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Research on Pattern Formation in 1D Dielectric-Barrier Discharges

Dr. Matthew Walhout

Summer Students

1998  Jon Niehof
1999  Jaclyn Guikema and Nathan Miller
2000  Mason Klein and Nathan Miller
2001  Mason Klein
2002  Mason Klein

Funding from Calvin College, Research Corporation, and the National Science Foundation (Grants NSF-PHYS-9876679 and NSF-PHYS-0140135)

Publications:
M. Klein*, N. Miller*, and M. Walhout, "Time-resolved imaging of spatiotemporal patterns in a one-dimensional dielectric-barrier discharge system," Phys. Rev. E, 64, 026402 (2001)

J. Guikema*, N. Miller*, J. Niehof*, M. Klein*, and M. Walhout. "Spontaneous pattern formation in an effectively one-dimensional dielectric-barrier discharge system," Phys. Rev. Lett. 85, 3817 (2000)

Senior Research Projects

2001-2002  Mason Klein (Computational Modeling of DBD Patterns)

What is a dielectric-barrier discharge?
Dielectric-barrier discharges (DBD’s) comprise a specific class of high-voltage, ac, gaseous discharges that typically operate in the near-atmospheric pressure range.  Their defining feature is the presence of dielectric layers that make it impossible for charges generated in the gas to reach the conducting electrode surfaces.  With each half-cycle of the driving oscillation, the voltage applied across the gas exceeds that required for breakdown, and the formation of narrow discharge filaments initiates the conduction of electrons toward the more positive electrode.  As charge accumulates on the dielectric layer(s) at the end(s) of each filament, the voltage drop across the filament is reduced until it falls below the discharge-sustaining level, whereupon the discharge is extinguished.  The low charge mobility on the dielectric not only contributes to this self-arresting of filaments but also limits the lateral region over which the gap voltage is diminished, thereby allowing parallel filaments to form in close proximity to one another.  Thus, the entire gas-filled space between parallel electrodes can become, on average, uniformly covered by transient discharge filaments, each roughly 0.1 mm in diameter and lasting only about 10 ns.

The DBD’s unique combination of non-equilibrium and quasi-continuous behavior has provided the basis for a broad range of applications and fundamental studies.  Its use in industrial ozone reactors has generated interest in optimizing conditions for specific chemical reactions.  To this end, experimental DBD studies have explored different gas mixtures, electrical characteristics, and geometries [1-3].  Related work has focused on maximizing the ultraviolet radiation from excimer molecules produced in DBD’s [4-6].  Several groups have modeled single-filament dynamics in order to account for the many two- and three-body reactions involving electrons, ions, neutral atoms, and photons [7-10].  These efforts have been moderately successful in explaining and predicting the chemical and radiative properties of various DBD systems.  On another research front, it has been seen that the transverse spatial distribution of discharge filaments in 2D, parallel-plate DBD’s can take the form of stable, large-scale patterns reminiscent of those associated with magnetic domains or Rayleigh-Bénard convection [11-14].  These patterns have been modeled with some success using methods that apply generally to pattern formation in nonlinear dynamical systems [15-17].  Thus, the dynamical interactions between filaments, as well as the chemical and electronic interactions within filaments, have proven interesting.

Experimental Setup
Our discharge cell is a 30-cm-long, cylindrical glass tube with inner diameter 2.0 mm and outer diameter 7.5 mm.  Stripes of silver paint, 3 mm in width, are applied on diametrically opposite portions of the outer surface.  In order to prevent sparking around the outside of the cell, we enclose the discharge tube and electrodes in a larger glass tube and fill the annular space with insulating transformer oil.  The electrodes extend through rubber seals at opposite ends of the tube, providing the contacts across which a sinusoidally varying high voltage is applied.  The 1-kHz-to-20-kHz signal is derived from a function generator, fed through a 2 kW audio amplifier, and then stepped up with a high-voltage transformer.  Adjustable balance valves on either side of the tube provide precise control over the rate and direction of mixed gas flow through the discharge region.

SCHEMATIC DIAGRAM:


 

PHOTO OF SETUP:


Owing to the curvature of the inner surface of the tube, our DBD is tightly constrained in one lateral dimension and supports purely 1D patterns along the tube’s length.  Having chosen a tube with an inner radius smaller than the characteristic size of a discharge footprint (ie. patch of deposited surface charge), we observe a suppression of any filaments that are not localized to the electrode axis.  Thus, we call this an effectively 1D system.

We use two diagnostic tools in the present experiments.  First, a camera and computerized image- acquisition system allow us to record pictures of the discharge and to analyze the digitized frames. Second, the circuit shown below allows us to monitor the voltage across the tube (V = Vosin(2pi*ft)) and the voltage across a series capacitor (Vc), the latter being proportional to the charge (Q) stored on the electrodes.  In the voltage range below breakdown, a Vc-vs-V oscilloscope trace (or QV plot [10]) falls along a line with slope proportional to the capacitance of the discharge tube. With a discharge running, the jumps in Q corresponding to distinct discharge stages cause the trace to take on an open, sliver-like shape.  As will be seen below, these jumps help us understand the DBD pattern-formation dynamics.

