Modeling of a Steady Low-Current Arc Discharge in Air at Atmospheric Pressure

A. Risacher, S. Larigaldie, G. Bobillot, J.-P. Marcellin and L. Picard
ONERA, Chemin de la Huniere, F-91761 Palaiseau Cedex, France
Abstract. Low current ( 250 mA), high voltage ( 700 V), DC arc discharges are observed to operate in air at atmospheric
pressure when a close loop is included for current regulation of the power supply. A model of the low-current arc column
is developed. Calculation results of the current and temperature on the axis of the discharge with and without the current
regulation model taken into account show that the discharge steadiness is attributed to a dynamic process of the close loop.
Keywords: atmospheric discharge, low-current discharge, steady discharge, simulation of arc discharge, depending time Elenbaas-Heller
equation, current regulation
PACS: 50.00.00, 52.80.-s, 52.80.Mg
INTRODUCTION
Research on atmospheric pressure stable discharges in air is motivated by various applications such as instantly
activated reflectors and absorbers for electromagnetic radiations, detoxification of polluted air, or surface treatment
[1, 2]. A steady low current high-voltage arc discharge can be obtained in air at atmospheric pressure with a relatively
high value of the ballasted resistor contained in the external circuit (about 15 MW [3, 4]). As a result, the electrical
energy supplied might be rather dissipated on the external ballast resistor than utilized in sustaining the arc’s plasma.
On the other hand, an example of a steady low-current arc discharge obtained in atmospheric-pressure air by means
of a DC current-regulated power supply ballasted by a resistor as low as 1 kW is observed in [5] and the author suggests
that a direct link should exist between the dynamic properties of the generator and the low power arc stabilization.
In this work, a steady electric discharge in air at atmospheric pressure is observed. A model of the low-current arc
column is developed. Then, the simulation exposes that the discharge steadiness is attributed to a dynamic process of
the close loop included to the current regulation system of the power supply.
EXPERIMENTATION
The experiments with the steady electric discharge are conducted in ambient air at atmospheric pressure. An experimental
device is shown schematically in figure 1. The electric arc discharge is generated between a tiny pyramidal
anode and a plate cathode, separated by an inter-electrodes gap of L=47 mm. The electrodes are ballasted by a resistor
Rp of 14.92 kW connected in series with the power supply. The generator consists in a DC high voltage power supply
operating on current regulation mode (Technix: SR-80-N-20.000). The maximum output voltage and current are about
80 kV and 250 mA, respectively. Nevertheless, for the experiment, the output voltage is about 5 kV and the current
is restricted to its maximum value of 250 mA. The current regulation device consists in a differential amplifier that
compares, through 100 kW resistors, the command value of the current to the actual value measured by an internal
sensor. The feedback loop includes a 47 nF capacitor in series with a 5.6 kW resistor, thus the circuit mainly acts as an
integrator with a time constant of about 5 ms.
The plasma voltage Vp is measured with a high voltage probe (Tektronix, P6015A, 20kV DC, 75MHz) and the
current Ip is monitored by means of a current probe (Tektronix, TCP202, 15 A AC/DC current, 50MHz). The plasma
electric measures are complemented by the power supply electric measures V0 processed by a numerical oscilloscope
(Tektronix TDS 2024, 200 MHz, and 2G).
The discharge operating in the above-defined standard configuration is shown in figure 2. Careful adjustment of the
time exposure allows to avoid any saturation effect on the photograph (except for the cathode and anode spots). This
view demonstrates that a whitish halo of heated air effectively surrounds the 3 mm-diameter inner core of plasma. This
also confirms that the plasma does not exhibit the vertical stratifications which are typical of glow discharges.

MODELING
Belinov and Naidis [6] have performed simulations of direct current (DC) arc discharges in molecular gases at
atmospheric pressure in tubes of 1.3 and 10 mm diameters. Usually based on the approach of the local thermodynamic
equilibrium (LTE), this approach is justified if the gas temperature in the discharge core is high enough (typically
higher than 4000 K), which is the case if the electric current is higher than several tenths of an ampere. Moreover, the
results of the non-LTE and LTE models nearly coincide for currents greater than approximately 50 mA. According to
the authors, the transition from the LTE to the non-LTE plasma state with a decrease in the discharge current is related
to the change in the ionization mechanism. At high currents, when the gas temperature is rather high, the dominant
process of production of electrons is the associative ionization N + O ! NO+ + e. The gas temperature Tg then
determines the ionization rate independently of the electronic temperature Te. Furthermore, until the current rises up
to  1 A, the gas temperature should not exceed 6000 K and radiation losses may be neglected.
As the electric discharge is obtained for a current of 250 mA, we can then describe the arc discharge as a positive
column at the LTE state where radiation losses are neglected. Thus, the temperature range of the plasma lies between
4000 K and 6000 K. Additionally, we assume that the plasma string has an axial symmetry with r as the radial variable.
Within the framework of the proposed surmises, the time-dependent Elenbaas-Heller equation can then describe the
evolution of the plasma:

Where, n0 is the gas concentration and Cp(T) the specific heat. c and s are the thermal and electrical conductivity
coefficients and E the axial homogeneous electric field. We suppose that the electric field is uniform and parallel
to the symmetric axis, then, it is an independent parameter of the temperature and can be deduced from the simple
resistive-divider formula :

and Rb has a constant value. Furthermore, using the results published in [7] and [8], we determine s, c and Cp as
function of the temperature.
At the initial time t = 0, the distribution of the temperature follows a Gaussian profile in the radial direction with
a maximum value on the axis of the discharge T0 (4000 K < T0 < 6000 K). The initial size of the radius, defined by
rp, corresponds to the width of the Gaussian function (T(t = 0, rp) = 0.5T0). The temperature matches 300 K at the
boundary of the domain:

The atmospheric DC discharge is simulated with a length L about 47 mm and an initial radius rp of 1.5 mm.
Additionally, calculations were carried out for initial axis temperature T0 = 5500 K. The ballasted resistor Rb is
14.92 kW, as the experimental value, whereas the initial value of the power supply voltage is given by the electrical
measurement of 4400 V according to the steady value for Ip = 250 mA.
Results
Time-evolution of the arc discharge is first calculated in the case where a power supply delivers a constant voltage
V0 to the plasma and the ballast resistor Rb connected in series. It is striking to observe, in figure 3, the collapse of the
computed current Ip(t) and temperature T(r =0, t) on the axis, showing that the arc cannot be permanently sustained in
this configuration but that it extinguishes in time duration shorter than 1.7 ms. These numerical results are comparable
to an experiment which was also performed within similar conditions, but by using this time a standard rectified high
voltage generator. In that configuration the device only included a high voltage transformer loaded by a diode bridge
and a capacitor. It was then noticed that the use of a non-electronically regulated power-supply ballasted by such low
resistor leads to series of recurrents sparks.
Moreover, the simulation is also performed by introducing a numerical model of the electronic feedback loop
amplifier to drive the output voltage V0. The current command being fixed to the reference value Ic = 250 mA, the
figure 3 shows too the dramatic effect of the electronic regulation on the maintenance of the discharge.

FIGURE 3. Evolution of the current Ip (blue) and the temperature T on the axis (red) when the current regulation is off (solid
line) and on (broken line), for an initial axis temperature T0=5500K.
CONCLUSION
A electrical discharge at atmospheric pressure-air is observed. This low-current discharge presents a startling stability.
We tried then to expose that the regulation device based upon feedback loop acting on the current via the voltage
delivered by the generator can prevent the plasma to turn off, so dynamically stabilizing the discharge. To analyze this
discharge, we use a classical model for plasma simulation, known as time-dependent Elenbaas-Heller equation. The
simulation of the arc discharge thus developed illustrates very well the dramatic effect of the electronic regulation on
the maintenance of the discharge.
ACKNOWLEDGMENTS
The author’s wish to thank M. Teboul and M. Uberti, from the Technix Society, for their help to simulate the closed
loop for the current regulation on the power supply.
REFERENCES
1. E. E. Kunhardt, IEE Trans. Plasma Sci., 28, pp. 189, 2000
2. A-A. H. Mohamed, R. Block and K. H. Schoenbach, IEE Trans. Plasma Sci., 30, pp. 182, 2002
3. Y. Akishev and al., J. Phys. D : Appl. Phys., 34, 18, pp. 2875, 2001
4. Z. Machala, C. O. Laux, C. H. Kruger and G. V. Candler, 42nd Aerospace Sciences Meeting and Exhibit (Reno, Nevada) 2004
5. G. Coduti, “Etude de l’interaction d’une onde électromagnétique avec un plasma d’air”, Orsay, Ph. D. of Paris XI, 2005
6. M. S. Benilov and G. V. Naidis, J. Phys. D: Appl. Phys., 36, pp. 1834, 2003
7. K. Raznjevic, Handbook of Thermodynamic Tables, edited by Begell House, 1995
8. J. M. Yos, Transport Properties of Nitrogen, Hydrogen, Oxygen and Air to 30000oK, edited by Wilmington, Massasuchett,1963

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