Transitions of an atmospheric-pressure diffuse dielectric barrier discharge in helium for frequencies increasing from kHz to MHz

To illustrate the extent of the diffuse conditions, figure 2 shows the rms current and voltage evolution for most of the frequencies available. The ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves are obtained by increasing the voltage of the waveform generator while measuring the rms voltage and current. Experiments always started at 0 V of applied voltage and stopped before leak discharge or instabilities could occur (arbitrary upper boundary). Let us note that the illustrated data were recorded only during the increase of the applied voltage. Additional conditions are also accessible considering the decreasing part of the applied voltage. For instance, at some frequencies, it is still possible to sustain a discharge significantly below the breakdown voltage (see section 5). Based on long exposure camera measurements together with oscillograms of current and voltage, the discharge is always found diffuse except between 3.7 and 4.9 MHz where the discharge displays some instabilities when high voltage is applied. Diffuse conditions are represented by open symbols in figure 2.

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Although precise quantitative analysis of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves would require to consider the discharge current and the voltage applied to the gas instead of the measured current and voltage, important information with respect to the classification of the discharge modes can be found in figure 2. For instance, inflections of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves of figure 2 can be interpreted as major change in the discharge behavior, i.e. mode transitions. Accordingly, figure 3 shows examples of gas gap pictures (wavelength integrated from 300 to 900 nm) for different ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ conditions reported in figure 2. Power density is indicated on the pictures to better compare conditions at different frequencies. From these images only two emission patterns can be distinguished: either emission is concentrated in the bulk or it is concentrated in the sheath regions. Actually, emission is concentrated in the bulk from 50 kHz to 4.9 MHz, when the applied voltage is close to breakdown voltage (up to inflection). For every other conditions the light emission is concentrated close to the solid dielectrics. This is after inflection (when it exists) or during the whole curve (when no inflection occurs). Let us note, that picture 3(g) exhibits instabilities that occur at 3.7 and 4.9 MHz when the applied voltage is high enough.

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Going back to figure 2, one can foresee some discharge modes with respect to the inflections of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves. Whatever the frequency is, we will refer to the low-power mode before the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ inflection i.e. when emission takes place in the gas bulk. Similarly, we will refer to the high-power mode after the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ inflection, when the light is emitted close to the dielectric surfaces. In the low-frequency range (solid blue lines), the inflection of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curve gives rise to the low-power LF and to the high-power LF modes. In the MF range (dotted black lines), the inflection of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curve gives rise to the low-power MF and the high-power MF modes. Finally, from 10 MHz and above (dashed red lines), when no inflection occurs in the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves, the corresponding mode will be referred as the high-power HF mode. The boundaries of these modes with respect to the frequency are difficult to identify in figure 2. Consequently, the gray lines represent transitions for which the classification of the modes are still to be determined. Discharge modes are roughly indicated in table 2.

Before deploying efforts to understand the mechanisms underlying these discharge modes and investigating their boundaries, we briefly comment some spectroscopic features of the discharge modes.

Even if the discharge behavior is completely different when the frequency grows from 25 kHz to 15 MHz, some features are quite similar, as illustrated by the time integrated spectra shown in figure 4. The same emitting species are present in all spectra. Significant intensity of OH(${A}^{2}{{\rm{\Sigma }}}^{+}\to {X}^{2}{\rm{\Pi }}$) (λ = 306.4 nm), N₂(C${}^{3}{{\rm{\Pi }}}_{u}\to$ ${{\rm{B}}}^{3}{{\rm{\Pi }}}_{g}$) (λ = 337.8 nm) and ${{\rm{N}}}_{2}^{+}$(B${}^{2}{{\rm{\Sigma }}}_{u}^{+}\to$ ${{\rm{X}}}^{2}{{\rm{\Sigma }}}_{g}^{+}$) (λ = 391.4 nm) molecular bands as well as He(3³S → 2³P) (λ = 706.4 nm) and O(${3}^{5}{\rm{P}}\to {3}^{5}{\rm{S}}$) (λ = 777.5 nm) atomic lines are observed. We note that while the lines present in the visible spectrum are the same for each frequency and power density, their ratios can vary substantially with respect to experimental parameters (e.g. figure 4(a) compared to (b)). While the plasma composition should be constant whatever the frequency is, this suggests changes in the electron dynamics.

