# On the different regimes of positive DC corona discharges as a function of electrical and geometrical parameters

Huijie Yan, Nicolas Benard, Éric Moreau

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Huijie Yan, Nicolas Benard, Éric Moreau. On the different regimes of positive DC corona discharges as a function of electrical and geometrical parameters. Journal of Applied Physics, 2023, 133 (1), pp.013301. 10.1063/5.0131122. hal-04129598

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# On the different regimes of positive DC corona discharges as a function of electrical and geometrical parameters

Huijie YAN¹,², Nicolas BENARD¹, Eric MOREAU¹

¹ University of Poitiers, Pprime institute, CNRS, ISAE-ENSMA, Téléport 2, BP 30179, 86962 Futuroscope, France

² Dalian University of Technology, Scholl of Physics, Ganjingzi District, Dalian City, Liaoning Province, China

corresponding author : eric.moreau@univ-poitiers.fr

## Abstract

This experimental study aims at better understanding the electrical and optical properties of a positive DC corona discharge and to highlight the influence of the applied voltage and electrode gap on the discharge regime. When the high voltage is increased, three successive regimes have been observed, including one that has never been reported in the literature to the best of our knowledge. This is certainly due to the fact that the tungsten needle used in these experiments is a commercial needle, with a tip of perfect surface finish. In fact, after the ignition voltage, the mean current slowly increases, and it perfectly follows the theoretical Townsend's law; this is the glow regime. When the voltage reaches a first threshold, a few small current pulses appear. However, this is not the breakdown streamer regime because photographs and iCCD visualizations highlight that the propagation of the streamers toward the grounded plate is limited to half of the gap. In this regime, the time-averaged current becomes higher than that of Townsend's law. Each current pulse is composed of only one bump, and the pulse frequency is higher (approximately 20 kHz) than that of the breakdown streamers. When the voltage reaches a second threshold, the magnitude of the current pulses suddenly increases, but their frequency decreases (a few kHz); this is the transition toward the breakdown streamer regime. In this regime, each current pulse is composed of two bumps: the first one corresponds to the arrival of a primary streamer at the plate, and the second one corresponds to a secondary
streamer. Finally, we investigated the effects of the electrode gap. The magnitude and frequency of the current pulses increase when the gap decreases. Consequently, the offset between the Townsend's curve and the experimental I-V characteristics increases when the gap decreases, because the pulse component of the total discharge current increases.

# 1. Introduction

Corona discharge is a common self-sustained atmospheric air discharge that occurs when a high voltage is applied between two electrodes, one of which having a very small radius of curvature compared to the other. For instance, a corona discharge can be ignited between a high-voltage needle and a grounded plate.

On the one hand, in most engineering applications, the capability of corona discharges can be used to modify the gas chemistry for ozone production$^{1,2}$, reduction of gaseous pollutants$^{3,4}$, surface treatment$^{5}$ or assisted-combustion$^{6,7}$ for instance. On the other hand, it can be used for its electrohydrodynamics properties, either for manipulating the trajectory of particles in electrostatic precipitators$^{8,9}$ or to induce ionic wind. In the latter, there are many applications, such as ion-driven pumps$^{10,11}$, airflow control by plasma actuators$^{12-15}$, enhancement of thermal transfers$^{16,17}$ and EHD propulsion$^{18,19}$.

In the present study, we focus on the electrical and optical properties of a needle-to-plate DC positive corona discharge to investigate the different discharge regimes. Usually, when a positive high voltage is applied at the needle electrode, several regimes can be observed thanks to the voltage value and sometimes the electrode gap, these regimes having been widely studied in the past$^{20-28}$. Below a certain voltage threshold, there is no discharge, then the discharge starts to occur at the ignition voltage. Just above this ignition voltage, there may be a pulse corona regime composed of small onset streamers. The current associated with this regime is pulsed and the mean current is very weak$^{29}$. However, this regime has rarely been observed in literature. To the best of our knowledge, and although we have studied these
discharges for a few years³⁰⁻³², we have never observed it before. Subsequently, when the voltage is increased gradually, a stable and pulseless Hermstein's glow regime is observed²⁸; it is characterized by a small ionized region in the vicinity of the needle tip and the associated discharge current is constant with time. In practice, this regime is usually named "glow regime". With an increase in the applied voltage, a regime composed of breakdown streamers crossing the electrode gap appears. It is characterized by the appearance of current pulses of a few milliamperes with a repetition rate of a few kilohertz, each current pulse corresponding to the propagation of a breakdown streamer from the needle toward the plate electrode³⁰,³¹,³³. Finally, before a spark occurs, there is sometimes a diffuse corona regime for which the current versus time is constant. This regime is not always observed because it seems related to the electrode gap.

