**2.2 Positive corona micro-discharge under DC voltage condition**

Let consider a mono pin-to-plane electrode corona reactor filled with dry air at atmospheric pressure and ambient temperature (Dubois et al., 2007). A DC high voltage supply is connected to the pin through a mega ohm resistor. When the applied voltage is raised gradually there is no sustained discharge current as much as the electrical gap field remains less than the onset one. Then, a sudden current pulse appears marking the beginning of the self sustained onset streamer regime. The associated current pulses occur intermittently and randomly and the mean current is very low (of few µA). Using a CCD camera with a large time shutter, we can observe a low intensity spot light just around the pin (see Fig. 2a). If we continue to increase the DC voltage, the current pulses vanish. However, the spot light near the point is always observed but with a quite higher intensity (see Fig. 2b). This regime corresponds to the classical glow corona discharge which is characterised by a drift of charged particles in the inter-electrode gap. The average current can reach some tens of µA.

Fig. 1. Sample of pin-to-plane and wire-to-cylinder corona discharge reactors. The light blue material corresponds to a dielectric material. Depending on applications, design and reactor efficiency, the High Voltage (HV) shape can be DC, pulsed, AC or a combination of them. chemical activity triggered by the micro-discharge during the plasma process. All these information can be used in order to improve the reactor design and to achieve the best operating conditions (such as the reactor geometry, the flue gas resident time, the applied voltage shape and magnitude, among others) as a function of the chosen applications. The present chapter is devoted to description of the main electro-hydrodynamics phenomena that take place in non-thermal plasma reactors at atmospheric pressure activated by corona micro-discharges. The first section describes the micro-discharges characteristics using the experimental results obtained in a mono pin-to-plane reactor stressed by either DC or pulsed high voltage. The physics of the micro-discharges development is explained and a complete hydrodynamics model is proposed based on the moments of Boltzmann equations for charged and neutral particles. Then before to conclude, the previous described model is used in order to simulate the strongly coupled chemical and hydrodynamics phenomena generated by micro-discharges in a non thermal

In this first section, we describe the main characteristics of the corona micro-discharge formation and development as a function of several operating parameters such as the geometry of electrodes or the shape and magnitude of applied high voltage. Then, based on Boltzmann kinetic theory, we describe the strongly coupled electrical, hydrodynamics and chemical phenomena that take place in a compressible gas crossed by micro-discharges.

Let consider a mono pin-to-plane electrode corona reactor filled with dry air at atmospheric pressure and ambient temperature (Dubois et al., 2007). A DC high voltage supply is connected to the pin through a mega ohm resistor. When the applied voltage is raised gradually there is no sustained discharge current as much as the electrical gap field remains less than the onset one. Then, a sudden current pulse appears marking the beginning of the self sustained onset streamer regime. The associated current pulses occur intermittently and randomly and the mean current is very low (of few µA). Using a CCD camera with a large time shutter, we can observe a low intensity spot light just around the pin (see Fig. 2a). If we continue to increase the DC voltage, the current pulses vanish. However, the spot light near the point is always observed but with a quite higher intensity (see Fig. 2b). This regime corresponds to the classical glow corona discharge which is characterised by a drift of charged particles in the inter-electrode gap. The average current can reach some tens of µA.

HV HV HV HV

**2. Description of positive corona micro-discharges** 

**2.2 Positive corona micro-discharge under DC voltage condition** 

plasma reactor.

**2.1 Introduction** 

For a high voltage threshold value, some regular repetitive current pulses appear with a repetition frequency of some tens of kHz and a magnitude of some tens to hundred of mA. Each current pulse lasts some hundred of nanoseconds and corresponds to the propagation of a mono-filament corona micro-discharge shown in Fig. 2c.

Fig. 2. Photography of the different corona discharge regimes under positive DC voltage condition (inter-electrode distance = 7mm, pin radius = 20 µm, dry air, atmospheric pressure). a: onset streamer, DC voltage magnitude = 3.2kV, time camera shutter = 1s, b: glow discharge, DC voltage magnitude = 5kV, time camera shutter = 10ms, c: streamer micro-discharge, DC voltage magnitude = 7.2kV, time camera shutter = 10µs (Eichwald et al., 2008).

