics with respect to voltage–power curves of the plasma needle.³² Auzas et al. measured the electrical and thermal properties of 5 MHz pulsed RF corona in a single needle geometry at pressures above 1 bar (Ref. 33) and developed a model for it.³⁴ Price et al. derived a breakdown criterion using the electron continuity equation for low and high-frequency corona of an isolated cylindrical monopole.³⁵ They attained reasonable agreement of the predicted corona onset at 60 Hz and 300 MHz with experimental data.

In general, there has been a collective effort in piecing together a better understanding of RF corona. Despite this, there are some properties of RF corona that are not well documented as of yet. The goal of this paper is to extend the literature on RF corona by reporting the experimental measurements for a needle-plane geometry at 3.3 MHz, a frequency relevant to ionospheric heating that was previously lacking, and relating the results to operation and design considerations of the ESA. For the experimental setup verification, DC corona is measured first and compared with the literature. This is followed by the presentation and discussion of the RF results.

A 10-cm-diameter Bruce profile³⁶ electrode was fabricated from 304 stainless steel and served as the planar electrode in the needle-plane geometry. The stainless-steel electrode is polished to a mirror finish using Jewelers Rouge JR1 followed by white Rouge WR1. The residual compound remaining on the electrode surface from polishing is cleaned using a Kimwipe soaked in acetone. The electrode surface is cleaned between experiments to remove surface contamination. A schematic of the Bruce profile electrode used in the experiments is found elsewhere.⁴ 

Pure tungsten (>99.5% pure) and 2% lanthanated tungsten rods, commonly used for welding, of 3.175 mm diameter and 82 mm length, are sharpened to a point with a diamond electrode sharpener tool. The angle to which the electrodes are sharpened was adjusted depending on the experiment. The microstructure of lanthanated tungsten consists of micrometer-sized lanthanum oxide (La₂O₃) grains distributed in a tungsten matrix.^37–39 This is achieved through a powder metallurgy process, which involves heat treatment, pressing, and sintering of La₂O₃ and tungsten powder. Lanthanated tungsten was selected as an electrode material due to its known lower ignition voltage compared to pure tungsten in DC welding applications.⁴⁰ The diffusion and evaporation of La₂O₃ from the bulk tungsten to the electrode surface lower the work function, thus lowering the necessary voltage for igniting/sustaining the welding arc, presumably once high electrode temperatures are reached. It is of interest to see whether the low voltage ignition in lanthanated tungsten electrodes manifests at room temperature under high frequency excitation as well.

The needle-plane geometry, where the needle electrode is grounded, is separated by a 2 ± 0.05 cm gap and fed directly with a high potential tester. Two high-potential testers, capable of supplying positive and negative voltage, respectively, are used to bias the plane electrode to get a positive or negative corona, see Fig. 1. Two pure tungsten needles sharpened to 31.4 ± 0.1° and 44.2 ± 0.1° included angles are alternated to observe the effect of the tip angle on the corona onset voltage. The included angles of the needle electrodes are verified by taking images of the needles under a microscope and measuring them in an image manipulation software. The voltage fed into the needle-plane gap is increased by 1 kV steps, and the time-averaged current is recorded. The time averaged current is measured with high potential tester and is displayed concurrently with the applied voltage. The voltage is increased until the limit of the high potential tester in use is reached, or breakdown of the gap occurs.

The same electrode configuration as used in the DC setup with the gap increased to 3 ± 0.05 cm is fed with a custom-built, high-voltage RF source. A highly resonant, loosely coupled LC tank was constructed to generate sufficiently high RF voltage (upwards of 30 kV) at single-digit MHz frequencies. A variable vacuum capacitor is connected in parallel with the electrode gap to tune the LC circuit to the desired frequency. The RF voltage at the electrode gap is monitored through a custom-built capacitive voltage divider. The capacitive voltage divider is connected in series with the variable vacuum capacitor. More details on the RF circuit design and capacitive voltage divider are discussed elsewhere.⁴ 

The RF source consists of a signal generator connected in series with two amplifiers capable of delivering up to 700 W output to the load. A simplified diagram of the RF source signal path is illustrated in Fig. 2.