In this article, we will start by presenting a new method to determine the I-V curve of a corona discharge. We will then investigate the effect of the electrode gap (from 5 mm to 100 mm) on the I-V characteristics. We will highlight that this characteristics depends highly on the gap and then we will present the electrical and optical properties of a positive corona discharge for three different gap values: 10 mm, 30 mm and 70 mm.

## 2. Experimental setup

The corona discharge is produced by applying a high voltage to a tungsten needle electrode placed in front of a grounded plate electrode (Fig. 1). The tungsten needle used in this study is a commercialized products (Microworld PTG20-100). Its diameter is equal to 40 mm. Its curvature radius is equal to 100 µm, and the tip is particularly well-finished (Fig. 2). The ground plate electrode is made of stainless steel with a rectangular shape and rounded edges (20 × 20 cm²). The gap between the electrodes can be adjusted using a micrometric displacement system.

The high voltage V is generated using a TREK amplifier (±30 kV/±40 mA) supplied by a low voltage signal coming from a waveform generator (Lecroy WaveStation 3082).
The high voltage between the two electrodes is measured by using the internal voltage probe of the TREK amplifier.

A new method is used to plot the I-V curves. The mean current $I$ is measured across a capacitor of $1~\mu F$ connected in parallel with a resistor of $10~k\Omega$ (Fig. 1a). To determine the I-V curve, a high voltage ramp of 5 seconds is applied between the two electrodes, and the time-averaged current $I$ is measured every 10 ms with the help of an oscilloscope (Lecroy 24Xs-A, 500 MHz). This real-time automatic method will be more accurately explained below with a concrete case (Fig. 3). This new method is inspired by the one used by Tachibana et al³⁴. However, in their study, Tachibana et al used a fast voltage ramp (50 ms) and measured the instantaneous current $i(t)$ and not the time-averaged current. Furthermore, in the present study, the discharge current versus time $i(t)$ is always measured with a shunt resistor of $1~k\Omega$ placed in series between the plate electrode and the ground (Fig. 1b), the voltage being fixed at a given value without using a voltage ramp.

In addition to electrical diagnostics, two types of optical measurements were performed. First, time-integrated photographs of the discharge were recorded with a DLSR camera (Nikon D7100, resolution of $6036 \times 4020$ pixels, sensor size of $23.5 \times 15.6$ mm²). A telephoto micro lens (AF MICRO NIKKOR 200 mm 1:4 D) and a 2X telephoto extender were used, resulting in a spatial resolution of a few micrometers per pixel, depending on the electrode gap. Second, plasma visualizations were performed using an iCCD camera (Princeton, PI-MAX4 1024EM, equipped with a lens AF-S MICRO NIKKOR 105 mm 1:2.8G), with a gate width fixed at 0.5 ms.

All the experiments were conducted in atmospheric room air with constant temperature and humidity conditions ($T = 20°C \pm 2°C, HR = 45\% \pm 5\%$).

### 3. Method to determine the I-V characteristics

First, we explain the method used to measure the time-averaged current $I$ as a function of the applied voltage $V$ to plot the I-V characteristics. The setup is shown in Fig. 1a ($R = 10~k\Omega$ and $C = 1~\mu F$). The gap is fixed here at 30 mm.
As we can see in Fig. 3, the voltage V (blue dashed line) is first increased linearly from 0 to +18 kV during a period of 5 seconds. Then it is decreased from +18 kV down to 0 kV during 5 seconds. The time-averaged current I is recorded simultaneously during 10 ms, every 10 ms. The main advantage of this method is that it is very fast, and then it can be carried out a large number of times to verify the reproducibility of the measure. However, Fig. 3 is not a typical I-V curve because it does not show I versus V, but simultaneously plots V and I versus time. In this study, this curve will be named I-V(t) curve. We will plot the usual I-V characteristics later in this article (Fig. 4, for instance).