More detailed information on the spatio-temporal evolution of the micro-discharge can be obtained thanks to the analysis of the streak camera picture shown in Fig. 3 and the corresponding current pulse shown in Fig. 4 (Eichwald et al., 2008, Marode, 1975). In Fig. 3, the X-axis is the time axis while the Y-axis is the inter-electrode distance. The electrode location is shown in the drawing at the left side of Fig. 3. For a given time on the X-axis, the light emission of the micro-discharge filament at each position is focused along the corresponding Y-axis coordinate. When 8.2kV is applied to the pin, three main phases can be distinguished in the corona micro-discharge development. The first one corresponds to the primary streamer propagation from the anode pin towards the cathode plane. The primary streamer propagates a luminous spot (called streamer head) which leaves the first narrow luminous trail shown on the streak picture of Fig. 3. During this first phase, the current rapidly increases as shown in Fig. 4 between 50ns and 75ns. The second phase

Fig. 3. Streak camera picture of a corona micro-discharge: Inter-electrode distance = 7mm, pin radius = 20 µm, dry air, atmospheric pressure, DC voltage magnitude = 8.2kV

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 273

Fig. 5. Instantaneous measured current for pulsed voltage conditions: Maximum voltage

0 50 100 150 200 250 300

Time (ns)

Fig. 6. Instantaneous corona current for pulsed voltage conditions: Maximum voltage magnitude=8kV, pulse voltage width=40µs, inter-electrode distance=8mm, pin

therefore gives a higher discharge current than in the case of DC voltage.

integrated picture of Fig. 7 clearly shows that there are several streamers starting from the pin towards the plane. This branching mechanism occurs in pulsed voltage conditions and

The evolution of the corona current in Fig. 6 is characterized by a first peak of about 70mA with a short duration (around 4ns) corresponding to the discharge ignition due to the

magnitude=8kV, pulse voltage width=40µs, inter-electrode distance=8mm, pin

radius=25µm, dry air at atmospheric pressure.

0

radius=25µm, dry air at atmospheric pressure.

50

100

Corona current discharge (mA)

150

200

Fig. 4. Instantaneous micro-discharge current (inter-electrode distance = 7mm, pin radius = 20 µm, dry air, atmospheric pressure, DC voltage magnitude = 8.2kV)

corresponds to the arrival of the primary streamer at the cathode. It is associated to both the sudden increase of the current pulse at around 75ns (see Fig. 4) and the first current peak. In the present experimental conditions, the current pulse magnitude reaches a maximum of 30mA. On the current curve of Fig. 4, we also observe that the primary streamer needs about 25ns to cross the inter electrode gap and to reach the cathode plane 7mm underneath the pin. Thereby, the mean primary streamer velocity can be estimated of about 3×107cm s-1. We also observe in Fig. 3 the development of a secondary streamer (Sigmond, 1984) starting from the point when the primary streamer arrives at the cathode plane. The associated light emission is more diffuse on the streak picture because the radiative species are distributed along the pre-ionized channel. The development and propagation of the secondary streamer induce a second current peak (see Fig. 4). Finally, each current pulse is characterised by the propagation of primary and secondary streamers which in turn create the thin ionized channels of the micro-discharge shown in Fig. 2c.

#### **2.3 Positive corona micro-discharge under pulsed voltage condition**

The morphology of micro-discharges under pulse voltage condition is quite different from the case of DC voltage condition (van Veldhuizen & Rutgers, 2002, Abahazem et al. 2008). However, we will see at the end of the present section the correspondence between both regimes using a large voltage pulse width. Fig. 5 shows a sample of a high voltage pulse applied on the pin of a pin-to-plane corona reactor and the resulting measured current pulse. The pulse voltage width is first chosen in order to obtain only one micro-discharge per pulse. The experimental conditions are very similar to those used for the DC voltage study described in previous section 2.2. In Fig. 5, the two current peaks superposed with the increasing and decreasing fronts of the pulse voltage are two capacitive current pulses generated by the equivalent capacitance of the pin-to-plane electrode configuration. The micro-discharge current pulse is positioned at time t=0ns in Fig. 5. A detailed description of this peculiar current pulse can be seen in Fig. 6. A rapid comparison with the DC current pulse in Fig. 4 indicates that the current pulse magnitude under pulse voltage condition is much higher (~175mA) than in the DC voltage case (~30mA). In fact, the ICCD time

(2) (3)

0 50 100 150 200

Time (ns)

Fig. 4. Instantaneous micro-discharge current (inter-electrode distance = 7mm, pin radius =

corresponds to the arrival of the primary streamer at the cathode. It is associated to both the sudden increase of the current pulse at around 75ns (see Fig. 4) and the first current peak. In the present experimental conditions, the current pulse magnitude reaches a maximum of 30mA. On the current curve of Fig. 4, we also observe that the primary streamer needs about 25ns to cross the inter electrode gap and to reach the cathode plane 7mm underneath the pin. Thereby, the mean primary streamer velocity can be estimated of about 3×107cm s-1. We also observe in Fig. 3 the development of a secondary streamer (Sigmond, 1984) starting from the point when the primary streamer arrives at the cathode plane. The associated light emission is more diffuse on the streak picture because the radiative species are distributed along the pre-ionized channel. The development and propagation of the secondary streamer induce a second current peak (see Fig. 4). Finally, each current pulse is characterised by the propagation of primary and secondary streamers which in turn create the thin ionized channels of the micro-discharge shown in

