ERCIM News No.44 - January 2001 [contents]

Pattern Formation in Electric Discharges

by Ute Ebert

If a material that normally does not conduct electricity, is exposed to strong electric fields, it can develop complex patterns of conducting areas, through which it ‘discharges’ the field. A group at CWI studies both fundamental and applied aspects of such patterns, in particular in so-called streamer and barrier discharges. The results can be used for combustion gas cleaning, ultrafast power semiconductor switches or for flat computer screens. 

Electric discharges (sparks) appear on a variety of length scales: in nature between a cloud and the ground (Figure 1 shows man-made lightning across about one meter), in the sparkplug of a car engine, or in computer chips. Sparks or their precursors, the so-called streamers, are also used for, eg, combustion gas cleaning (see Figure 2), or water purification. Streamer-like discharges in doped layered semiconductors can be used for ultrafast switching of high power electric circuits.

figure1 figure2

figure3Stationary discharges are also possible, the best known example being the neon tube. Since a discharge is a nonlinear process that easily can form patterns, the homogeneous and stationary glow of the neon tube is by no means trivial, and stays a continued challenge in the development of new energy saving and special purpose light sources, eg, at Philips. Figure 3 shows generic instabilities that can occur in such glow discharges. Particular effort is presently devoted to the development of so-called plasma display panels: flat and bright computer or TV screens operating essentially like an array of rapid, microscopic neon tubes.

The enormous increase of electric conductivity in a discharge is due to the multiplication of free charge carriers by an approximately local ionization reaction. It persists as long as the local electric field is high enough. However, conducting matter can redistribute its space charges and hence modify the externally applied electric field. Depending on the spatial distribution of the ionized areas, the ionization reaction then is enhanced at some places and suppressed at others. This nonlinear dynamical coupling of ionization and electric field accounts for the spatio-temporal patterns observed in discharge experiments. In some applications like combustion gas processing or spark plugs, pattern formation is the operating mode, while in others like light sources or ultrafast semiconductor switches, the onset of pattern formation limits the range of applicability.

There is a surprising universality in the set of partial differential equations describing discharge phenomena in different materials. They are of comparable simplicity and generality as, eg, the Navier-Stokes-equation in hydrodynamics. Nevertheless, despite the enormous economical importance of discharge technologies, very little is known about basic solutions of the fundamental equations. However, recent developments in the theory of nonlinear partial differential equations and nonlinear dynamics promise that progress can be made in unravelling these features.

At CWI the basic laws of propagation of the ionized streamer channels - that can be seen in Figure 2, and that have preceeded and determined the spark in Figure 1 - are studied analytically and numerically. A basic insight is a strong mathematical analogy to patterns formed in viscous fingering or in the growth of crystals from undercooled melts. Another study concerns ultrafast high-power semiconductor switches that operate in a streamer-like manner. Applications are found in radar and laser technology, for example a possible new generation of GaAs pulsed lasers. This is a collaboration with the Ioffe-Institute in St. Petersburg that is internationally leading in the production of these switches, and is headed by Nobel laureate Z.A. Alferov who received the prize for the invention of the semiconductor GaAs laser last fall. A third project concerns the basic instabilities in barrier discharges as in Figure 3. Barrier discharges consist of a sandwich structure of electrode, resistive layer, glow discharge and electrode, driven by dc or ac voltage. The mechanism of pattern formation is only partially understood, and we work on quantitative predictions of its onset and structure. Here mathematical analogies, eg, with temperature driven convection in fluids or with chemical systems are exploited.

Please contact:
Ute Ebert - CWI
Tel: +31 20 592 4206
E-mail: Ute.Ebert@cwi.nl