1 American Institute of Aeronautics and Astronautics 

                                                           

Rate of Plasma Thermalization of Pulsed Nanosecond Surface Dielectric Barrier Discharge

Maryia Nudnova1, Svetlana Kindusheva2, Nikolay Aleksahdrov3,

Moscow Institute of Physics and Technology, Dolgoprudny, RUSSIA

and

Andrey Starikovskiy4 Drexel University, Philadelphia, USA

Abstract: The paper presents a detailed explanation of the physical mechanism of the nanosecond pulsed surface dielectric barrier discharge (SDBD) effect on the flow. Actuator-induced gas velocities show near-zero values for nanosecond pulses. The measurements performed show overheating in the discharge region at fast (τ ~ 1 μs) thermalization of the plasma inputed energy. The mean values of such heating of the plasma layer can reach 70, 200, and even 400 K for 7-, 12-, and 50-ns pulse durations, respectively. The emerging shock wave together with the secondary vortex flows disturbs the main flow. The resulting pulsed-periodic disturbance causes an efficient transversal momentum transfer into the boundary layer and further flow attachment to the airfoil surface. Thus, for periodic pulsed nanosecond dielectric barrier discharge DBD, the main mechanism of impact is the energy transfer to and heating of the near-surface gas layer. The following pulse-periodic vortex movement stimulates redistribution of the main flow momentum.

 1. Introduction

In discharge plasmas, electrons gain energy from an external electric filed and transfer it in collisions into various degrees of freedom of other particles, most of this energy eventually being released into heat. Problems concerning the mechanisms of gas heating in molecular gas discharges have attracted considerable attention in the last decades due to their importance for almost all practical plasmachemical systems. The fast heating leads to significant kinetic changes. Also fast gas heating leads to the instability development for discharge plasmas [1] and glow-to-spark transition [2], favors the propagation of microwave discharges in sub-breakdown electric fields [3] and of leader discharges in ambient air to induce the breakdown of long air gaps and lightning discharges in extremely long gaps [4]. Thus the rate of system thermalization becomes important to operation of gas lasers [1], plasmachemical reactors [5], ozonators, lamps, microelectronics, plasma vapor deposition, surface treatmentand other discharge devices and processes in which the plasma should be uniform. Finally, heat release can play an important role in short-duration pulsed discharges used recently for plasma-assisted ignition of combustible mixtures [6] and for flow control [7,8].

A well-known mechanism of gas heating in molecular gases is the relaxation of vibrationally excited molecules forming a reservoir of energy in discharge plasmas. This process takes sufficiently long (longer than 1 μs at atmospheric pressure air) time. The channels of fast heating in air, molecular nitrogen and some other gases at shorter times have received considerable interest in the last years (see references in [9]). At low (< 20 Td, 1 Td = 10-17 V cm2) reduced electric fields, E/N (N is the gas number density), contribution to fast gas heating is controlled by elastic collisions between electrons and neutral particles and by electron impact rotational excitation of molecules followed by rotational-translational relaxation. At higher values of E/N, the fraction of electron energy transferred to the translational degrees of freedom of atoms and molecules due to elastic collisions and rotational excitation is less than 3 %. This disagrees with a number of observations in molecular nitrogen, air and other N2:O2 mixtures, in which the percentage of fast gas heating was as large as 10-15 % for E/N > 80 Td (see references in [9]). In this case, the mechanism of fast gas heating was explained by self-quenching reactions of the N2(A3Σu

+) state in pure nitrogen [10, 11, 12] and by electron-impact dissociation of O2, by quenching of electronically excited N2 states in collisions with O2 and by quenching of the O(1D) state in air and in some other N2:O2 mixtures [9]. Computer simulations showed that the fraction of fast heat release

 1 Senior Researcher, Department of Molecular and Biological Physics 2 PhD Student, Department of Molecular and Biological Physics 3 Professor, Department of Problems of Physics and Power Engineering 4 Research Professor, Drexel Plasma Institute 

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-465

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

increases with increasing electric field due to a growth in the electron energy fraction spent on excitation and dissociation of N2 and O2 molecules [9,13].

Recent observations in nanosecond high-voltage discharge [14-18] have shown that fast gas heating may be efficient even at E/N > 300 Td, when the electron energy fraction spent on excitation and dissociation of the molecules decreases with electric field and most of the electron energy is spent on electron impact ionization. The mechanism of fast gas heating has not been studied at extremely high electric fields, although it has been suggested that this effect is responsible for an extremely high efficiency of operation of aerodynamic plasma actuators using nanosecond pulsed surface dielectric barrier discharges [16,17]. In this case, observations by Starikovskii et al [16] have shown that fast gas heating for several tens degrees leads to a vortex formation in the near-surface gas layer, the mechanism which is opposed to a well-known ion-wind mechanism of plasma actuators based on barrier discharges driven by sinusoidal voltages in the 1-10 kHz range. As a result, the actuators using the nanosecond discharges turned out to be much more efficient over a wide velocity (M = 0.03 – 0.85) and Reynolds number (Re = 104 - 2×106) ranges. A 2D simulation of the discharge and gas dynamics under conditions similar to those of these experiments has supported these observations [19].

The process of fast plasma thermalization is very important for plasma assisted combustion. Energy release to translational degrees of freedom leads to the hot channels formation and changes the ignition kinetics [20]. This effect can be used to stimulate the breakdown development at high-pressure conditions [21,22]. Fast energy thermalization and gas heating allows to ignite air-fuel mixtures at low initial temperatures and to stimulate distributed multi-spot ignition.