Let us comment on Fig. 3. When the voltage is increased, we can see that the current starts to be measurable from $t \approx 1$ second, corresponding to a voltage V a little bit higher than 3 kV. This value corresponds to the discharge ignition voltage, which is usually referred to as $V_0$. Between $t \approx 1$ s and $t \approx 3.25$ s i.e. voltages between 3 kV and 12 kV, the measured current (red curve) perfectly follows the theoretical Townsend's law (black curve), which is given by $I = C \times V$ ($V-V_0$), where I is the mean discharge current, V is the applied voltage, $V_0$ is the ignition voltage, and C is a constant that depends on the electrode geometry and ion mobility $\mu$. From approximately 12 kV (point A in Fig. 3), the current suddenly increases and becomes higher than the theoretical current given by the Townsend's law. This highlights a change in the discharge regime. At $V \approx 15$ kV (point B in Fig. 3), the mean current decreases and then immediately increases until it reaches about 33 $\mu$A at +18 kV. One more time, this behavior highlights certainly a new change in the discharge regime at point B because the discharge current is the electrical signature of the physical phenomena occurring inside the discharge.

Moreover, when the voltage is decreased, the current curve is not completely similar to that observed when V is increased, highlighting that there is a hysteresis effect. This hysteresis effect had already been observed in the case of surface corona discharges³⁵. More precisely, there are two main differences. The first one is the voltage value at which the current suddenly decreases and then rises immediately. The
second difference concerns the continuity of the curve. When the voltage is raised, the current suddenly increased at +12 kV. On the contrary, when the voltage is decreased, the offset between the black and red curves decreases little by little and the two curves meet at approximately +8 kV. In fact, it seems that the transition between the two different discharge regimes is faster (and then more visible in the I-V curve) when the voltage is increased because the discharge is less stable in this case. Therefore, it is more relevant to decrease the voltage when one wants to plot an I-V curve, because the discharge is more stable.

4. Current versus voltage of a positive corona discharge for different electrode gaps

After explaining the new method to easily measure the current versus voltage, we plot the I-V curves of a positive corona discharge with electrode gaps g ranging from 5 to 100 mm. The different I-V characteristics are deduced from the I-V(t) curves.

As the current value varies according to whether the voltage is increasing or decreasing, Fig. 4a and 4b show the I-V characteristics when the voltage is decreased and increased, respectively. From these plots and our experimental observations during the measurement campaign, several remarks can be made.

First, the main behavior of the I-V characteristics when decreasing and increasing the voltage is similar, and the current values are not significantly different. However, as shown in Fig. 3, when the voltage is increased, the sudden current variations due to the transition from one discharge regime to another one are enhanced and more visible.

Second, it seems that there are four groups of curves depending on the electrode gap g. The first group corresponds to g = 5 mm and 10 mm. For such small gaps, the current increases slowly from the ignition voltage, and there is a sudden increase in the current when the voltage exceeds the ignition voltage by one or two kV. This is clearly visible in Fig. 4a for g = 5 mm at V = 4 kV (it is illustrated by the arrow showing a current increase). For g = 10 mm, it is also visible for a voltage slightly greater than +6 kV (see the arrow showing the current increase in Fig 4b). We will show later that
this sudden current increase corresponds to the transition from a pulseless Hermstein's glow corona to a pulsed corona. In the range between 30 mm and 60 mm (second group), the I-V curves behave as shown in Fig. 3; there is a sudden decrease and then an increase in the current, corresponding certainly to the transition between two regimes. This current variation appears at approximately 16 kV, 21 kV, 25 kV and 29 kV for gaps equal to 30 mm, 40 mm, 50 mm and 60 mm, respectively (see Fig. 4b). Of course, this remains visible in Fig. 4a, but less so. For the third group (g = 15 mm and 20 mm), the behavior of the I-V characteristics is intermediate between that of the first group and that of the second group. Finally, from g higher than or equal to 70 mm (fourth group), we can see that there is no sudden current decrease because the voltage is too small and does not reach the value for which this phenomenon occurs. In this case, the discharge remains stable even at +30 kV because the current is weak.

That is all we can say at the moment. We are now going to conduct an in-depth study of the electrical and optical properties of the positive corona discharge for three different gap values: 30 mm, 10 mm and 70 mm. We will see that the gap plays a strong effect on the electrical and optical properties of the discharge. From now, all the I-V characteristics will be plotted from the I-V(t) curves when the voltage V is decreased because the mean current evolves more monotonously than when V is increased.