For a repeatable corona ignition time measurement, a photomultiplier tube (PMT) was placed about 0.6 m away from the corona needle to detect the emergence of UV photons. The PMT is fitted with a UV-AR coated fused silica plano–convex lens (with a focal length of 50 mm) and a UG11 color filter to focus emitted UV onto the PMT detector while attenuating light outside the 275–400 nm range. Both the RF signal and PMT signal are synchronously recorded, which yields the corona onset voltage and time delay (see Fig. 3).

Three pure tungsten and three lanthanated tungsten electrodes are sharpened to the same angle (30 ± 0.05° included angle) using a commercial sharpening tool, see Fig. 4. The electrodes are fitted into an electric screwdriver and rotated slowly while being sharpened to create a symmetric taper. The order in which the needle electrodes are sharpened alternates between pure tungsten and lanthanated tungsten material, where the first needle sharpened is made of pure tungsten. A total of 30 shots are measured and recorded for each needle-plane configuration, amounting to 180 shots total. The PMT gain is set at the same level throughout the whole experiment. Before taking measurements, the tungsten needle is conditioned (ignited by RF voltage of ∼7 kV peak) for approximately 6 s to smooth micro protrusions from the electrode tip. Such a conditioning is believed to help with keeping consistency between all the needle electrodes before taking measurements.

RF breakdown using needle P3 (refer to Fig. 4) in the same needle-plane configuration used for RF corona was briefly measured. Using the same RF experimental setup (see Fig. 3), a 5000 cycle pulse with input power exceeding −5 dBm was applied to produce the sufficiently high voltage to bridge the gap reliably. A total of 20 RF breakdown measurements were recorded.

The acquired measurements for DC corona show that the needle with the smaller included angle ignited at a lower voltage than the needle with the larger included angle, see Fig. 5. It is reasonable to argue that the larger field enhancement of the smaller included angle electrode will amplify electron multiplication and ionization processes more readily, leading to corona ignition at a lower voltage. This behavior is observed in both positive and negative needle corona. As the voltage is increased, the current increases gradually up to some critical voltage where the current begins to rise at an increased rate, seen as an inflection point in Fig. 5 at approximately 5 kV. It is at this point at which the gap becomes much more conductive and draws more current, thus fully igniting the corona. Beyond this sharp increase, as the voltage applied to the needle-plane gap is further increased, the current rises more slowly, again similarly visible in both positive and negative corona. The origin of the additional inflection point for positive corona, with small included angle, at about 15 kV may be linked to the ultimate breakdown occurring already 3 kV later, at approximately 18 kV. We note that the 18 kV value is very close to a measured value of 17.55 kV in a 2 cm needle-plane geometry reported elsewhere.⁴¹ The negative corona case does not exhibit this secondary current inflection or breakdown. The breakdown in negative polarity is beyond the 30 kV limit of the experimental apparatus utilized. It is also believed that a secondary inflection would not appear if the applied voltage were increased to the point of breakdown. At 30 kV, the luminous region has the appearance of a glow discharge, similar to what is reported elsewhere.¹⁰ It is reasonable to assume that the glow discharge will exhibit a steady increase in current as the voltage is raised until the point of breakdown. Another mode of corona (negative feathers) in the negative needle configuration may manifest prior to breakdown and yield a secondary inflection, but it is only stable in large gaps under very high fields.⁹ In the experimental needle-plane gap, it is more likely that a single negative streamer will bridge the gap given sufficient voltage and initiate breakdown.

The lower breakdown voltage for positive corona agrees with what is reported in the open literature.²⁵ One finds as commonly accepted that in the case of positive DC corona, the electrons move toward the positive needle and leave behind a positive space charge. This positive space charge reduces the field strength near the positive needle but increases the size of the ionization region as space-charge expands toward the low field region in the gap.²⁵ The field at the edge of the positive space charge may become large enough to the point of initiating a cathode-directed streamer, which may lead to breakdown. Under negative needle corona, the electrons are deflected into the low field region of the electrode gap, leaving a positive space between the negative space charge and the negative needle. The positive space charge enhances the field at the negative needle, but the size of the ionization region is heavily reduced.²⁵ When ionization ends, i.e., when the electron avalanche generated from the initiatory electron reaches the grounded plane electrode and conducts away, the positive and negative space charges are removed from the gap by the applied field, and the cycle is repeated, presenting as Trichel pulses.^42,43 In this experiment, only average current was measured and Trichel pulses were not explicitly observed. A higher bias voltage is required to overcome this phenomenon, hence the breakdown voltage for negative needle corona is higher. Based on the experimental data reported in the literature,⁴¹ the breakdown voltage for the negative needle with a 2 cm gap is expected to be ∼40 kV, more than two times the value measured for the positive needle.