Quantitative experimental description of efficient fast heating has not been given so far at very high electric fields. Indeed, measurements by [18] have shown that 40±10% of the total input energy in nanosecond air discharges is spent on fast gas heating. However, electric fields have not been controlled in this case. Concerning other studies of this effect [14-17], an additional analysis is required to extract quantitative data from these measurements in nanosecond discharges.

The purpose of this work is (a) to analyze available experimental data for fast plasma thermalization at high reduced electric fields and to extract quantitative information about fast heating as a function of electric field and (b) to elaborate kinetic mechanism to simulate the electron energy transfer to translational degrees of freedom of the gas at very high electric fields when most of the energy input is spent on gas ionization in order to understand the channels of fast gas heating under the conditions considered. 2. SDBD Plasma Thermalization Installation used is shown in the Figure 1. To initiate sliding discharge magnetic compression generator was used. Pulse amplitude was up to 50 kV, rise time 7 ns, pulse duration 25 ns. The high-voltage pulses were transferred from the pulse generator to the high-voltage electrode by means of 50-Ohm coaxial RC-50-11-11 cable.

Figure 1. Scheme of experimental setup for temperature measurements. 1) actuator, 2) focus system, 3) monochromator MDR23, 4) high speed ICCD camera PicoStar HR12, 5) back current shunt, 6) coaxial cable from the HV generator, 7) back current shunt, 8) coaxial cable, 9) oscilloscope Tektronix TDS 3054.

Typical asymmetric plasma actuator geometry was used to initiate surface nanosecond barrier discharge. The high-voltage electrode and low-voltage electrodes were made of copper foil with thickness of 0.05 mm, width of 5 mm, and

2 American Institute of Aeronautics and Astronautics 

length of 85 mm. The low-voltage electrode was covered by a fluorocarbon film with a thickness of 0.3 mm. The scheme of the discharge geometry is presented in Fig. 2.

Figure 2. Scheme of the discharge gap. 1—high-voltage electrode; 2—dielectric layer; 3—low-voltage electrode, 4—zone of discharge propagation, 5—insulating layer.

Electric field measurement A reduced electric field was measured using the emission profiles of first negative system of nitrogen ions and second positive system of nitrogen molecules. The given spectroscopic technique to estimate E/n values can be applied when the upper emitting electronic levels are excited by direct electron impact from the ground state. For a short high-voltage pulse metastable state concentration cannot reach the level when the cascade processes would significantly contribute to populating the upper levels. High values of E/n also increase the role of direct population by electron impact. In these conditions the electric field could be measured using ratio of emission profiles at 337.1 (second positive system of nitrogen) and 391.7 nm (first negative system of nitrogen ion). This technique has been successfully applied to measure the fields in streamer and barrier discharges.

The emission profiles at 337.1 and 391.7 nm were obtained with nanosecond temporal resolution. Typical oscillograms are shown in Figure 3 for anode-directed discharge. The emission spectral range was selected using a monochromator MDR-41 (grating 3000 lines/mm, f = 300 mm, dispersion 0.95 nm/mm), which was placed in front of the plasma actuator. The widths of the front and back slits of the monochromator were 0.2 and 0.35 mm, respectively.

0 10 20 30 40 50 60 70-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

12

Time, ns

Emis

sion

,a.u

.

Figure 3. Typical oscillogram of N2 second positive and N2

+ first negative systems emission dynamics. 1 – 337.1 nm, 2 – 391.7 nm.

The measurements were performed with and without the aperture to block the emission from certain spatial regions. The aperture allows measurement of the emission flux only from the discharge's central part. In the latter case, the optical system catches emission from the region of the high-voltage electrode edge. The mean electric field measured without the aperture was higher in both the anode- and cathode-directed discharges. This comparison allows us to conclude that the E/n value is almost uniform along the streamers' zone and is higher near the exposed electrode edge.

3 American Institute of Aeronautics and Astronautics 

200 300 400 500 600 700 8000

100200300400500600700800900

1000110012001300

Elec

tric

Fiel

d,Td

Pressure, Torr Figure 4. Reduced electric field value E/n in anode-directed discharge.

Figure 4 shows the mean electric field in the center of the discharge zone. Emission from the edges of high- and low-voltage electrodes was blocked by the aperture. The electric field reaches the maximum at lowest pressures (1150 Td at pressure of 220 Torr) and decreases while the pressure increases (800 Td at atmospheric pressure). The uncertainty of the experimental data is mainly due to statistical pulse-to-pulse discharge variation and fluctuation of emission of the first negative system of the nitrogen ion. The value of emission of the second positive system of molecular nitrogen was quite stable. This fluctuation of emission of the first negative system is connected with a higher excitation threshold of the system and greater sensitivity of the population rate constant of N2

+(B2) state to the discharge development. Plasma layer geometry

Figure 5. Images of surface nanosecond barrier discharge development taken with nanosecond time resolution. Gate is

equal to 0.5 ns. Voltage on discharge gap is equal to 14 kV, half-width time of pulse t1/2 = 25 ns. Air, P = 1 atm. Cathode-directed discharge.

A PicoStar HR-12 ICCD camera with Helios-44M lens (f = 50 mm, D = 2.0) was used to determine spatial-temporal characteristics of the discharge. The discharge propagation for both polarities of the high-voltage pulse was investigated (Fig. 5). The camera was focused onto the top plane of the electrodes and dielectric layer (Fig. 2). The images were obtained with a nanosecond exposure time τ = 0.5 ns. The repetition frequency of the incident high-voltage pulses was equal to 1 Hz, and the pulse amplitude was 14 kV in the 50-Ohm coaxial cable. The half-width of the pulse was equal to 25 ns. The rise time of the pulse was equal to 7 ns, and the fall time was 15 ns.