**5. Electrical and optical properties of a positive corona discharge with g = 30 mm**

Here, we focus on the electrical and optical properties of the corona discharge with a gap of 30 mm. First, we observe the discharge from pictures and iCCD visualizations. Second, we discuss its I-V characteristics and we explain its behavior with the help of the curves of the discharge current versus time i(t). Finally, the analysis of the current pulses of i(t) will allow us to highlight the different regimes that occur when the voltage is gradually decreased from 18 kV down to 0 kV.

**5.1 Optical measurements and current versus time**

The first goal of this section is to understand what is at the origin of the two sudden changes in the slope of the I-V characteristics. In fact, they certainly correspond to the
transitions between two discharge regimes.

Fig. 5 and 6 show photographs and iCCD visualizations of the positive discharge for several voltage values (9 kV, 12 kV, 15 kV, 15.6 kV, 16.5 kV and 18 kV). Fig. 7 presents some curves of the discharge current versus time for the same voltage values.

First, for voltage values smaller than approximately 8.5 kV, the visible part of the discharge on both the images and the iCCD visualizations is confined to the vicinity of the tip; this corresponds to an ionized zone smaller than 1 mm (not shown in Fig. 5 and 6). This is the well-known pulseless Hermstein's glow regime, which is usually called the glow regime. In this regime, the current is constant versus time.

Then, from approximately 8.5 kV, the discharge changes. For instance, photographs and iCCD visualizations at 9 kV shows that there is a thin ionized channel that propagates from the needle tip toward the plate, whose length is limited to a few millimeters. If we measure the current versus time, we can see small pulses with amplitude of 0.1-0.2 mA (Fig. 7). This highlights that there is a regime change; however, contrary to what is usually reported in the literature, it is not the breakdown streamer regime because the frequency and amplitude of these pulses do not correspond to those of breakdown streamers with a so high electrode gap (this will be explained later in the article). Furthermore, this is not the onset streamer regime because the latter has always been observed for voltages just above the ignition voltage³⁶, which is not the case here.

At higher voltages, one can see that the length of the ionized filament increases. From the iCCD visualizations, it is estimated that it is equal to 10 mm and 17 mm for V values of 12 kV and 15 kV, respectively. In parallel, if we look at Fig. 7, we can see that the voltage increase is associated with an increase of the amplitude of the current pulses (between 0.25 and 0.5 mA at 12 kV, between 0.5 and 1 mA at 15 kV).

At 15.6 kV, there is a second strong change. First, the photograph shows that the blue light is visible through the entire electrode gap. Moreover, the iCCD visualization highlights that the streamer ignites at the tip and propagates toward the plate until it impacts it, indicating that the two electrodes are connected by a continuous ionized
channel. Concerning the morphology of the breakdown streamers, it corresponds to what has already been reported many times in the literature: in the first millimeters, the streamer is composed of one single ionized channel, and after a few millimeters of propagation, a branching process occurs, illustrated by several ionized channels. Finally, the last difference when the regime changes at +15.6 kV is that the current versus time i(t) changes; the small current pulses start to disappear and are replaced by new current pulses whose the frequency is smaller (see between t = 0 and t = 1 ms for instance). These observations are confirmed by the visualizations and current curves at V = 16.5 kV and V = 18 kV (for these two values, the current range on the ordinate axis is not 2 mA as for the previous curves but it is equal to 5 mA).

Let us summarize all these results in Fig. 8, which presents the I-V characteristics of the positive corona discharge for g = 30 mm, when the voltage is decreased from 18 kV down to 0 kV. Two curves are present in this figure. The blue curve corresponds to the measured I-V characteristics, and the red curve corresponds to the theoretical Townsend's law. For V smaller than about 4 kV, there is no discharge, the discharge igniting at approximately 4 kV. Then, the current starts to increase, following the Townsend's law because the discharge is glow. At V = 8 kV, the discharge regime changes, which is associated with the appearance of small current pulses (see Fig. 7 for V = 9 kV and 12 kV) and an increase in the time-averaged current I. To the best of our knowledge, this regime has never been observed previously and has never been reported in the literature for needle-to-plane DC corona discharges. Furthermore, we did not observe it in our previous studies, for which we directly observed the breakdown streamer regime immediately after the glow one³⁰⁻³². We can then ask ourselves why this new regime occurs in the present study. Would this regime be the onset streamer regime generally observed by some authors for voltages slightly above the ignition voltage? We have no way to verify this because there is insufficient data in the literature on this particular regime. However, the difference between our study and others is that the needle used in the present study is a commercialized tungsten needle with a well-finished surface and a very precise curvature radius, in contrast to
many previous studies that used sewing needles or tungsten needles with a tip whose geometry was not well controlled. We also assume that these phenomena were very reproducible because they have been observed a large number of times with different tungsten needles from the same manufacturer.