The morphology of micro-discharges under pulse voltage condition is quite different from the case of DC voltage condition (van Veldhuizen & Rutgers, 2002, Abahazem et al. 2008). However, we will see at the end of the present section the correspondence between both regimes using a large voltage pulse width. Fig. 5 shows a sample of a high voltage pulse applied on the pin of a pin-to-plane corona reactor and the resulting measured current pulse. The pulse voltage width is first chosen in order to obtain only one micro-discharge per pulse. The experimental conditions are very similar to those used for the DC voltage study described in previous section 2.2. In Fig. 5, the two current peaks superposed with the increasing and decreasing fronts of the pulse voltage are two capacitive current pulses generated by the equivalent capacitance of the pin-to-plane electrode configuration. The micro-discharge current pulse is positioned at time t=0ns in Fig. 5. A detailed description of this peculiar current pulse can be seen in Fig. 6. A rapid comparison with the DC current pulse in Fig. 4 indicates that the current pulse magnitude under pulse voltage condition is much higher (~175mA) than in the DC voltage case (~30mA). In fact, the ICCD time

0

5

10

15

Current (mA)

Fig. 2c.

(1)

20 µm, dry air, atmospheric pressure, DC voltage magnitude = 8.2kV)

**2.3 Positive corona micro-discharge under pulsed voltage condition** 

20

25

30

Fig. 5. Instantaneous measured current for pulsed voltage conditions: Maximum voltage magnitude=8kV, pulse voltage width=40µs, inter-electrode distance=8mm, pin radius=25µm, dry air at atmospheric pressure.

Fig. 6. Instantaneous corona current for pulsed voltage conditions: Maximum voltage magnitude=8kV, pulse voltage width=40µs, inter-electrode distance=8mm, pin radius=25µm, dry air at atmospheric pressure.

integrated picture of Fig. 7 clearly shows that there are several streamers starting from the pin towards the plane. This branching mechanism occurs in pulsed voltage conditions and therefore gives a higher discharge current than in the case of DC voltage.

The evolution of the corona current in Fig. 6 is characterized by a first peak of about 70mA with a short duration (around 4ns) corresponding to the discharge ignition due to the

Electro-Hydrodynamics of Micro-Discharges in Gases at Atmospheric Pressure 275

To summarize, the voltage pulsed corona micro-discharges are characterized by a streamer branching structure and the propagation of multiple primary and secondary streamers. Relations between pulsed and DC voltage conditions can be pointed out using a large width voltage pulse. In this case, several micro-discharges are able to cross the inter-electrode gap during a single voltage pulse. Fig. 9 shows the morphology of the first the 18 corona microdischarges generated between a pin and a plane using a high voltage pulse of 20ms of

Fig. 9. Streak pictures of the successive corona micro-discharges induced in dry air by a

The branching phenomenon is clearly observed in the first corona micro-discharge with the simultaneous development of a high number of filaments (see the first corona microdischarge in Fig. 9). Then, during about 400µs, the following discharges present a trunk expansion (shown by the red line in Fig. 9) in front of which a low number of filaments develop. A complete mono-filament structure appears after tens of discharges. Their characteristics are the same as those observed under DC high voltage condition. Thus, the more luminous trails in the discharge pictures of Fig. 9 correspond in fact to the development of the secondary streamers which extend gradually from the point towards the plane. Therefore, the formation of the mono-filament structure can be explained as a result of complex thermal and kinetics memory effects induced in the secondary streamer between

Even if micro-discharges are non thermal plasmas, their propagation can affect the neutral background gas (Eichwald et al. 1997, Ono & Oda b, 2004, Batina et al, 2002). In all cases, the micro-discharges modify the chemical composition of the medium (Kossyi et al. 1992, Eichwald et al. 2002, Dorai & Kushner 2003). In fact, the streamer heads propagate high energetic electrons that create radicals, dissociated, excited and ionized species by collision with the main molecule of the gas. Indeed, we have to keep in mind the low proportion of electrons and more generally of charged particles present in non-thermal plasma. At atmospheric pressure, and in the case of corona micro-discharge, we have about one million of neutral particles surrounding every charged species. Therefore, the collisions chargedneutral particles are predominant. During the discharge phase (which is associated to the

pulse voltage of 20 ms duration and 7.2 kV magnitude (Abahazem et al. 2008).

duration.

each successive discharge.

