On the streamer propagation in methane plasma discharges

The initial stages of formation and propagation of a streamer in methane at atmospheric pressure were studied using a 2-dimensional axial symmetric hydrodynamic model. The model is based on the drift diffusion approximation and exploits electron transport parameters determined using an external Boltzmann equation solver. The resulting system of equations was solved using the finite element methods and integrated in time with an Euler backward algorithm. An approach useful to alleviate the numerical difficulties determined by the steep gradients that appear on the streamer front was developed. It is based on a proper choice of the adaptation algorithm of the integration time step. Three phases in the streamer development could be identified, in agreement with analytical and numerical models reported in the literature: ionization avalanche, streamer, and shielded plasma. The properties of the three phases have been characterized analyzing the evolution in time of the most important variables characterizing the system (ion and electron densities, potential, and electric field). Finally, the influence of some operative parameters, such as inter-electrodic gap, seed electron density, and applied potential, has been investigated in order to determine how it affects the evolution of the micro-discharge, and in particular, the transition from ionization avalanche to streamer.