Results
With a 2:1 mix of He and Ar, interesting spatial structures appear as Vo is increased. The images below were taken with a color digital camera.  Stationary (repeating) filaments are seen as bright, vertical stripes that widen at the tube wall.  The patterns formed by these stationary filaments are of three distinct kinds, which we give the following names:  Type A patterns appearing in the general range of 450 V < Vo < 610 V and exhibiting narrow filaments with relatively wide separations;Type B patterns (610 V < Vo < 940 V), with narrow filaments separated by roughly half of the typical Type A spacing; and Type C patterns (980 V < Vo < 1200 V), characterized by alternating bright, wide filaments and dim, narrow filaments.

Type A (450 V < Vo < 610 V)

 

Type B (610 V < Vo < 940 V)

 

Type C (980 V < Vo < 1200 V)

 

Spatial disorder (Vo > 1200 V)

In the voltage range between 940 V and 980 V, individual filaments strike randomly at apparently uncorrelated positions.  This type of behavior, also seen for Vo > 1250 V, is suggestive of spatiotemporal chaos.  Such a characterization must be qualified by the time-resolved Vc data shown below.  In plots a-c, sharp steps in Vc reveal that discharge types A, B and C are associated, respectively, with the presence of 1, 2 and 3 distinct discharge stages in each voltage half-cycle.  However, for conditions producing spatial disorder on time scales down to the half-cycle, all but one or two of the Vc steps disappear and discharges occur over an extended interval during each half-cycle (plot d).  The disappearance of Vc steps indicates that an abrupt increase in temporal disorder accompanies the transition to spatial disorder.

            Top:  Replica of the driving voltage signal.
            (a)  Vo = 500 V; one discharge stage per half-cycle; Type A patterns produced in tube.
            (b) Vo = 630 V; two discharge stages per half-cycle; Type B patterns produced in tube.
            (c) Vo = 980 V; three discharge stages per half-cycle; Type C patterns produced in tube.
            (d) Vo = 1380 V; structure of  discharge stages is lost (partially at least); spatially disordered discharge.

After measuring the average filament spacing (lambda) for a wide range of Vo settings, we obtained the following graph:

 

Discussion
To begin to understand the observed patterns, we would like to answer the following questions:

1.  Why do filaments remain stationary?
2.  What competing effects are at equilibrium when a stable pattern is formed?
3.  What destabilizes each pattern when Vo reaches the transition value?

We're actually still working on all of these questions, we have some answers to 1 and 2:

 

Explanation for transition from Type A pattern to Type B pattern

   The following sequence of pictures shows what we think happens in the system
    as Vo is increased.


 
 

References
[1] B. Eliasson and U. Kogelschatz, IEEE Trans. Plasma Sci. 19, 309 (1991).
[2] B. Eliasson and U. Kogelschatz, IEEE Trans. Plasma Sci. 19, 1063 (1991)
[3] D. Braun, U. Kuchler and G. Pietsch, J. Phys. D:  Appl. Phys. 24, 564 (1991).
[4] B. Gellert and U. Kogelschatz, Appl. Phys. B 52, 14 (1991).
[5] K. Stockwald and M. Neiger, Contrib. Plasma Phys. 35, 15 (1995).
[6] J-Y. Zhang and I.W. Boyd, J. Appl. Phys. 80, 633 (1996).
[7] S. Yagi and M. Tanaka, J. Phys. D:  Appl. Phys. 12, 1509 (1979).
[8] B. Eliasson, M. Hirth and U. Kogelschatz, J. Phys. D: Appl. Phys. 20, 1421 (1987).
[9] W. Sun, B. Pashaie, S. Dhali and F.I. Honea, J. Appl. Phys. 79, 3438 (1996).
[10] Z. Falkenstein and J.J. Coogan, J. Phys. D:  Appl. Phys. 30, 817 (1997).
[11] D. G. Boyers and W.A. Tiller, Appl. Phys. Lett. 41, 28 (1982).
[12] E. Ammelt, D. Schweng and H.-G. Purwins, Phys. Lett. A 179, 348 (1993).
[13] Y. A. Astrov, E. Ammelt and H.-G. Purwins, Phys. Rev. Lett. 78, 3129 (1997).
[14] Y. A. Astrov, I. Muller, E. Ammelt and H.-G. Purwins, Phys. Rev. Lett. 80, 5341 (1998).
[15] M.C. Cross and P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).
[16] C.P. Schenk, M. Or-Guil, M. Bode, and H.-G. Purwins, Phys. Rev. Lett. 78, 3781 (1997).
[17] I. Brauer, C. Punset, H.-G. Purwins and J.P. Boeuf, J. Appl. Phys. 85, 7569 (1999).

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