4 American Institute of Aeronautics and Astronautics 

An ICCD camera intensifier was synchronized with the high voltage pulse to obtain a time-series of photo images. The discharge develops from the edge of the high-voltage (exposed) electrode (upper part of the picture Fig. 5) along the surface above the covered low-voltage electrode. The plasma layer then splits into several "streamer" channels. This is a result of an instability developed in the flat ionization front. A sequence of images was obtained using pulse-by-pulse technique. The intensifier delay was shifted by 0.5 ns relative to the pulse start for each high-voltage pulse. The propagation of the cathode-directed discharge subdivides into four stages. The streamers start from the upper electrode during the first stage and run along the surface above the lower electrode (1st, 3d and 4th ns, Fig. 5). The velocity of the discharge propagation during this stage was about 1 mm/ns. Emission from the whole streamer channel, not only from the leading ionization front, was observed. Then, the streamer's length exceeds the length of the covered electrode and its velocity slows down (0.3 mm/ns). Emission from the ionization front near the streamer's heads takes place during this stage. This stage lasts 5 ns (6th and 10th ns, Fig. 5). Then, the "silent" phase of the discharge follows when no sufficient discharge emission is observed (13th to 20th ns, Fig. 5). During the streamers' propagation, the dielectric surface is charged. Thus, when the trailing edge of the high-voltage pulse reaches the electrode, the electrode potential becomes lower than the potential of the dielectric surface in the discharge gap. This leads to start of a second flash, which corresponds to the charge removal from the surface (22nd , 37th ns, Fig. 5). This flash is similar to the first one with just one difference. The surface covered by discharge shortens because of the absence of a sufficient surface charge outside the low-voltage electrode (34th and 37th ns, Fig. 5).

a b

c d

Figure 6. Plasma volume measurements. U = 14 kV, pulse duration 25 ns, voltage rise time 7 ns. Air, P = 1 atm. a) side view of the discharge; b) top view; c) emission averaged along Y-axis; d) emission averaged along X-axis. Calculated full discharge volume is 17 mm3. Total discharge energy is 6 mJ. Full electrode length 80 mm, covered electrode width

5 mm, dielectric layer – 0.6 mm PVC multi-layer film. The main problem for atmospheric pressure gas discharge analysis is plasma inhomogeneity. The volume occupied by plasma should be measured very carefully because it determines energy density and total energy balance of the system. To measure the plasma volume two types of images were obtained with nanosecond resolution. One was a side view of the discharge (Figure 6, a), and another – top view (Figure 6, b). Discharge emission decreases with the distance from

5 American Institute of Aeronautics and Astronautics 

the actuator’s surface (Fig. 6, c) and with the distance from the edge of the exposed electrode (Fig. 6, d) . Analysis of effective surface, covered by plasma (Fig. 6, b) and effective thickness of plasma layer (Fig. 6 a) allowed to estimate the plasma volume.

In the Figure 6 we demonstrate the procedure of the plasma volume calculations. We have measured the emission distribution of 2+ system of nitrogen in the discharge. This emission distribution reflects the total energy distribution on the system taking into account high electrical field both in front of the ionization wave and in the channels, which lead to effective gas excitation in entire plasma region (Figure 5).

We have taken into account reflection of the emission from the dielectric surface using absolute position of the dielectric layer (Figure 6,c). The longitudinal distribution of the energy deposition was also nonuniform (Figure 6,d). Emission intensity decreases almost linearly with the distance from the edge of the exposed electrode. Time-resolved temperature measurements give average temperature in the plasma region. Thus we always obtain average value from entire plasma volume, including averaging through complex streamer’s structure (X-axes), distance from the edge of the high-voltage electrode (Y-axes) and distance from the dielectric surface (Z-axes).

We have calculated the discharge energy spatial distribution using assumption that the distribution os proportional to the emission of the second positive system of nitrogen. It is clearly seen (Figure 7), that the highest energy density (about 1 J/cm3) is observed in very small region with compare to entire plasma volume. The rest of the discharge volume demonstrates much less density of the energy deposited. Specific energy value decreases more than order of magnitude when the distance from the exposed electrode’s edge reaches 5 mm.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.04

0.060.080.1

0.2

0.4

0.60.8

1

2

Q, m

J/m

m3

Part of Plasma Volume

 Figure 7. Energy density in plasma in dependence on the selected plasma region. U=17 kV, negative polarity.

Thus different parts of the discharge can have significantly different temperature. The summary influence of different parts of plasma on the emission spectra registered is also different and depends on the energy distribution. We measured the average rotational distribution of the second positive system through entire discharge volume. To answer the question which part of the plasma volume participates in the emission formation we have modeled synthetic spectra composed with the emission from different zones (Figure 8). A synthetic spectrum was built as a linear combination of emission from several plasma regions with different temperature and different volume. We taken into account specific energy deposition for each plasma part and volume occupied by part with given specific energy. Generated synthetic spectra demonstrate non-Botzmann behavior but could be approximated by single-temperature distribution with “effective” temperature (Figure 8). This approximation shows that the summary discharge emission distribution can be described as an effective excitation with “effective” temperature. Thus, for conditions depicted in Figure 6 the most “hot” part of distribution has a temperature 1300 K, while the most “cold” – 350 K. It should be noted that both “hot” and “cold” parts play only minor role in the formation of the average spectra because of small amount of energy deposited both in the region with high and low specific energy. As a result the entire distribution can be approximated using a single temperature (for conditions of Figure 8 it is T = 600 K).