**2.4 Induced neutral gas perturbations** 

Fig. 7. Time integrated picture of corona discharge in dry air at atmospheric pressure for a time exposure of 10ms: Maximum voltage magnitude=8kV, pulse voltage width=40µs, interelectrode distance=8mm and pin radius=25µm.

intense ionization processes generated by the high geometric electric field near the pin. This phenomenon can be seen in the first picture of Fig. 8 which shows an intensive spot light around the pin. After this first current peak, as soon as the electron avalanches reach a critical size, the accumulated charge space splits into several streamer heads that begin to propagate towards the cathode (see Fig. 8). During this primary streamer propagation, the corona current begins to steeply increase up to reach a peak value of about 175mA at the streamers arrival at the cathode for a time around 50ns (see Fig. 6). The streamer branches arrive separately at the cathode with an average propagation velocity of about 2.7× 107 cm.s-1. Above this instant, the corona current peak, after a first decrease due to transition between displacement and conduction currents, slows down during a short duration (around 70ns) corresponding to the secondary streamer propagation. This is then followed by a slower and monotonic fall of the corona current corresponding to the relaxation time that lasts above the 300ns displayed in the time axis of Fig. 6.

t 21 ns t 33 ns t 48 ns Fig. 8. Time resolved corona discharge pictures at different instants for dry air at atmospheric pressure: Maximum voltage magnitude=8kV, pulse voltage width=40µs, interelectrode distance=8mm and pin radius=25µm, exposure time = 3ns, reference intensity image=21ns

Fig. 7. Time integrated picture of corona discharge in dry air at atmospheric pressure for a time exposure of 10ms: Maximum voltage magnitude=8kV, pulse voltage width=40µs, inter-

intense ionization processes generated by the high geometric electric field near the pin. This phenomenon can be seen in the first picture of Fig. 8 which shows an intensive spot light around the pin. After this first current peak, as soon as the electron avalanches reach a critical size, the accumulated charge space splits into several streamer heads that begin to propagate towards the cathode (see Fig. 8). During this primary streamer propagation, the corona current begins to steeply increase up to reach a peak value of about 175mA at the streamers arrival at the cathode for a time around 50ns (see Fig. 6). The streamer branches arrive separately at the cathode with an average propagation velocity of about 2.7× 107 cm.s-1. Above this instant, the corona current peak, after a first decrease due to transition between displacement and conduction currents, slows down during a short duration (around 70ns) corresponding to the secondary streamer propagation. This is then followed by a slower and monotonic fall of the corona current corresponding to the relaxation time that lasts above

2=9 ns t

t 21 ns t 33 ns t 48 ns

21ns 33ns 48ns

atmospheric pressure: Maximum voltage magnitude=8kV, pulse voltage width=40µs, interelectrode distance=8mm and pin radius=25µm, exposure time = 3ns, reference intensity

Fig. 8. Time resolved corona discharge pictures at different instants for dry air at

3ns 9ns 12ns

3=12 ns

electrode distance=8mm and pin radius=25µm.

the 300ns displayed in the time axis of Fig. 6.

<sup>1</sup>=3 ns t

t

image=21ns

To summarize, the voltage pulsed corona micro-discharges are characterized by a streamer branching structure and the propagation of multiple primary and secondary streamers. Relations between pulsed and DC voltage conditions can be pointed out using a large width voltage pulse. In this case, several micro-discharges are able to cross the inter-electrode gap during a single voltage pulse. Fig. 9 shows the morphology of the first the 18 corona microdischarges generated between a pin and a plane using a high voltage pulse of 20ms of duration.

Fig. 9. Streak pictures of the successive corona micro-discharges induced in dry air by a pulse voltage of 20 ms duration and 7.2 kV magnitude (Abahazem et al. 2008).

The branching phenomenon is clearly observed in the first corona micro-discharge with the simultaneous development of a high number of filaments (see the first corona microdischarge in Fig. 9). Then, during about 400µs, the following discharges present a trunk expansion (shown by the red line in Fig. 9) in front of which a low number of filaments develop. A complete mono-filament structure appears after tens of discharges. Their characteristics are the same as those observed under DC high voltage condition. Thus, the more luminous trails in the discharge pictures of Fig. 9 correspond in fact to the development of the secondary streamers which extend gradually from the point towards the plane. Therefore, the formation of the mono-filament structure can be explained as a result of complex thermal and kinetics memory effects induced in the secondary streamer between each successive discharge.