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The emission at 706.4 nm is the strongest one among helium emissions and it can easily be detected in all conditions. Therefore, in the following sections, many experimental investigations will be devoted to this transition. In order to understand the upcoming results, let us note that the He(3³S) state can be populated by three main mechanisms, namely direct electron impact on helium ground state (threshold energy of 22.7 eV) [25], electron impact with He(2³S) metastable state (threshold energy of 2.9 eV) [26] and dissociative He₂⁺ recombination with low-energy electrons [27]. Therefore, the presence of the He(3³S → 2³P) emission should be related to either a significant concentration of electrons with energy higher than 22.7 eV or a few high-energy electrons compensated by a significant concentration of metastable atoms or He₂⁺ ions. For a deeper discussion on the observed transitions and the origin of their emission, see [23].

The emission from nitrogen molecule, N₂(C${}^{3}{{\rm{\Pi }}}_{u}\,\to$ ${{\rm{B}}}^{3}{{\rm{\Pi }}}_{g}$), is also present in all of the conditions tested. Its presence is usually associated with impurity desorption from the solid dielectrics [28]. In fact, N₂(C${}^{3}{{\rm{\Pi }}}_{u}$) has been used as a thermal probe in similar cases [23, 29, 30]. Here, the transition N₂(C${}^{3}{{\rm{\Pi }}}_{u}\to$ ${{\rm{B}}}^{3}{{\rm{\Pi }}}_{g}$) is used as a thermal probe via rotational spectroscopy. By fitting the recorded rotational spectra with the Specair program [31], we calculated the gas temperature by multiplying the fitted rotational temperature by 1.095 (rotational factor correction of the ground state [32]). By means of a thermocouple probing the dielectric surface near the electrode area, the dielectric temperature (T_die) was also recorded. Both measured temperatures are shown for selected frequencies in figure 5.

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Figure 5 shows that, at each frequency, both rotational and dielectric temperatures increase with power. Whatever the frequency is, at the lowest power, the dielectric temperature is at room temperature and the gas temperature calculated from N₂ rotational spectra is slightly lower (likely due to the gas temperature drop from the pressure release between the gas bottle and the reactor). In the LF range, at 100 kHz, the gas temperature increases very steeply up to 360 K with the power while the dielectric temperature is constant at 300 K. This suggests that, in the LF range, surface cooling by the helium feed at room temperature is more efficient than surface heating by the discharge. For frequencies in the MF range (e.g. at 1 and 1.6 MHz), both temperatures vary in a similar manner. Their variations are clearly related to the discharge modes: low-power and high-power MF modes. In this case, the gas temperature maximum is 400 K and the maximum dielectric temperature is 335 K. Finally, in the HF range, for 13.56 MHz, both temperatures are almost constant. In agreement with discharge in similar conditions (HF range in pure helium), the gas temperature does not exceed 300 K [33].

In order to describe the basic mechanisms behind frequency transitions, let us consider the time-resolved optical emission (wavelength integrated from 300 to 900 nm). Figure 6 shows the spatio-temporal distribution of the spectrally integrated emission along the gas gap over one cycle for various frequencies from the LF to the HF range. The high-voltage electrode lies above the solid dielectric located at 2 mm (along the z axis) while the grounded electrode lies below the solid dielectric located at 0.0 mm. To represent the light distribution from one electrode to the other as a function of time, each picture is integrated along the direction parallel to the gas flow (the x axis) and the results are adjoined to get the variation of the spatial distribution of the light from an electrode to the other as a function of time. Results are presented over one cycle. Each figure is made from at least eight pictures and time resolution is increased from 100 to 15 ns when the frequency increases. The first picture of a series is triggered when the measured voltage intersects 0 V towards positive values. This means that the upper electrode is the anode for the first half-period and the cathode for the second half-period.

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Considering the optical emission spectrum of the discharge in figure 4 and the spectral response of both camera and lens (more sensitive in UV than in visible), the light emission of figure 6 should represent mainly OH(A${}^{2}{{\rm{\Sigma }}}^{+}$), N₂(C${}^{3}{{\rm{\Pi }}}_{u}$), and ${{\rm{N}}}_{2}^{+}$(B${}^{2}{{\rm{\Sigma }}}_{u}^{+}$). While OH(A${}^{2}{{\rm{\Sigma }}}^{+}$) and ${{\rm{N}}}_{2}^{+}$(B${}^{2}{{\rm{\Sigma }}}_{u}^{+}$) are mostly populated by stepwise excitation using helium metastable atoms, N₂(C${}^{3}{{\rm{\Pi }}}_{u}$) is usually populated by direct excitation [23, 25]. Accordingly, the emission recorded in figure 6 represents the excitation from various contributions (direct excitation, stepwise excitation, etc) and can barely be associated with the ionization rate. Nonetheless, let us describe figure 6 with respect to the discharge modes previously suggested from LF to HF:

• (i)  
  High-power LF mode. First, at 25 kHz (figure 6(a)), the discharge exhibits features expected from a typical LF APGD [4, 34]: the maximum light emission occurs on the cathode side and, during the discharge development, light emission propagates mostly from the anode to the cathode. At each position in the gas gap, the emission falls below 10% of the maximum value over about 20% of the cycle suggesting that very few energetic species remain in the gas between two pulses. From 50 kHz, the discharge behavior starts to slightly deviate from that of a typical LF APGD. While the maximum intensity value is similar to that of 25 kHz, the emission intensity never falls below 10% (on the whole gap) because of the reduction of the half period. We observe that the tail of the glow at the cathode connects to the ignition of the following pulse in the spatial region newly became the anode side. There is still a region where the emission is below 10%, namely the anode side before it becomes the cathode side. At 100 kHz (figure 6(c)), not only the tail of the cathode region connects to the anode region half a cycle later but it also connects to the cathode region one complete cycle later. Only in the bulk there is a small delay during which the emission is below 10% of the maximum. However, the discharge is still clearly a LF APGD as the pulse grows from the anode to the cathode and the maximum emission is on the cathode side.
• (ii)  
  Transition. At 125 kHz (figure 6(d)), the emission pattern becomes more spatially symmetric, i.e. the emission does not grow simply towards the cathode. The emission starts from the sheath region and increases from the middle of the sheaths towards both the dielectric surface (cathode side) and the bulk. On the other hand, the intensity of the sheath falls as low as 20% of the maximum, illustrating the still largely fluctuating emission.
• (iii)  
  High-power MF mode. At 200 kHz (figure 6(e)), the cycle duration is 500 ns. The intensity fluctuation during the cycle becomes very weak (about 50% of the maximum intensity in the sheath). In addition, the light emission of the bulk is almost constant over the whole cycle. This suggests that the positive column of the APGD is now very homogeneous over the time-period. Let us note that the maximum emission is always on the cathode side while no relative maximum appears on the anode side, hence, the emission on the anode side should only be due to the long-lived species that remains from the previous cycle. Because of its continuous positive column and light evolution from the sheath region towards both the bulk and the dielectric surface, this mode can no longer be identified as an APGD (in the LF APGD sense [35]). However, since there is no relative maximum on the anode side (α mode signature), it cannot be identified as the RF-α mode either. Therefore, we will refer to this mode as the hybrid mode. A similar behavior occurs up to 1.6 MHz. However, at 1.6 MHz, the power density is significantly higher than at lower frequencies in the MF range. The light emission is also slightly closer to the solid dielectrics. This corresponds to one of the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves with an rms current jump in figure 2. In fact, even if the light emission proposes that the same discharge mechanism underlies the discharge from 200 kHz to 2.7 MHz, the discharge mode appears to be slightly different below and above 1 MHz.
• (iv)  
  Transition. Between 2.7 and 5 MHz, according to figure 3(g) there is a transition region. However, no time-resolved data was recorded in this range.
• (v)  
  High-power HF mode. From 5.0 MHz (figure 6(j)), the α mode is finally well established. The emission becomes more symmetric between the anode and the cathode, i.e. there is a relative maximum on both sides at about the same time. This is similar to the RF-α mode of atmospheric-pressure discharges in helium [33, 36]. In addition, this mode is identified as α rather than γ on the basis of the following arguments: (1) the observed ratio between the intensity near the surfaces and the intensity in the bulk is much lower than in the γ mode [36, 37], (2) the recorded light emission is located much farther from the surface than it would be in the γ mode [36, 37], and (3) the measured light emission pattern displays the same space and time relative maxima than the simulated electric field [8]. Let us note that, the same behavior is observed at 13.56 MHz (figure 6(k)) although the time resolution of the recorded data is not as good as for other frequencies because of the shorter time-period (73.7 ns).

A better understanding of the discharge evolution can be reached from the helium He(3³S → 2³P) emission as a function of the frequency. This emission is measured with a 10 nm bandpass filter centered on 707 nm. Using the same procedure as for figure 6, figure 7 shows the spatial distribution of the helium emission along the gas gap.

