Multiple scales in streamer discharges, with an emphasis on moving boundary approximations

Abstract

Streamer discharges determine the very first stage of sparks or lightning, and they govern the evolution of huge sprite discharges above thunderclouds as well as the operation of corona reactors in plasma technology. Streamers are nonlinear structures with multiple inner scales. After briefly reviewing basic observations, experiments and the microphysics, we start from density models for streamers, i.e. from reaction-drift-diffusion equations for charged-particle densities coupled to the Poisson equation of electrostatics, and focus on derivation and solution of moving boundary approximations for the density models. We recall that so-called negative streamers are linearly stable against branching (and we conjecture this for positive streamers as well), and that streamer groups in two dimensions are well approximated by the classical Saffman-Taylor finger of two fluid flow. We draw conclusions on streamer physics, and we identify open problems in the moving boundary approximations.

Nanosecond pulsed sliding dielectric barrier discharge plasma actuator for airflow control: Electrical, optical, and mechanical characteristics

“…This is in agreement with simulated investigation about streamers propagation over a dielectric surface observed in Ref. 40, where ionized species and charges are concentrated on the ionized front. From t ¼ 18 ns to 38 ns, secondary thin ionization channels corresponding to a corona-like regime occur at the electrode edge during the falling part of the pulsed voltage.…”

Sprites identification and their spatial distributions in JEM-GLIMS nadir observations

“…Studies on the sprite generation mechanisms have thus far shown great progress (Pasko et al 1997(Pasko et al , 1998Ebert et al 2006Ebert et al , 2011Liu and Pasko 2006;Luque et al 2007;Pasko 2010;Luque and Ebert 2012). However, the physical parameters that determine the horizontal distributions of sprites, i.e., the occurrence conditions, are not fully understood.…”

Saffman-Taylor fingers with kinetic undercooling

“…[32]). Streamers are finger-shaped electrical discharges which occur during the early stages of electric breakdown in sparks or lightning, for example.…”

“…The result is Laplace's equation for the electrostatic potential outside the interface. For the case in which there is a periodic array of two-dimensional streamers with equal spacing, all propagating in thex direction with a constant electric field E --x i in the far field as X -» oo, one can impose Neumann conditions to isolate a single streamer [32][33][34], Under this periodic geometry, if the electric field or periodic spacing is sufficiently small (strong interaction between neighboring streamers), the streamers evolve from their initial conditions to a traveling wave profile, so they propagate uniformly. The approximate model is then given by Eqs.…”

“…A further relevant discussion is contained in Ref. [32], Here the kinetic undercooling parameter c is proposed to account for the thickness of the ionization front. In the present paper, we shall employ the language of Hele-Shaw flows but keep in mind the application of streamers, discussing the relevance of the analysis and results in Sec.…”