Finally, at $V = 15.6$ kV, the current suddenly decreases and immediately increases; this is the transition toward the breakdown streamer regime. It is surprising that the current decreases. This will be explained in the following section.

To conclude this section of our article, we should note one important point concerning the new regime occurring for voltages between 8 kV and 15.6 kV. In the present article, this regime will be named "filamentary regime" because Fig. 6 shows that a filament develops in the inter-electrode region without connecting the two electrodes. However, these filaments are undoubtedly "streamers" but they are not "breakdown streamers" because they do not link the two electrodes.

## 4.2 Analysis of the current peaks

In this section, we are going to more precisely analyze the properties of the current pulses as a function of the applied voltage, in the two discharge regimes: the filamentary one and the breakdown streamer one. Fig. 9 shows the waveform of one single current pulse at different voltages. For $V = 15$ kV (filamentary discharge), the current peak and the pulse width are small. At $V = 15.6$ kV (green and red curves), as shown in Fig. 7, there is a transition between the two regimes, and we can observe two different types of current pulses. On the one hand, if we zoom on a pulse that corresponds to a filament (typically between $t = 1.5$ ms and $2$ ms in Fig. 7), its waveform corresponds to the one of the green curve in Fig. 9. Although it is higher and wider than that measured at $V = 15$ kV, it is similar. However, if we zoom on a pulse corresponding to a breakdown streamer (red curve in Fig. 9), the waveform of the current peak is completely different. First, its amplitude is higher. Moreover, it is composed of two bumps. In fact, the first one corresponds to the arrival of the primary streamer at the plate and the second one corresponds to a secondary streamer, as
reported for the first time by Marode³⁷ in 1975 and more recently by Dubois et al³⁸ and Eichwald et al³³,³⁶. Finally, for V = 16.5 kV (black curve), the breakdown streamer takes place and all the current pulses behave as the one presented by the black curve in Fig. 9. More accurately, we can see that the first current peak occurs at t ≈ 100 ns, meaning that the primary streamer velocity is equal to approximately 0.3 × 10⁶ m/s. This value is a little bit higher than that reported by Moreau et al³¹ (0.2 × 10⁶ m/s). However, in this study, the gap was 25 mm, illustrating that the streamer velocity increases with the electrode gap.

To further investigate the discharge regime transition, some characteristics of the discharge current pulses are determined. These characteristics include the peak amplitude, full width at half maximum (FWHM), charge transferred by one single current pulse, and time interval between two successive pulses. These characteristics are shown in Fig. 10. In practice, to obtain these four statistical values, we recorded the discharge current versus time during 10 ms with a time resolution of 10 ns (one million points) for every positive DC voltage value. We then analyzed all the pulses occurring during these 10 ms to compute, for each case, the time-averaged value of each characteristics at every voltage value, as well as its standard deviation (see error bars in Fig. 10).

First, for all the plots in Fig. 10, there is always a significant change in the behavior of the curves between 15 kV and 16.5 kV (transition from the filamentary regime to the breakdown streamer regime). Concerning the magnitude of the current pulses, one can see that between 9 kV and 15 kV, it increases monotonously from about 0.25 mA to 0.5 mA; it is the filamentary regime. From 15 kV, it suddenly increases in a linear manner with a slope of approximately +0.5 mA/kV. Moreover, the standard deviation of the peak magnitude increases with the applied voltage, indicating that the discharge is less stable. With respect to the pulse width, its value increases suddenly from 15 kV, indicating that the current pulses in the two discharge regimes are not due to the same physical phenomena. As the amplitude and width of the current pulses increases with the voltage, the charge transferred by one single current peak also
increases from 15 kV, with a constant slope a little bit higher than +0.2 nC/kV (Fig. 10c).