6 American Institute of Aeronautics and Astronautics 

334 335 336 3371

10

100

1000 Synthetic Spectra Spectra for T = 600 K

N2

Emis

sion

Spe

ctra

Dis

tribu

tion

λ, nm

 Figure 8. Comparison of multi-temperature and single-temperature distributions.

Thus we can assume that the measured plasma emission could be assigned to “effective” plasma volume with average “effective” temperature. Model calculations show that we can assume that the discharge energy is distributed homogeneously through the plasma volume which emits 50% of the radiation both for side and top view (Figure 6, a, b). In this case the “effective” temperature calculated by emission spectroscopy corresponds to the average gas temperature. Figure 6, b shows the part of plasma volume which emits 50% of radiation (contoured with solid line). In this region 50% of the discharge energy dissipates. The same procedure for side view (Figure 6,a) gives effective thickness of plasma layer. Thus we can estimate effective plasma volume as a product of effective surface covered with plasma (Figure 6, b) and effective thickness of plasma layer (Figure 6,a). In this volume 25% (taking into account 50% reduction for top view and another 50% for side view) of the total discharge energy is deposited (Figure 9).

Fig. 9. Plasma volume measurements for surface dielectric barrier discharge.

Fig. 10 Plasma energy measurements for surface dielectric barrier discharge.

The energy input in the discharge was calculated as the difference between the energy stored in the incident pulse measured by back-current shunt (Fig. 1 (5)) and the energy in the pulse after the actuator (Fig.1 (1)) measured by back-current shunt (Fig. 1 (7)). Typically, the value of energy input was within the range of 3 to 10 mJ per pulse for HV pulse amplitude from 13 to 18 kV on the discharge gap.

7 American Institute of Aeronautics and Astronautics 

Energy input measured by back-current shunts was used to estimate the energy density in the plasma region (Fig.10). Typical specific energy input was less than Q = 0.5 mJ/mm3. These measurements give the total specific energy in the discharge. Gas temperature dynamics was measured using emission spectra of 0↔0 transition of 2+ system of Nitrogen with nanosecond resolution. The scheme of experimental setup is shown in Fig. 13. The lens (2) focus the emission of sliding discharge to the input monochromator's slit. Spectral dispersion of the monochromator was 0.6 nm/mm. Real spectral resolution of the system was limited by micro channel Intensifier of ICCD camera and was about 0.25 nm. The output monochromator's optical plane was adjusted to the photocathode of the high speed camera. The high speed camera was synchronized with the HV pulses. The camera gate was started when the HV pulse reached the plasma actuator. The exposure time was equal to 100 ns. During one experiment we obtained the full spectra of 0↔0 transition of 2+ system of molecular nitrogen. To increase a signal to noise ratio we collected 2000 spectra in one regime and summed them.

335, 5 336, 0 336, 5 337, 0 337, 5

0,1

1123

Inte

nsity

,ar.

u.

Wavelength, nm

335, 5 336, 0 336, 5 337, 0 337, 5

0,1

112

Inte

nsity

,ar.

u.

Wavelength, nm

Figure 11. Spectra of 2+ system of nitrogen, 1) experimental spectrum, Δλ=0.25 nm, camera gate τ = 0 →

30 ns, 2) calculations with given temperature T=330 K, Δλ = 0.25 nm, 3) calculations with given temperature

T=330 K, Δλ = 0.001 nm. U=14 kV on the discharge gap.

Figure 12. Spectra of second positive system of nitrogen Δλ=0.25 nm. 1) camera gate t=0 → 30 ns, 2) experimental spectra, camera gate t=1000 → 1030~ns. U=18 kV on the discharge gap.

We have compared this spectrum with calculated one at a given temperature. The comparison of experimental and theoretical spectra is shown in Fig. 11. Two theoretical curves are demonstrated: with spectral resolution Δλ =0.001 nm and with spectral function corresponded to real system resolution Δλ =0.25 nm on the half-width). A calculated spectrum demonstrates very good agreement with the measured one. The gas temperature was 330K. That means that the gas temperature increase during discharge phase is 40 K.

To obtain the gas temperature dynamic we used the additional coaxial cable connected with the actuator (Fig. 1(8)). The length of the additional cable was varied from 0 to 100 m. The HV pulse comes through the cable (6) to the actuator and starts to propagate trough the additional coaxial line (8). It reaches the end of the line in 500 ns. After that it reflects and propagates back to the actuator another 500 ns. We synchronized the camera gate with the HV pulse reaching the actuator after this additional delay (1 μs). This pulse initiates weak discharge with the energy input about 0.1 of the first HV pulse. We obtained 2000 spectrums for summing. The final profiles are shown in Fig.12 (2).

Direct temperature measurements with nanosecond temporal resolution were performed to estimate part of the energy which quickly converts into the heat. It was found that the temperature increase is 40 K (290 → 330 K) during the discharge phase and additional 100 K (330 → 430 K) after 1 μs at U = 18 kV (energy input 11 mJ). At lower voltage (U = 14 kV) it was found that the temperature increase was 40 K (290 → 330 K) during the discharge phase and 50 K (330 → 380 K) after 1 μs (energy input 3 mJ) (Figure 13).