• (i)  
  APGD mode. At 25 kHz, the helium emission grows from the anode to the cathode and no emission is detected during a significant part of the time-period. This is quite similar to the integrated emission shown in figure 6(a) with the difference that the helium emission last for a shorter period of time than the integrated emission.
• (ii)  
  Hybrid mode. At 550 kHz, unlike the integrated emission, the helium emission is neither connected in space nor in time and falls below the detection level between two half-cycles. We note that the emission starts from the sheath regions and grows towards both the bulk and the dielectric surface but in contrast to the integrated emission, no significant helium emission is recorded on the anode side. Above 500 kHz (1/f ≤ 2 μs), assuming that the density of helium metastable atoms is almost constant during the whole cycle and across the entire gas gap (the lifetime of He(2³S) metastable atoms was measured to be 2.3 μs by using a diode laser [24]), the He(3³S) state should be easily populated by stepwise excitation. As a consequence, the absence of He(3³S → 2³P) emission on the anode side suggests that unlike the RF-α mode [8], ionization does not occur significantly in this region (see figure 7(c) for comparison).
• (iii)  
  RF-α mode. At 5.0 MHz, the helium emission is maximum on the cathode side (similarly to all other frequencies in their high-power mode). However, in agreement with ionization rate simulated in similar conditions [8], there is a small increase of the helium emission on the anode side. This suggests that the hybrid mode is different than the RF-α mode. Let us note that the signal to noise ratio is not as good as for other frequencies.

Finally, in order to compare the hybrid mode to the APGD mode, the decay of the He(3³S → 2³P) emission as a function of time is illustrated in figure 8 for both the APGD and the hybrid modes. Emission at the position z = 1.5 mm (see figure 7) is considered with t = 0 μs chosen at the maximum intensity. Since the He(3³S) state is radiative, it is expected that its loss is controlled by spontaneous emission (collisional quenching can become important at atmospheric pressure but it should be the same in every condition under investigation). Then, the intensity should be proportional to the population of He(3³S) which should depend on the electron density and metastable density as the He(3³S) is created by electron collisions from the fundamental level or from the metastable level by a two-step process. In figure 8, very different behaviors are observed for frequencies above (figure 8(b)) and below or equal to 100 kHz (figure 8(a)). From 200 kHz, the usual exponential decrease is replaced by a slower decrease. This occurs when the time scale of the memory effect shifts from half a cycle to a full cycle, resulting in a longer accumulation of different species which induce higher densities. Thus, a possible explanation for this observation is that the recombination of He₂⁺ and electrons significantly participate to the population of He(3³S) when the memory time scale increases. However, when the frequency increases from 200 to 1000 kHz, the He(3³S → 2³P) decays faster while still governed by the same decreasing function. This could be explained by the lower electron energy considering that the ignition phase is reduced, thereby reducing the contribution of direct and stepwise excitations in the He(3³S) population.

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When the applied voltage is close to its breakdown value and the frequency lies between 50 kHz and 2.7 MHz, the spectrally-integrated emission is concentrated in the bulk (see figure 3). In order to investigate the behavior of the discharge in such conditions, let us consider time-resolved optical imaging. Figure 9 shows the spatial distribution of the spectrally integrated emission along the gas gap.

• (i)  
  Low-power LF mode. At 100 kHz, one observes that the emission is stronger on the anode side than on the cathode side. This behavior significantly differs from the APGD at 100 kHz depicted in figure 6(c). To be more precise, let us consider the He(3³S → 2³P) transition. This is achieved in figure 10 where the time evolution of the distribution of He(3³S → 2³P) line emission along the gas gap is illustrated at 100 kHz. Helium emission reaches a maximum at the anode with a strong increase from the cathode. This behavior is similar to the APTD and can be explained by a quasi-uniform electrical field in the gap. As the electron energy is constant over the gap, emission is maximum where the density of electrons is the highest, i.e. at the anode [38]. This suggests that the ion density is too weak to enhance the electric field locally and form a cathode fall. Such a behavior is a characteristic of APTD and the corresponding mode will be refered as APTD-like (APTD-L) mode.
• (ii)  
  Transition. Between 100 and 200 kHz, there is a transition region. However, no time-resolved data was recorded.
• (iii)  
  Low-power MF mode. From 200 kHz to 2.7 MHz, light emission behaves very similarly. It is concentrated in the bulk and oscillates according to the applied voltage. The emission is continuous over the whole cycle, which means that the light intensity never falls below 70% of the maximum value (at position z = 1 mm). Like for the APTD-L mode, there is no cathode fall signature and the ion density is low. In addition, the emission builds up from the bulk to the dielectrics. This behavior is in agreement with that occurring for the Ω mode [8, 11] previously reported in the MF range [23].

