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- Modelling self-organization on electrodes of DC glow dischargesPublication . Bieniek, Matthew Simon; Benilov, Mikhail; Almeida, Pedro Jorge Gomes Camacho deO trabalho apresentado nesta dissertaªo refere-se modelaªo de padrıes de autoorganizaªo de densidade de corrente em elØtrodos de descargas DC luminescentes. Padrıes de manchas andicas foram modelados de forma auto-consistente pela primeira vez e os fenmenos nas manchas foram investigados. As soluıes que descrevem as manchas foram encontradas num intervalo de correntes com mœltiplas soluıes. Foi descoberta uma inversªo da densidade de corrente local do nodo no centro de cada uma das manchas, isto Ø, mini-cÆtodos sªo formados dentro das manchas; poder-se-ia dizer, as manchas do nodo funcionam como uma descarga luminescente unipolar. As soluıes nªo se enquadram no padrªo convencional de auto-organizaªo em sistemas dissipativos nªo-lineares biestÆveis; por exemplo, as transiıes de um modo para outro nªo se realizam atravØs de bifurcaıes. Padrıes auto-organizados de manchas catdicas em descargas luminescentes foram modelados na camada de plasma junto ao cÆtodo, numa geometria igual utilizada na maioria das experiŒncias descritas na literatura. O efeito da geometria da cmara de descarga nas manchas foi investigado. Os padrıes de manchas modelados sªo idŒnticos aos observados nas experiŒncias e similares aos calculados na conguraªo de elØtrodos planos em paralelo. Uma tentativa foi feita para modelar quantitativamente a descarga DC luminescente com manchas catdicas. Uma descriªo detalhada desta modelaªo, a mais precisa deste fenmeno atØ data, Ø apresentada. Em geral, os padrıes calculados sªo semelhantes aos observados nas experiŒncias, mas as CVC sªo qualitativamente diferentes. CenÆrios de transiıes entre modos com diferentes padrıes de manchas em elØtrodos de descargas DC luminescentes e em cÆtodos de descargas de arco sªo investigados. No caso de transiıes entre padrıes em cÆtodos de descargas DC luminescentes, foram encontradas as transiıes observadas nas experiŒncias que podem estar diretamente relacionados a bifurcaıes de soluıes estacionÆrias, e as bifurcaıes correspondentes foram modeladas. Os padrıes encontrados na modelaªo numØrica estªo em conformidade com os observados no decurso das transiıes nas experiŒncias. No caso dos cÆtodos de descargas de arco, mostra-se que qualquer transiªo entre diferentes modos de transferŒncia de corrente estÆ relacionada a uma bifurcaªo de soluıes estacionÆrias.
- Self-consistent modeling of self-organized patterns of spots on anodes of DC glow dischargesPublication . Bieniek, M. S.; Almeida, P. G. C.; Benilov, M. S.Abstract Self-organized patterns of spots on a flat metallic anode in a cylindrical glow discharge tube are simulated. A standard model of glow discharges is used, comprising conservation and transport equations for a single species of ion and electrons, written with the use of the drift-diffusion and local-field approximations, and the Poisson equation. Only processes in the near-anode region are considered and the computation domain is the region between the anode and the discharge column. Multiple solutions, existing in the same range of discharge current and describing modes with and without anode spots, are computed for the first time. A reversal of the local anode current density in the spots was found, i.e. mini-cathodes are formed inside the spots or, as one could say, anode spots operate as a unipolar glow discharge. The solutions do not fit into the conventional pattern of self-organization in bistable nonlinear dissipative systems; In particular, the modes are not joined by bifurcations.
- Modelling cathode spots in glow discharges in the cathode boundary layer geometryPublication . Bieniek, M. S.; Almeida, P. G. C.; Benilov, M. S.Self-organized patterns of cathode spots in glow discharges are computed in the cathode boundary layer geometry, which is the one employed in most of the experiments reported in the literature. The model comprises conservation and transport equations of electrons and a single ion species, written in the drift-diffusion and local-field approximations, and Poisson’s equation. Multiple solutions existing for the same value of the discharge current and describing modes with different configurations of cathode spots are computed by means of a stationary solver. The computed solutions are compared to their counterparts for plane-parallel electrodes, and experiments. All of the computed spot patterns have been observed in the experiment.
- Bifurcations in the theory of current transfer to cathodes of dc discharges and observations of transitions between different modesPublication . Bieniek, M. S.; Santos, D.; Almeida, P. G. C.; Benilov, M. S.General scenarios of transitions between different spot patterns on electrodes of dc gas discharges and their relation to bifurcations of steady-state solutions are analyzed. In the case of cathodes of arc discharges, it is shown that any transition between different modes of current transfer is related to a bifurcation of steady-state solutions. In particular, transitions between diffuse and spot modes on axially symmetric cathodes, frequently observed in the experiment, represent an indication of the presence of pitchfork or fold bifurcations of steady-state solutions. Experimental observations of transitions on cathodes of dc glow microdischarges are analyzed and those potentially related to bifurcations of steady-state solutions are identified. The relevant bifurcations are investigated numerically and the computed patterns are found to conform to those observed in the course of the corresponding transitions in the experiment.