8 American Institute of Aeronautics and Astronautics 

9 10 11 12 13 14 15 16 17 18

300

350

400

450

500

550

600

650 20 ns - Spectr 1000 ns - Spectr 100% Energy Thermalization

Tem

pera

ture

, K

Voltage, kV

Fig. 13. Dynamics of temperature increase in plasma layer. 1) measurements gate 0-30 ns, 2) measurements gate 1000-1030 ns.

Due to very short relaxation time the gas can be considered as a motionless. In this case the total energy balance

could be estimated in constant volume assumption Q = CV ΔT. Using this assumption we can directly compare the specific energy input into the plasma (Figure 12) and temperature increase in the plasma layer measured by emission spectroscopy with different delay times. Calculations show that during 1 μs approximately 61±10% of the discharge energy was converted from molecular internal and chemical degrees of freedom into a heat (Figure 14). During the discharge phase the rate of energy conversion is much smaller and can be estimated as 35±5% from the total discharge energy. This value is in a good agreement with numerical model [9,13] where the mechanism of fast heating during the discharge phase has been proposed. This mechanism is based on the direct excitation of molecules by electron impact followed by fast quenching or decomposition with “hot” atoms formation. Under atmospheric pressure conditions in air this mechanism can explain fast heating during the discharge phase (20-30 ns) but cannot explain further temperature increase in microsecond time scale. Another important point is that the mechanism [9] predicts the decrease of the portion of energy which can be converted into a heat in a short time scale with reduced electric field increase. Experimental observations summarized in the current work contradict with this assumption demonstrating increase of fast thermalized energy portion up to 50-60% at E/n 800-1000 Td.

As it was mentioned the existing kinetic models cannot explain observed in the experiments rate of fast thermalization of non-equilibrium plasma at high reduced electric fields. Next chapter will be devoted to kinetic analysis of energy transfer mechanisms and possible explanations of the observed phenomena. 3. Kinetic model

It was assumed that a pulsed high-voltage discharge is maintained at a constant electric field for a short period of time, τ. The initial electron density was ne0 = 105 cm-3. (In practical situations it takes some time to produce initial electrons; we neglect this because the calculated percentage of fast gas heating is almost independent of the discharge duration under the conditions studied.) The value of τ was selected such that the electron density ne at t = τ was equal to nef = 1014 or 1015 cm-3, typical values of ne under the conditions of the experiments of [16,17]. The time τ decreased from 2 to 0.06 ns as the reduced electric field E/N increased from 300 to 1000 Td. The evolution in time of the density of all active species (atoms and excited and charged particles) was calculated on the basis of a numerical simulation of the corresponding balance equations. The energy conservation equation was simultaneously solved to follow temperature evolution. In addition, the electron energy conservation equation

9 American Institute of Aeronautics and Astronautics 

9 10 11 12 13 14 15 16 17 180.0

0.2

0.4

0.6

0.8

1.0

Portion of Energy Thermalized

- τ = 0 - 30 ns - τ = 1000 - 1030 ns

Frac

tion

of F

ast T

erm

aliz

atio

n

Voltage, kV

Fig. 14. SDBD: Fraction of the “fast” thermalization during different time intervals.

( ) pe

epee

epeeee n

dTdkTnn

dTdk

TnnIkTTTdt

dT 22323 3

232

32)( −−+−−= εν (1)

was simultaneously solved in the discharge afterglow to follow the evolution of the electron temperature Te, which was defined as 2<εe>/3, where <εe> is the average electron energy. Here, T is the gas temperature, νε(Te) is the frequency of electron energy relaxation in collisions with molecules, I is the ionization energy released in electron-ion recombination, np is the density of positive ions and k3 and k2 are, respectively, the rate constants of three-body and dissociative electron-ion recombination. The last three terms on the right-hand side of equation (1) describe the effect of so-called “recombination heating” [23], which can be important when the loss of electrons is dominated by three-body electron-ion recombination.

The system of these equations was solved in the zero-dimensional approximation in the discharge phase and in the discharge afterglow when electric field is absent. Active particles under consideration were N, O, O(1D), O(1S), N2(A3Σu

+), N2(B3Πg), N2(a’1Σu-), N2(C3Πu), N2(ΔE = 13 eV) (singlet N2 states with a threshold of around 13 eV),

electrons, O2+, O4

+, N2+, N4

+, and O2-.

Kinetic model elaborated includes electron impact dissociation, excitation and ionization of neutral particles, quenching of electronically excited particles, charge exchange in collisions between ions and neutral particles, dissociative and three-body electron-ion recombination and electron attachment and detachment from negative ions. The rate coefficients for electron impact excitation, dissociation and ionization of molecules were calculated by solving the electron Boltzmann equation in the classical two-term approximation with the BOLSIG+ code [24]. In this code, we used self-consistent set of electron collision cross sections for O2 and N2 [24]. The two-term approximation used seems to be reasonable under the conditions considered because this may introduce only a ~ 20 % error into calculated transport and reaction coefficients in N2 and similar gases at reduced electric fields E/N < 1500 Td (N is the gas number density) [25].

The rate coefficients for reactions between thermal electrons and heavy particles and between heavy particles were taken from [9,26]. Branching ratios for dissociative electron recombination with N2

+ and O2+ ions were taken from

[27,28]. It is known that the ambient electron gas may increase the rate of dissociative recombination [29]. This effect has been quantitatively studied only for Ar2

+ ions; we neglected it in this work although the point deserves further investigation.

The rate coefficient for three-body electron-ion recombination was taken from the calculation [30, 31] in which the effect of nonideality on the recombination rate was taken into account. This effect may be important at high electron densities and leads to an order of magnitude decrease in the rate of reaction (O2

+ + 2O2 → O4+ + O2) at an electron

10 American Institute of Aeronautics and Astronautics 

density of 1015 cm-3 and room gas temperature. The frequency of electron energy relaxation, νε, was calculated by analogy with [32].