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In section 3.2, the gas temperature in the discharge was obtained at several frequencies. Going back to the rotational temperature of N₂, one observes that for each mode at each frequency, the rotational temperature increases linearly with the power. The slopes S(f) of these curves were calculated and are presented in figure 11 as a function of the frequency. The slope of the rotational temperature as a function of the power corresponds to the amount of injected energy converted into rotational energy. In other words, the higher S(f) is, the higher is the power loss to increase the rotational temperature. Therefore, figure 11 indicates that as S(f) decreases with the frequency, less energy is converted into rotational temperature at higher frequencies.

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Figure 11 shows that S(f) varies over three orders of magnitude in the frequency range investigated. It is also clearly correlated to the discharge mode. While the value of S(f) decreases from the APGD mode, to the hybrid mode (from 1 MHz and above) to the α mode, it does not seem to follow the same trend for the Ω and the hybrid (below 1 MHz) modes. For the Ω mode, both light emission and power density are very low (see figure 3(e), for instance) and the discharge should be almost purely resistive. As a consequence, the energy transfer to rotation should be important, hence leading to high S(f) values. Below 1 MHz, S(f) is also quite high in the hybrid mode. This could be explained by spontaneous oscillations (intermittent hybrid mode) that are observed between the Ω and the hybrid modes (more details about this phenomenon are provided in [24]). Since S(f) is quite high in the Ω mode, measurements corresponding to averages over the two modes should result in intermediate values (much closer to Ω mode value since the discharge spends more time in the Ω than in the hybrid mode [24]). We further note that the small difference between the value of the actual Ω mode and the intermittent hybrid mode (below 1 MHz) is not significant according to the uncertainties. In fact, the relative uncertainty on the power is much larger for the Ω and the hybrid (below 1 MHz) modes than for the other modes. Consequently, the uncertainties are actually significantly larger than the error bars shown in this mode. Finally, we note that he APTD-L mode is absent from this figure because not enough data were available to derive the slopes.

As reported in a previous study [23], an interesting feature of the MF range (f > 1 MHz) is the occurrence of a hysteresis when the applied voltage is increased and decreased in the same experiment. It was observed that during the transition from the Ω mode to the hybrid mode, the rms current jumps significantly while the measured rms voltage slightly drops. On the other hand, during the transition from the hybrid mode to the Ω mode, both the rms current and the rms voltage decrease smoothly. In the present study, we found out that this hysteresis is restricted to the hybrid mode above 1 MHz. Examples of complete ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves are shown in figure 12 where a small hysteresis is also observed at 4.9 MHz. This occurs when instabilities are observed, i.e. when the discharge is not purely diffuse (data indicated by filled symbols in figure 2).

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From figure 12, it s also possible to infer that the slope of the Ω mode decreases when the frequency increases. In addition, the discharge is sustained at rms current and voltage significantly lower than the breakdown value at and beyond 10 MHz. This behavior is only observed in the HF range and is associated with the time averaged light emission becoming concentrated in the bulk. This suggests that the α mode smoothly switches to the Ω mode when the applied voltage is decreased, as expected at such frequency [8]. However, the transition is smooth so that it cannot be observed in electrical measurements in contrast to the hybrid mode.

Based on the fast imaging pictures presented above along with the ${I}_{{\rm{r}}{\rm{m}}{\rm{s}}}\mbox{--}{V}_{{\rm{r}}{\rm{m}}{\rm{s}}}$ curves of figure 2, it is possible to extrapolate the boundaries of the discharge modes. Using the power density calculated from equation (1), these modes are illustrated in figure 13 as a function of the frequency.

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Even though the power density in the LF range remains always lower than in the HF range, it is still convenient to separate the discharge modes in low and high power for each frequency. For the high-power discharge, we can see that the APGD is obtained up to 100 kHz. Between 100 and 200 kHz, the APGD behavior is harder to identify and the frequency range is thus better referred as transition region, which is associated with a change in the memory time scale. Up to 100 kHz, the memory effect impacts the discharge one half-cycle later, while the effect last for (at least) one complete cycle above 200 kHz. Then, the hybrid mode is observed until another transition region occurs at 3.7 MHz where the discharge exhibits instabilities. Only a few data were acquired between 5 and 10 MHz. Nonetheless, the instability region appears very narrow (between 3.5 and 5 MHz) and occurs at high applied voltage only.

For the low-power discharge, the APTD-L mode is observed in a narrow range from 50 to 100 kHz. Beyond 200 kHz, the Ω mode is already present with only a narrow region of transition between 100 and 200 kHz. The Ω mode was observed up to 2.7 MHz. However, due to the similar nature of the Ω and the α modes, it is expected that the Ω smoothly converts to the α mode as the frequency increases. This is in agreement with the conversion of the α mode the Ω mode when the applied voltage is decreased below the ignition level at frequencies above 10 MHz.