Dielectric breakdown patterns and active walker model

Abstract

Pattern formation is one of the central problems of nonlinear sciences. In particular, patterns observed in dielectric breakdown ~DB! are of immense interest. The DB process is a highly nonlinear phenomenon. During this process many variables such as the material contents, environmental temperature and pressures, as well as the electric field distribution are changing interactively. All these variables will determine where the next breakdown is going to happen. The system is one of the so-called complex systems @1#. Kuchinski @2# and Suehle and Chaparala @3# elucidated the microscopic mechanisms for DB in many situations. Experimental observations and theoretical modeling of the DB patterns have also been studied by a number of authors @4–9#. The configuration of electrodes employed in most of these works is of the needle-plate type. The electric field distribution is not uniform and changes with the development of DB pattern in this configuration. On the other hand, simulations have been carried out for both local critical field effect and nonlinear polarizability effect. Nonetheless, in all of these simulations, the electric field needs to be recalculated at each step of the simulations @4–7#. We have previously studied experimentally the DB patterns with electrodes configured as in a parallel-plates capacitor @10,11#. The dielectric liquid is inserted in between the electrodes. In this configuration, the electric field between the electrodes is essentially perpendicular to the pattern plane. The field distribution is always uniform. We have shown that the track patterns left on the electrodes after DB can be categorized qualitatively as either ‘‘dense and winding,’’ ‘‘radial,’’ or ‘‘radial center with dense and winding tips.’’ For convenience, we call them type I, type II, and type III patterns, respectively. Typical patterns for these three types are shown in Fig. 1. Significantly, these patterns are similar to those created by other groups in the works mentioned above. This suggests that the field distribution may not be the direct factor for the pattern formations in DB. There could be a more general and fundamental mechanism to explain the patterns obtained. In this paper we show that it is possible to reconstruct our experimental results @10,11# by simulation using the active walker model ~AWM!. The AWM is a commonly used tool to model a complex system such as DB. The micromechanisms for the observed DB patterns are assumed to be the ‘‘thermal effect and active material depletion effect.’’ The