It was observed that negative corona using the smaller included angle needle drew 2–3 times more current than positive corona in the range of 7–16 kV. Ferreira et al. also noted the same degree of current draw occurring over the same voltage range between their negative and positive corona experimental measurements in a needle-plane geometry.²⁴ In the case of the larger included angle needle, the negative corona draws about 1.5 times higher than the positive corona in the range of 7 to 12 kV and falls below unity above 13 kV. This reduced current draw is believed to be a consequence of the smaller field enhancement of the larger angle tip geometry, which effectively reduces the degree of ionization in the surrounding gas, and consequently, less current is drawn.

Having established that the corona setup produces results that are consistent with DC experiments reported elsewhere, the experimental focus was moved toward RF corona.

Different from the DC corona, the RF excitation occurs with a rise time of the RF amplitude on the microsecond timescale, see Fig. 6. The first significant spike in the PMT signal identifies RF corona onset in the sense that ionization processes via electron collisions are always accompanied by excitation processes. Owing to the chosen wavelength range of detection, the PMT detects the de-excitation primarily from nitrogen's positive system.^44–46 The time delay is found by taking the difference between the time at which RF voltage is applied (reference line A) and the time at which the corona onset occurs (reference line B), cf. Fig. 6. The corona onset voltage is determined by measuring the amplitude of the instantaneous RF voltage at which the corona onset falls upon (horizontal reference line C, −6.1 kV).

Due to the inherent statistics associated with the corona onset and gaseous breakdown, in general, the onset time delay varies from one RF pulse to the next, even if the same, identical pulse is applied every time. Consequently, the amplitude of the initial PMT signal spike is affected. That is, for short time delays (less than 70 μs), the measured PMT signal approached the PMT's noise floor with values as small as −5 mV. For longer time delays, the PMT signal ranged from −15 mV to as large as −200 mV. Without providing an in-depth analysis, it is fair to assume that this behavior is driven simply by the moment of appearance of initiatory electrons in the needle-plane gap coupled with the electric field amplitude at that moment. Initiatory electrons that appear early (small RF envelope amplitude) will gain less kinetic energy than one which appears later (close to the peak of the RF amplitude) as a result of the electric field amplitude at those points in time. Electrons that gain higher energy will make more collisions with the neutral gas, resulting in a larger number of excitation events. This creates additional UV photons that are emitted via spontaneous emission and detected by the PMT, yielding the observed larger voltage spike.

Envelope detection of the RF and PMT waveforms was applied to several of the corona measurements. The RF and PMT envelopes of shot 7 and 30 for needle L2, which encompass the extremes of the measured time delay in that data set, are analyzed, Fig. 7. Note that the PMT signal onset is set as time zero.

The graphed PMT and RF envelopes reveal that corona onset occurring on the rising edge of the RF signal reduced the final peak voltage of the circuit, approximately 6.6 kV rather than 7.5 kV for the shown example. This general behavior is observed across the board owing to the corona loading the resonant, exciting circuit.

The total RF corona onset voltage and time delay data points for the three pure tungsten and three lanthanated tungsten needles are plotted in Fig. 8.

The time delays measured for the six needles span from 58 μs to 1.14 ms. The majority of the measured waveforms exhibited time delays of less than 200 μs. One of the tested needles, P1, did not initiate corona reliably at the input power level used for the rest of the needles. Thus, the input power to the exciting circuit was increased by 2 dB to achieve consistent corona ignition, which consequently yielded higher measured onset voltages compared to the other needles. The higher onset voltages measured for the P1 needle was presumed to be a result of having a smoother or larger radius tip compared to the other needles. To confirm this, the needle electrode tips were imaged with a Carl Zeiss Crossbeam 540 FIB-SEM Microscope, Fig. 9.

On the microscale, the tip geometries of the needles are all strikingly different from one another, which is expected since a simple mechanical procedure for sharpening the electrodes was utilized. The pure tungsten needles were the most uniform, showing little or no signs of cracking around the tip. The surface on the tip of P1 is remarkably smooth in comparison with the rest of the needles and is thus believed to be responsible for the higher corona onset voltages measured for P1. The lanthanated needle L2 and L3 exhibited the least uniform tip geometries, featuring cracks and jagged structures on the surface. L1 was the most uniform of the set of lanthanated needles but still exhibited some cracks on the surface as well. This suggests that the 2% La₂O₃ infused into the tungsten makes the resulting material physically weaker or more brittle.