4. Results and discussion

We simulated numerically the evolution in time of active species during the discharge and in its afterglow and calculated the energy transferred into heating through various channels by the instant t = 1 μs. The initial value of Te was assumed to be in the range 1-10 eV corresponding to the mean electron energy in the discharge. The calculated results are not sensitive to this magnitude because the rate of electron energy exchange is higher for higher energies. Indeed, hot electrons rapidly lose their energy in the inelastic collisions with excitation of electronic states of N2 and O2 molecules; however, when the electron energy decreases below the energy threshold of these processes, the effective frequency of electron energy exchange drops drastically. The reason is that in this case electrons can lose their energy only in elastic collisions and in the inelastic collisions with excitation of vibrational and rotational levels of N2 and O2.

Figure 15 compares the calculated ratio of this energy to the total energy deposited in the discharge phase with the results by [13] and with the ratio calculated under the assumption that 28 % of the energy spent on the excitation of electronic N2 and O2 states is quickly transferred into gas heating (see [9]). We carried out calculations for dry air and for air with 1 % H2O. At E/N = 100 – 200 Td the results obtained agree with the other calculations, which were made for dry air. Here, the fast gas heating is dominated by electron impact dissociation of O2, by quenching of N2(A3Σu

+), N2(B3Πg) and N2(a’1Σu

-) states in collisions with O2 and by quenching of O(1D) states in collisions with N2 [9]. Our calculations showed that the percentage of the energy transferred quickly to gas heating increases with E/N and reaches 44 - 49 % at E/N = 1000 Td, depending slightly on the electron density at t = τ, nef, and humidity. At high E/N, the deposited energy is first spent on ionization and fast heating is controlled by the processes of plasma decay.

100 10000

10

20

30

40

50

60

70

11 American Institute of Aeronautics and Astronautics 

28% of energy spent on N2(el) + O2(el)(Popov (2001))

Hea

ting

perc

enta

ge, %

E/N, Td

ne0=1014 cm-3; dry air

ne0=1015 cm-3; dry air

ne0=1014 cm-3; 1 % H2O

ne0=1015 cm-3; 1 % H2O

SDBD, 1 atm, Air FIW-SW, 20 Torr, Air

Figure 15. The percentage of the input energy transferred into gas heating in dry and humid (with 1 % H2O) for 1 μs as a function of the reduced electric field at which the energy was deposited in a high-voltage nanosecond discharge. The calculations were carried out for various values of electron density at the end of the discharge, nef. Closed circles correspond to calculations by [13] and red curve corresponds to the calculations assuming that 28 % of the energy spent on the excitation of electronical N2 and O2 states is quickly transferred into gas heating (see [9]).

Under the conditions considered, the plasma decays due to electron-ion recombination and electron attachment to O2 molecules followed by ion-ion recombination. Electron-ion recombination includes dissociative recombination and three-body recombination with a third body M = e or M = H2O in humid air. The rate of reaction (e +AB+ +e →A + e ) depends strongly on Te. On the assumption that the relaxation of Te is much faster than the plasma decay, we obtained that this reaction is the dominant mechanism of the plasma decay at nef = 1014 or 1015 cm-3. The contribution of this process into the plasma decay decreased when taking into account the evolution in time of Te. Our calculation showed that the rate of this reaction was noticeably less than the rates of dissociative electron-ion recombination when considering the effect of so-called “recombination heating” [23] and the effect of nonideality [30,31]. In this case, the role of this reaction in the plasma decay is relatively small and is reduced to decreasing the rate of electron energy relaxation in the discharge afterglow (see figure 16).

10-4 10-3 10-2 10-1

103

104

nef=1014 nef=1014

nef=1015 nef=1015

T e, K

time, μs

Figure 16. The evolution in time of the effective electron temperature in the afterglow of the high-voltage nanosecond

discharge sustained in dry air at E/N = 103 Td for nef = (a) 1014 and (b) 1015 cm-3. The solid curves correspond to calculations taking into account three-body electron-ion recombination and the dash curves correspond to calculations

neglecting this process. Figure 17 shows the evolution in time of the densities of charged particles in the afterglow of a discharge

sustained at E/N = 1000 Td in dry air for nef = 1014 or 1015 cm-3. Our calculations showed that in this case the dominant positive-ion species evolves in time in the following way:

N2+ → N4

+ → O2+ → O4

+ (2) Here, the electron density decreases by an order of magnitude for ~ 15 ns when the dominant positive ion is O2

+, whereas the densities of other ion species are around an order of magnitude lower. However, the rate of dissociative recombination for N4

+ and O4+ ions are an order of magnitude higher than that for O2

+ ions [27,28]. Therefore, the contributions of these processes into electron loss are comparable and the analysis of our results showed that these processes are also important to the plasma decay.

12 American Institute of Aeronautics and Astronautics 

 

10-4 10-3 10-2 10-11012

1013

1014

O2-

N2+

O4+

N4+

O2+

e

E/n = 1000 Td, nef=1014cm3

Dens

ity, c

m-3

time, μs10-4 10-3 10-2 10-1

1012

1013

1014

1015

O2-

O4+N2

+N4

+

O2+

e

E/n = 1000 Td, nef=1015cm3

Dens

ity, c

m-3

time, μs

 Figure 17. The evolution in time of the densities of charged particles in the afterglow of the high-voltage nanosecond

discharge sustained in dry air at E/N = 103 Td for nef = (a) 1014 and (b) 1015 cm-3.  

