Ionization waves (striations) in a low-current plasma column revisited with kinetic and fluid models

Abstract

A one-dimensional Particle-In-Cell Monte Carlo Collisions (PIC-MCC) method has been used to model the development and propagation of ionization waves in neon and argon positive columns. Low current conditions are considered, i.e. conditions where stepwise ionization or Coulomb collisions are negligible (linear ionization rate). This self-consistent model describes the development of self-excited moving striations, reproduces many of the well-known experimental characteristics (wavelength, spatial resonances, potential drop over one striation, electron "bunching" effect) of the ionization waves called p, r and s waves in the literature and sheds light on their physical properties and on the mechanisms responsible for their existence. These are the first fully kinetic self-consistent simulations over a large range of conditions reproducing the development of p, r and s ionization waves. Although the spatial resonances and the detailed properties of the striations in the non-linear regime are of kinetic nature, the conditions of existence of the instability can be obtained and understood from a linear stability analysis of a three-moment set of quasi-neutral fluid equations where the electron transport coefficients are expressed as a function of electron temperature and are obtained from solutions of a 0D Boltzman equation. An essential aspect of the instability leading to the development of these striations is the non-Mawellian nature of the electron energy distribution function in the uniform electric field prior to the instability onset, resulting in an electron diffusion coefficient in space much larger than the energy diffusion coefficient.

On constriction and striation of a diffuse DBD in large gap filled with moderate pressure helium diluted by the air and easily ionized impurity

“…To date, a good understanding of the strata formation mechanisms in low-pressure discharges under conditions of nonlocality of the electron energy distribution function (EEDF) has been achieved (for details, see [48][49][50][51][52] and the literature cited therein). Under higher pressures when the fluid description of discharge processes becomes correct, it is shown the stepwise ionization of metastables or a Maxwellization of the EEDF can be responsible for the strata formation in a diffuse discharge in inert gases.…”

The principle of minimal power

“…Recent progress has been achieved by computer simulations of plasma stratification in noble gases using fluid [30,31] and hybrid [32] models and PIC simulations [33]. New implicit and coupled fluid plasma solvers enabled studies of ionization waves in diffuse and constricted discharges at relatively high plasma densities.…”

“…PIC model with periodic boundary conditions [34] allowed self-consistent simulations of moving striations in a positive column of DC discharges in argon and neon at low currents without metastable atoms and Coulomb collisions. A hybrid model [33] using a gridbased Fokker-Planck kinetic solver for electrons and a fluid model for ions enabled self-consistent simulations of standing and moving striations in argon discharges between electrodes at low currents. Standing striations in RF discharges at low plasma densities have been recently obtained in reference [34] with the same hybrid solver.…”

“…The kinetic theory of the anode region is not fully developed [49]. Both ion and electron sheaths at the anode have been experimentally observed and appeared in computer simulations of stratified discharges [32,33]. Still, the conditions for the electric field reversals and the formation of trapped electrons remain unclear.…”

Formation mechanisms of striations in a filamentary dielectric barrier discharge in atmospheric-pressure argon

“…For instance, the relaxation of electrons to spatially homogeneous state and different striation modes in collision dominated plasma normalised by pressure have been investigated using a kinetic approach [23][24][25]. Besides this, the majority of theoretical studies have been carried out for low or moderate pressure [22,[26][27][28][29][30][31][32][33][34][35][36], and fewer of them have dealt with discharges at atmospheric or sub-atmospheric pressure [8,19,21,[37][38][39][40][41]. A thorough investigation of the stratification of discharges in inert gases at low pressure (ranging from 5 mTorr to 2 Torr) has been conducted using kinetic or discrete dynamic models [22,[26][27][28][29].…”