Of the tungsten needles, one might argue that, after P1, P2 may have the most uniform tip geometry of all the needles imaged. However, upon closer inspection, P2 has many protrusions present on its tip surface, Fig. 10.

These microprotrusions are scattered about the tip with radii of less than 1 μm. One notes the round geometry of these microprotrusions, which is likely due to melting during the previously mentioned initial conditioning of the needles (running corona for ∼7 s), a process, therefore, deemed successful in removing the sharpest corners.

The zoomed-in temporal signals, cf. Fig. 6, enable determining the half cycle at which corona onset occurs; see Fig. 11 for representative examples. It was observed that the corona had some preference for the polarity of the half-cycle in which it ignites when the pure tungsten needles are used, while such a distinction could not be made in the lanthanated case, see Table I. However, the sample size is considered too small to be truly statistically significant. Given the short duration of the negative ignition pulse, cf. Fig. 11, it is reasonable to assume this is not a Trichel pulse but instead an incomplete avalanche.⁴⁷ 

It was initially thought that field emission may be the mechanism causing the preferential negative ignitions observed in P1 and P2. To investigate, an 2D axisymmetric electrostatic simulation was performed with the detailed geometry of needle P2 used as input for the electrostatic simulation. For simplification, the tip geometry in the simulation is approximated to a flat tip with a radius of 10 μm. Using an onset voltage of 5.8 kV, which was found by averaging the onset voltages measured for the P2, yielded a maximum enhanced electric field of 1.5 × 10⁸ V/m at the curved edge of the tip. Thus, the enhancement factor of the needle, found by dividing the maximum electric field calculated from the simulation by the 1.93 kV/cm macrofield of the needle-plane gap, is β ∼790. The magnitude of the enhanced field found by the electrostatic simulation is not large enough to support appreciable field emission, which typically starts around 10⁹ V/m.^9,48 SEM imaging of needle P2 revealed microprotrusions on the tip surface. An ellipse with semi-major axis 0.9 μm and semi-minor axis 0.5 μm is incorporated into the simulation geometry, Fig. 12, to investigate the impact of these microprotrusions on the field.

Adding the microprotrusion into the simulation geometry increased the maximum electric field magnitude at the tip by ∼73% (2.64 × $108 V/m$⁠). Despite the increase in the field, it is not on the order of 10⁹ V/m, indicating that the microprotrusions in P2 are not sources of field emission. The applied gap voltage would need to be at least 38 kV to yield an enhanced field on the order of 10⁹ V/m. Since the protrusions appear to be melted, as mentioned previously, it is reasonable to assume that thermionic field emission occurred while the corona was ignited. However, it is not likely that it was the mechanism responsible for yielding a high percentage of negative ignitions seen in P1 and P2. A microprotrusion on the surface would already need to be emitting a current density on the order of $106−107$ A/cm² for Joule heating to begin on the tip and transition into thermionic field emission.⁴⁹ Using the field emission formulation from Raizer¹³ and a calculated Fermi energy for tungsten of 5.78 eV, which is similar to values for tungsten reported elsewhere,⁵⁰ one finds that the calculated current density via field emission is negligible (on the order of $10−68 A/cm2$⁠) assuming a work function of pure tungsten (4.54 eV) and the maximum electric field magnitude calculated from the simulation. Repeating the same field emission calculation for the lanthanated tungsten electrode, assuming the same Fermi energy used in the previous case, maximum electric field magnitude, and a reduced work function for lanthanated tungsten (2.8 eV),⁵¹ the change in the calculated current density rises many order of magnitudes, but is still negligible, on the order of $10−30 A/cm2$⁠. It is further noted that the enhanced field would need to be at minimum $7.84×109$ V/m to yield appreciable current density to transition into thermionic field emission. Thus, it is postulated that the emission of initiatory electrons causing the high number of negative ignitions may be due to surface contamination on the needle tip surface. Surface contamination, in the form of dielectric inclusions, is known to give rise to pre-breakdown currents in vacuum gaps under fields ranging from 10 to 30 MV/m.⁵² A more rigorous derivation and explanation of this physical process may be found elsewhere.^48,52,53

Energy dispersive x-ray spectroscopy (EDS) was performed on regions of needles P1 and P2 thought to be surface contamination, see Fig. 13. EDS identified the presence of carbon in regions of the tip surface of needles P1 and P2. The carbon is thought to have embedded itself during the electrode sharpening process, where a diamond grinder tool was used. It is also noted that no lanthanum was identified on the surfaces of P1 and P2, suggesting that no cross contamination between the pure tungsten and lanthanated tungsten needles had occurred during the sharpening process.