Finally, as we can see in Fig. 10d, the interval between two successive peaks is equal to approximately 50 µs when V is smaller than 15 kV and is around 350 µs when V is equal to or higher than 15.6 kV. This highlights that the frequency of the filaments in the filamentary regime is nearly constant and equal to 20 kHz, whereas the breakdown streamer frequency is significantly smaller (approximately 2.8 kHz). Consequently, this last curve precisely indicates that the transition from the filamentary discharge to the breakdown streamer one is between 15 kV and 15.6 kV. In this voltage range, the standard deviation is very high because there are filaments and breakdown streamers simultaneously.

The last interesting point which has not been explained is the sudden decrease of the time-averaged current at V = 15.6 kV in Fig. 8. On the one hand, Fig. 10c shows that the transferred charge by one current pulse increases at such a voltage. However, the frequency of these pulses decreases. Therefore, it is not possible to conclude a priori on the behavior of the mean current value. To investigate this point, we computed the time-averaged current $I_p$ due only to the pulsed component of the discharge current. In practice, we used the data shown in Fig. 10c and 10d. Therefore, one can assume that the current $I_p$ corresponds to the total current (as in the I-V characteristics) minus the DC component of the current. The evolution of $I_p$ versus V is plotted in Fig. 11, which provides relevant information; the pulse current due to the breakdown streamers $I_p$ is smaller than that due to the filaments, except for 18 kV. This means that the decrease in the mean current at approximately 15 kV is due to the decrease in the pulse component of the discharge current.

## 6. Electrical and optical properties of a positive discharge with $g = 10$ mm and 70 mm

First, we focus on the electrical and optical properties of the corona discharge with a gap of 10 mm. We are going to see that the reduction of the electrode gap plays a key role on the discharge behavior.
Fig. 12 presents the current evolution when the voltage is increased up to 9 kV and then decreased to zero, and Fig. 13 shows the corresponding I-V characteristics. We can observe that the electrode gap impacts the I-V characteristics as the one obtained with $g = 10$ mm is different compared to the one measured with $g = 30$ mm. First, the current increase from approximately 5 kV is higher than that for $g = 30$ mm. For instance, for $g = 30$ mm, the current increase at 18 kV was approximately +30% compared with the Townsend's law (the measured current is 34 µA when the Townsend's law results in a current on 26 µA). For $g = 10$ mm, this increase is equal to about +160% at 9 kV (from 19 µA to 50 µA). Second, the sudden decrease/increase in the discharge current observed in Fig. 8 around 15.6 kV is not present with $g = 10$ mm. However, it appears that the slope of the current curve increases from approximately 6 kV (point A in Fig. 13), indicating that there may be a change in the discharge regime at this voltage threshold.

To better understand what happens around 6 kV, Fig. 14 and 15 present the current versus time $i(t)$ and zoomed views of a single current pulse for different applied voltage values, respectively. From Fig. 14, it is not possible to determine if there is effectively a regime change around 6 kV. It can be only observed that the magnitude and frequency of the current pulse increase monotonously with the applied voltage. However, from Fig. 15, it can be deduced that the transition between the filamentary regime and breakdown streamer one occurs at approximately 6 kV. Indeed, for smaller voltage values, the current peak is composed of only one bump. At 6 kV, there is sometimes one bump and sometimes two bumps. From 6.3 kV, there are always two bumps, highlighting the presence of the breakdown streamer regime. For 6.6 kV and 7.5 kV, we cannot see clearly the two bumps because the first one is taken over by the second one that is more intense, as already observed by Dubois et al³⁸ for a gap equal to 7 millimeters. This transition is confirmed by the photographs of the corona discharge presented in Fig. 16; the streamers start to cross the entire electrode gap at approximately 6 kV.

The last remark concerns the current versus time $i(t)$ (Fig. 14). Indeed, with a gap
of 30 mm, there was a sudden change in $i(t)$ when the filamentary-to-streamer transition occurs, because the amplitude of the current pulses suddenly increased and their frequency decreased. For $g = 10$ mm, this is not the case because these two physical quantities increase monotonously, even during the filamentary-to-streamer transition. As an example, for $V = 5.4$ kV, 6 kV, 6.3 kV and 6.6 kV, the amplitude of the current peaks is equal to about 1 mA, 1.15 mA, 1.3 mA and 1.5 mA, respectively. For the same four voltage values, the pulse frequency is equal to approximately 6 kHz, 7.7 kHz, 9 kHz and 10 kHz. This highlights that in the voltage range of the present study, the magnitude and frequency of the current pulses are higher at $g = 10$ mm than at $g = 30$ m, resulting in a higher pulsed component of the discharge current. This explains why the time-averaged current $I$ increases more compared with the Townsend's law at $g = 10$ mm than at $g = 30$ mm (see Fig. 13).