Although the initial electron density was high, the role of electron attachment followed by ion-ion recombination was important to the plasma decay for the following two reasons. Firstly, the rate of electron-ion recombination was relatively low because of the predominance of simple positive ions. Secondly, due to the effect of “recombination heating”, the electron density decayed at the electron temperatures Te ~ 0.1 eV (see figures 16 and 17) at which the rate of three-body electron attachment to O2 has a wide peak [33,34]. The role of the processes with negative ions turned out

to be even more important to fast heating because, in dissociative electron-ion recombination, only around one-half the released energy is transferred to gas heating, whereas another half the energy is spent on dissociation of molecular ions and excitation of the products. As opposed to electron-ion recombination, there is reason to believe that almost all ionization energy released in three-body recombination of positive and negative ions, the dominant mechanism of ion-ion recombination under the conditions considered, is transferred into gas heating. Indeed, three-body ion-ion recombination occurs in the following way [34]. One ion loses a fraction of its energy in a collision with a neutral particle in the vicinity of an ion of opposite charge and hence becomes captured by this ion. Then, the charge exchange occurs between the ions and the ionization energy is expected to be transferred to the translation degree of freedom of the particles because excitation of internal states of the particles is inefficient in this process [34].

The analysis of our calculated results showed that, under the conditions studied, ion-ion and dissociative electron-ion recombination made the major contribution into fast gas heating; ion recombination provided a 24 % contribution at nef = 1014 cm3 and a 14 % contribution at nef = 1015 cm-3, whereas the contribution of electron ion recombination was, respectively, 5 and 12 % in these cases.

  

10-10 10-9 10-8 10-7 10-6300

305

310

315

320

325

330

335

ne0=1014, dry air

ne0=1015, dry air

ne0=1014, humid air

ne0=1015, humid air

T, K

time, s10-10 10-9 10-8 10-7 10-6

300

301

302

303

304

ne0=1014, dry air

ne0=1015, dry air

ne0=1014, humid air

ne0=1015, humid air

T, K

time, s 

Figure 18. The evolution in time of the gas temperature in the near afterglow of the high-voltage nanosecond discharge sustained in dry and humid (1 % H2O) air at E/N = 103 Td for nef = 1014 and 1015 cm-3. In these cases, the total specific

deposited energy was, respectively, 6.07 and 0.607 mJ cm-3. Figure 18 shows the evolution in time of the gas temperature in the near afterglow of the high-voltage nanosecond

discharge sustained in dry and humid air at E/N = 103 Td. Here, the gas was heated via the mechanisms under consideration only for 40 ns, the time required for the plasma decay. Figure 19 shows the evolution in time of the percentage of the input energy transferred into gas heating in these cases.

10-10 10-9 10-8 10-7 10-60

10

20

30

40

50

ne0=1014, dry air ne0=1015, dry air ne0=1014, humid air ne0=1015, humid air

%

time, s

 Figure 19. The evolution in time of the percentage of the input energy transferred into gas heating in the near afterglow of the high-voltage nanosecond discharge sustained in dry and humid (1 % H2O) air at E/N = 103 Td for nef = 1014 and

1015 cm-3.

13 American Institute of Aeronautics and Astronautics 

The 1 % addition of H2O does not affect noticeably the percentage of fast heating (see figure 1). In this case, the dominant positive-ion species evolves in a more complicated way (see figure 20):

N2

+ → N4+ → O2

+ → H2O+ → H3O+ → H3O+H2O → H3O+(H2O)2 → H3O+(H2O)3 . (2)

However, the plasma decays when the dominant positive ions are simple molecular ions (O2+, H2O+ and H3O+) with

relatively low rates of dissociative electron-ion recombination and the situation is similar to that in dry air.

14 American Institute of Aeronautics and Astronautics 

10-4 10-3 10-2 10-1 1001010

1011

1012

1013

1014

N4+

H9O4+

H7O3+

H5O2+

O4+

O2+

H3O+

N2+

10-4 10-3 10-2 10-1 1001010

1011

1012

1013

1014

1015

H9O4+

H7O3+

O4+

H5O2+

H2O+

O2+

N4+

N2+

O2+H2O

H2O+

e

Dens

ity, c

m-3

time, μs

O2+H2O

H3O+

e

Dens

ity, c

m-3

time, μs

O2-

O2-

 Figure 20. The evolution in time of the densities of charged particles in the afterglow of the high-voltage nanosecond

discharge sustained in humid (with 1 % H2O) air at E/N = 103 Td for nef = (a) 1014 and (b) 1015 cm-3. 5. Conclusions Analysis of the experimental results of fast nonequilibrium plasma thermalization has been performed. It was shown that significant part of energy deposited into the non-equilibrium plasma at high electric field converts to translational degrees of freedom during plasma recombination.

Summarizing the results of temperature measurements in atmospheric pressure SDBD we estimated the energy release into translational degrees of freedom during first microsecond of atmospheric pressure air plasma recombination as 55-65% for investigated range of parameters. Reduced electric field measured for these conditions was E/n = 800-900 Td and slightly increased with a pressure decrease.

Kinetic model of fast plasma thermalization at high and ultra-high electric field has been proposed. This model is able to explain existing experimental data and broadens the theory range to strong electric field region up to the electrons run-away threshold.