As discussed earlier, there is a group of data points with noticeably larger onset voltages originating from needle P1, cf. Fig. 8, because of a smooth tip geometry compared to the other needle tip geometries. Thus, the data of Fig. 8 is replotted without the inclusion of P1 to analyze the data for needles that were grouped more closely together, Fig. 14.

The measured data for the pure tungsten and lanthanated tungsten corona onset voltage follow the RF envelope as expected. It is noted that the majority of the onset events occurred during the rising edge of the RF envelope. Overall, there appears to be no significant difference between the pure tungsten and lanthanated tungsten data, indicating that the choice of lanthanated tungsten material does not impact the onset voltage at 3.3 MHz. In DC welding, lanthanated tungsten electrodes are known to maintain the arc at lower voltages than pure tungsten.⁴⁰ The results shown here indicate that the actual ignition, that is the initial current flow, will largely remain unaffected by the added lanthanum. It is reasonable to assume that once the welding discharge starts, the associated hotter temperatures result in the more favorable welding arc stability for the lanthanated tungsten. Clearly, the process resulting in the diffusion and evaporation of La₂O₃ in welding is much larger than the current being drawn by the needle electrode in the RF experiment (tens to hundreds of A vs a few mA). The high current used in welding will heat up the lanthanated tungsten electrode causing the La₂O₃ to diffuse toward the tip of the electrode.^40,54 Upon reaching the surface, the La₂O₃ is vaporized and ionized under the strong electric field at the tip.⁵⁵ The vaporized La₂O₃ is then redeposited onto to the surface, forming a monolayer of emitter atoms. The deposited La₂O₃ on the tip surface reduces the work function of the electrode, which reduces the necessary voltage to keep the arc going.⁵⁴ The current drawn in the experimental setup is too small to sufficiently heat the lanthanated tungsten electrode to cause diffusion of the La₂O₃ embedded in the bulk material. While lanthanum is also present for the surface of the cold electrode, the difference to the pure tungsten electrode is insufficient to generate a clear difference in corona onset behavior. That is, only when sufficiently high temperatures are reached the benefit of the lower work function of lanthanum, 2.8 vs 4.54 eV for tungsten, makes a beneficial impact on the discharge behavior. The RF corona is self-sustained by a combination of the mechanisms discussed earlier for positive and negative corona, that is volume photoionization and photoemission from the electrode surfaces.

Corona, given sufficient applied voltage and time, is often a precursor to breakdown. The amplification of ionization in the air surrounding the needle over time creates the right conditions for a streamer to make the jump across the gap and initiate breakdown. After the corona is well established (3324 cycles after initiation), the RF and PMT voltages are shown in Fig. 15. Clear voltage spikes are observed in the PMT signal when the needle is positive while smaller voltage spikes are observed when the needle is negative. This behavior is consistent in both pure tungsten and lanthanated tungsten needles.

Given the observation of large PMT voltage spikes occurring during the positive needle at a time well after corona inception voltage, there was interest in observing whether the needle-plane gap breaks down primarily on the positive needle as elsewhere reported for low frequencies.⁹ By pushing the RF envelope to a higher maximum voltage (from ∼7.5 to 10.5 kV), a total of 20 RF breakdown measurements using needle P2 were recorded. Figure 16 shows a representative waveform for this breakdown case.

The peak of the applied RF pulse climbs to approximately 10.7 kV, a value that exceeds the inception voltages for RF corona measured for needle P3 by roughly 50%, cf. Fig. 8. That is, the RF corona ignites at some point along the initial rising edge of the RF pulse. When the corona ignites, the impedance of the gap partially collapses, leading to detuning of the circuit and a reduction in voltage. This can be seen after the maximum voltage is reached after 25 μs. With a continued decrease in voltage, the corona streamers bridge the gap at 60 μs. The voltage collapses for a moment, followed by a swift partial recovery of the breakdown plasma, which allows the Q of the RF circuit to rise again. The measured voltage collapses again to zero once more at ∼105 μs and partially collapses at 140 μs, albeit at lower voltage amplitude compared to the initial breakdown. After the partial collapse, the voltage stabilizes until the end of the RF pulse.