Finally, we briefly present the properties of the corona discharge with a gap equal to 70 mm, with the I-V(t) curve (Fig. 17), the I-V characteristics (Fig. 18), the current versus time, a zoomed view of one single current peak for different voltage values (Fig. 19 and 20), and finally a photograph of the discharge at $V = 30$ kV (Fig. 21). From Fig. 21, we can assume that the breakdown streamer regime is never reached, even at $V = 30$ kV, because the streamers do not cross the electrode gap. This is because the applied voltage is not sufficient to reach this regime at this gap value. This is confirmed by Fig. 20, which shows that all the current pulses are composed of only one bump. Furthermore, Fig. 19 shows that the time interval between two successive current pulses is not constant, as their occurrence is erratic; this highlights that the discharge is certainly not as stable as for smaller gaps. Finally, the last remark concerns the I-V characteristics (Fig. 18): the measured current follows correctly the Townsend's law. This is surprising because the filamentary regime is observable from about 21 kV (see Fig. 19). However, up to approximately 28 kV, the peak value of the pulses is so small that the pulse component $I_p$ is negligible compared with the DC component, and the current curve and its interpolation by the Townsend's law are superimposed. From 28 kV, a slight shift between the two curves can be observed because $I_p$ is no longer
negligible.

## 7. Conclusion

This experimental study aimed to better understand the electrical and optical properties of positive DC corona discharges.

First, a new method was developed to plot the I-V characteristics of corona discharges in real time. It consists of applying a high voltage ramp of a few seconds and simultaneously measuring the time-averaged discharge current with a high bandwidth oscilloscope at a high sampling frequency. The main advantage of this method is that it is very fast and can be performed a large number of times to verify the reproducibility of the measurements. Second, we found that the electrical and optical properties of such a discharge depend highly on the electrode gap and applied voltage.

Four successive discharge regimes were observed in this study. After the ignition voltage, the current slowly increases, and it perfectly follows the theoretical Townsend's law. We are then in the presence of the well-known pulseless Hermstein's glow, usually called the glow regime. However, the onset streamer regime was never observed. When the voltage reaches a first voltage threshold, some small current pulses appear. However, this is not the breakdown streamer regime, as the ionized channels do not cross the entire electrode gap. In this regime, called the filamentary regime in the present article, the time-averaged current becomes higher than Townsend's law; each current pulse is composed of only one bump, and the pulse frequency is higher than that of breakdown streamers (for instance, for a gap equal to 30 mm, it is approximately 20 kHz when the frequency of breakdown streamers is around 3 kHz). Moreover, photographs and ICCD visualizations highlighted that the propagation of the streamers toward the grounded plate was limited to a few millimeters (up to half of the gap), this value increasing with the applied voltage. We do not believe that this regime corresponds to the onset streamer regime because the latter has always been observed for voltages lower than those necessary to reach the
pulseless Hermstein's glow regime, but there can be a debate on this.

When the voltage reaches a second threshold, the magnitude of the current pulses suddenly increases, but their frequency decreases; this is the transition toward the breakdown streamer regime. The morphology of the breakdown streamers corresponds to what has already been reported in the literature: in the first millimeters, the streamer is composed of one single ionized channel, and after a few millimeters of propagation, a branching process occurs, illustrated by several ionized channels. If we focus on one single current pulse, we can see that it is composed of two bumps. In fact, the first one corresponds to the arrival of the primary streamer at the plate, and the second one corresponds to a secondary streamer, as already reported in the literature.

Finally, we investigated the effect of the electrode gap on the electrical and optical properties of the discharge, even when the breakdown streamer regime was not reached with gaps higher than or equal to 70 mm. The following three main remarks can be made. First, the magnitude of the current pulses decreases when the gap increases. Second, the frequency of the breakdown streamers is higher when the gap is small (for instance, it is around 3 kHz and 8 kHz for gaps of 30 mm and 10 mm, respectively, these values of course depending on the value of the applied voltage). Finally, the offset between the Townsend's curve and the measured current, which occurs when the current becomes pulsed, is higher at small gaps. To summarize, when the electrode gap decreases, the frequency and amplitude of the current pulses increase, and the mean pulsed component of the total current increases; therefore, the offset between Townsend's law and the measured current increases.