The analysis of the model showed that, under the conditions studied, ion-ion and dissociative electron-ion recombination made the major contribution into fast gas heating; ion recombination provided a 24 % contribution at nef = 1014 cm3 and a 14 % contribution at nef = 1015 cm-3, whereas the contribution of electron ion recombination was, respectively, 5 and 12 % in these cases. Acknowledgements The work was partially supported by Russian Foundation for Basic Research under the project “Nonequilibrium plasma thermalization”, AFOSR under the project “Fundamental Mechanisms, Predictive Modeling, and Novel Aerospace Applications of Plasma Assisted Combustion”, and NEQLab Research Company under the program “Reforming of Hydrocarbon Fuels”. References 1. Y. P. Raizer: Gas Discharge Physics, ed. J. E. Allen (Springer-Verlag, Berlin, Heidelberg, 1991) 2. Marode E 1975 J. Appl. Phys.46 2005–15 3. Vikharev, A. L.; Gil'Denburg, V. B.; Golubev, S. V.; Eremin, B. G.; Ivanov, O. A. Zhurnal Eksperimental'noi i

Teoreticheskoi Fiziki (ISSN 0044-4510), vol. 94, April 1988, p. 136-145. 4. E. M. Bazelyan and Yu. P. Raizer, Spark Discharge (MFTI, Moscow, 1997; CRC, Boca Raton, 1997) 5. Slovetskiy D.N., Khimiya plazmy, Moscow, Energoatomizdat, 1981, P. 189-229

15 American Institute of Aeronautics and Astronautics 

6. S. Starikovskaia, J. Phys. D: Appl. Phys. 39 (2006) R265-R299. 7. Bletzinger, P., Ganguly, B. N., VanWie, D., and Garscadden, A. Journal of Physics D: Applied Physics, Vol. 38,

2005, pp. R33–R57. 8. Moreau, E., Journal of Physics D: Applied Physics, Vol. 40, 2007, pp. 605–636. 9. Popov N.A., Plasma Phys. Rep., 27, 886 (2001). 10. Boeuf J.P., Kunhardt E.E., J. Appl. Phys. 60, 915 (1986). 11. Berdyshev A.V., Vikharev A.O., Gitlin M.C., Derugin A.A., Ivanov O.A., Kochetov I.V., Litvak A.G., Napartovich

A.P., Polushkin I.N., Stepanov A.N., Scherbakov A.I., Teplofiz. Vys. Temp., 26, 661 (1988). 12. Aleksandrov A.F., Kuzovnikov A.A., Shibkov V.M., Inzh. Fiz. Zurn., 62, 726 (1992). 13. Flitti A., Pancheshnyi S., Eur. Phys. J. Appl. Phys. 45, 21001 (2009). 14. E.M.Anokhin, S.M.Starikovskaia, A.Yu.Starikovskii. 42nd AIAA Aerospace Sciences Meeting and Exhibit, Reno,

Nevada, 2004. Paper AIAA 2004-674 15. D. Roupassov, M. Nudnova, A. Nikipelov, A. Starikovskii. 46th AIAA Aerospace Sciences Meeting and Exhibit 7 -

10 Jan 2008 Grand Sierra Resort Hotel Reno, Nevada. Paper AIAA-2008-1367. 16. D. Roupassov, A. Nikipelov, M. Nudnova, A. Starikovskii, AIAA Journal (2009) 0001-1452 vol.47 no.1 (168-

185); 17. A.Starikovskii, A.Nikipelov, M.Nudnova, D.Roupassov. Plasma Sources Sci. Technol. 18 (2009) 18. Bazhenova T.V., Znamenskaya I.A., A.E. Lutskii A.E., Mursenkova I.V., Teplofiz. Vys. Temp., 45, 1 (2007). 19. T. Unfer and J.P. Boeuf, J. Phys. D: Appl. Phys. 42 194017 (2009) 20. M. Uddi, N. Jiang, E. Mintusov, I. Adamovich, W. Lempert, Proc. Combust. Inst. 32 (2009) 929-936. 21. S V Pancheshnyi, D A Lacoste, A Bourdon, and C O Laux (2006) IEEE Transactions on Plasma Science 34 2478-

2487 22. G V Naidis J. Phys. D: Appl. Phys. 41 (2008) 234017 23. Bychkov V.L., Eletskii A.V., In: Chemistry of plasma, ed. B.M.Smirnov, No. 12, p. 1119, Moscow:

Energoatomizdat (1985). 24. Hagelaar G.J.H., Pitchford L.C. Plasma Sources Sci. Technol., 14, 722 (2005). 25. Phelps A.V., Pitchford L.C., Phys. Rev. A, 31, 2932 (1985). 26. Kossyi I.A., Kostinsky A.Yu., Matveyev A.A., Silakov V.P., Plasma Sources Sci. Technol., 1, 207 (1992). 27. Florescu-Mitchell A.I., Mitchell J.B.A., Phys. Rep., 430, 277 (2006). 28. Mitchell J.B.A., Phys. Rep., 186, 215 (1990). 29. Bates D.R., J. Phys. B: Atom. Molec. Phys. 13, L51 (1980). 30. Lankin A.V. JETP, 107, 870 (2008). 31. Lankin A.V., Norman G.E., J. Phys. A: Math. Teor., 42, 214042 (8pp) (2009). 32. Aleksandrov N.L., Kindysheva S.V., Kirpichnikov A.A., Kosarev I.N., Starikovskaia S.M., Starikovskii A.Yu., J.

Phys. D: Appl. Phys., 40, 4493 (2007). 33. Massey H. Negative ions, Cambridge: Cambridge University Press (1976). 34. Smirnov B.M. Negative ions, New York: McGraw-Hill (1982).