The RF breakdown behavior observed in the needle-plane geometry is very different than RF breakdown in a parallel plate geometry. In a parallel plate geometry, where the field is homogeneous, the voltage collapses when the breakdown event occurs and remains collapsed for the duration of the pulse, see Fig. 8 in Ref. 4. This is due to there being a sufficient amount of charge carriers in the gap to sustain the arc. In the case of the needle-plane gap, RF corona ignites prior to breakdown, which detunes the circuit and limits the maximum voltage that the RF circuit can produce. There is still charge accumulation in the needle-plane gap, so the streamers eventually bridge the gap. However, the space charge in the gap is insufficient to support a self-sustaining arc. Hence, the discharge returns to the corona state until sufficient space charge accumulation is achieved again. It is believed that switching the voltage source with one that has a lower effective output impedance, i.e., capable of driving higher current to the load, would produce breakdown in the needle-plane gap that completely collapses and self-sustains for the duration of the applied voltage.

The half-cycle in which the RF breakdown occurs cannot be ascertained due to measured events exhibiting a rapid decline in amplitude instead of collapsing abruptly. It is obvious that RF breakdown in a homogeneous gap does not exhibit a preference on the half-cycle it occurs on.

The IV characteristics of positive and negative corona with pure tungsten needle electrodes of varying included angles revealed that a smaller included angle resulted in a sharp rise in current at lower voltages. Breakdown of the positive needle occurred at ∼18 kV, which agrees with results found elsewhere.⁴¹ The negative needle corona did not transition into a breakdown event at amplitudes up to 30 kV (a 40 kV threshold is estimated).

While RF corona for pure and lanthanated tungsten needles showed a strong and no preference, respectively, for igniting during the negative half cycle, the sample size is too small to draw statistically significant conclusions. No distinct difference in the measured RF corona onset voltage vs time delay were noted between the pure tungsten and lanthanated tungsten needles. This also means that the lanthanum or La₂O₃ with its lower work function than the pure tungsten made no difference in corona onset for electrodes at room temperature. Thus, the initial electron must be sourced from elsewhere, such as field-detachment of electrons from ion clusters.

The accumulation of the ions and electrons in the gap occurs in both pure tungsten and lanthanated tungsten needle configurations, which is more likely to negate material contributions to the corona development than would be possible in low frequencies and DC. Finally, RF breakdown in a needle-plane gap did not present a clear distinction to which half cycle it initiates as observed in RF breakdown in a homogeneous field. Instead, the voltage collapses and recovers, sometimes more than once during the applied RF pulse. This is believed to be due to the small amount of charge carriers in the gap to sustain a self-sustaining discharge once breakdown occurs. The presented experimental data on 3.3 MHz RF corona and breakdown under a non-uniform field will aid in expanding the present literature and support efforts in design considerations of ESAs used for ionospheric heating research. For instance, based on the experimental RF corona onset and time delay data, a majority of corona ignitions occurred between 80 and 100 μs. The fast formation of corona in electrically small antennas would be a limiting factor for experiments demanding application of longer timescale signals to the antenna, such as those performed at the High Frequency Active Auroral Research Program (HAARP) and other heater facilities.⁵⁶ The results in conjunction with conclusions drawn from an earlier study⁴ emphasize the need to minimize any geometric field enhancements in the ESA to avoid corona losses in the high-field capacitive gap. While RF breakdown at approximately 24 kV/cm is important to avoid, RF corona—occurring at a lower field—is the chief limiting factor in power and transmission length capability of highly resonant antennas.

This work is based upon work supported by the Air Force Office of Scientific Research under Award No. FA9550–14-1–0019. One of the authors, I.A.A., would like to thank the Los Alamos National Laboratory for their support. The authors would like to acknowledge the Texas Tech University College of Arts and Sciences Microscopy (CASM) center for use of Carl Zeiss Crossbeam 540 FIB SEM Microscope. I.A.A. would like to acknowledge and thank Dr. Bo Zhao for her expertise in acquiring SEM images, acquiring the EDS data, and operating the FIB-SEM Microscope.

The authors have no conflicts to disclose.

The data that support the findings of this study are available from the corresponding author upon reasonable request.