Model of periodic filament formation in laterally coupled gas discharges

A one-dimensional reaction-diffusion model was used to study periodic filament formation in a laterally coupled gas discharge. Our results demonstrate three types of pattern formation (localized solitary filaments, small oscillation and intermediate), which deform into one another subject to a control parameter θ(ψa/pd) and a boundary condition (where pd is the pressure-distance and ψa is the applied voltage). The work shows the same qualitative dependence as the experimental work of Guikema et al (2000 Phys. Rev. Lett. 85 3817)