On the one hand, we have been surprised to observe this new discharge regime unless this regime is the onset streamer regime. But in this case, why is it obtained for higher voltages than those to obtain the glow regime? On the other hand, there is no doubt about the existence of this regime, because all these measurements are fully reproducible and have been verified a very large number of times in the present study. Therefore, we must continue to study the influence of the needle material on the phenomena occurring within corona discharges, and more particularly the influence
of the surface finishing of the tip and its potential oxydation, as it seems that these
two parameters play a key role. As a prospect, we therefore plan to carry out
measurements of the surface finishing of the needle tip using scanning electron
microscopy (SEM) and to characerize its surface oxydation with the help of X-ray
photoelectron spectroscopy (XPS).

Acknowledgments

This work was funded by the French Government program INVESTISSEMENT D'AVENIR (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01) and pertains to the French government program "Investissements d'Avenir" (EUR INTREE, reference ANR-18-EUR-0010).

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<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /><figcaption>Figure 1. Experimental setup. The voltage v(t) is connected to the oscilloscope to record i(t), with i(t) = v(t)/R.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Figure 2. Photographs of the needle: large view (a) and zoomed (b)</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3. Discharge current when the high voltage is increased up to +18 kV and then decreased down to 0 kV. The electrode gap and the curvature radius of the tip are equal to 30 mm and 100 µm, respectively. The red curve shows to the measured mean discharge current and the black curve is the corresponding Tonwsend's law.</figcaption></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>Figure 4. I-V characteristics for electrode gap ranging from 5 mm up to 100 mm when the voltage is decreased (a) and increased (b).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 5. Photographs of the positive corona discharge with an used needle for different voltage values. The gap is equal to 30 mm, the plate is illustrated by a white dash line.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 6. ICCD visualizations of the positive corona discharge with an used needle for different voltage values. The gap is equal to 30 mm. the gate width is equal to 0.5 ms.</figcaption></figure>
<figure><img src="image_10.png" /><figcaption>Figure 7. Current versus time for different voltage values. Gap = 30 mm.</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>Figure 8. I-V characteristics of the positive corona discharge when the gap equal to 30 mm. The blue curve shows the measured mean current and the red curve is the corresponding Townsend's law.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig.9. Zoom view of one single current peak for different applied voltage values. Gap = 30 mm.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 10. Analysis of the current peak characteristics versus applied voltage: current peal amplitude (a), peal width FWHM (b), charge transferred by one single current pulse (c) and time interval between two successive current peaks (d). Gap = 30 mm.</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Fig. 11. Time-averaged additional current caused by the streamer current pulses. Gap = 30 mm.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 12. Discharge current when the high voltage is increased up to +9 kV and then decreased. The electrode gap is equal to 10 mm.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 13. Measured I-V characteristics of the positive corona discharge (blue curve) and Townsend's law (red curve). The gap is equal to 10 mm.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>Figure 14. Current versus time for different voltage values. Gap equal to 10 mm.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Fig.15. Zoom view of one single current peak for different applied voltage values. Gap equal to 10 mm.</figcaption></figure>

<figure><img src="image_19.png" /><figcaption>Fig. 16. Photographs of the positive corona discharge with an used needle for three voltage values. The gap is equal to 10 mm, the plate is illustrated by a white dash line.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>Figure 17. Discharge current when the high voltage is increased up to +30 kV and then decreased. The electrode gap is equal to 70 mm.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Figure 18. Measured I-V characteristics of the positive corona discharge (blue curve) and Townsend's law (red curve). The gap is equal to 70 mm.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure 19. Current versus time for different voltage values. Gap equal to 70 mm.</figcaption></figure>

<figure><img src="image_23.png" /><figcaption>Fig.20. Zoom view of one single current peak for different applied voltage values. Gap equal to 70 mm.</figcaption></figure>
<figure><img src="image_24.png" /><figcaption>Fig. 21. Photograph of the positive corona discharge with an used needle and a gap equal to 70 mm. Voltage is equal to +30 kV.</figcaption></figure>