This paper presents a broad research to understand the self-generated field enhancement at the head of the discharge channel, growing streamers and branching concepts. They discuss the several types of streamers observed in nature such as lightning and sprite discharges. The comprehensive photographs obtained with ICCD in nanoscale provide the propagation pattern clearly. Since the streamers carry highly energetic electrons, there are many different applications emerging in the areas of deposition, chemical processing or gas convection. In the paper, the physical mechanisms behind the streamer formation are evaluated in detail to proceed a full-scale computational model. Some arguments are included to the model. In the regions with high electric field, electrons and ions are produced. Those electrons move with drift velocity and diffuse. The applied electric field is distorted by the space charges.
The electron and ion densities are solved coupled with electric field. Townsend’s first constant is the characteristic scale for ionization cross section and field strength. In the model, ions are considered to be stable while electrons are diffusing. Non-dimensionalization is conducted and it is observed that the ionization is in the order of 10^14 cm^-3. The scaling relations are used to compare the laboratory test and the natural events like sprites. The model shows the change in the net charge density, equipotential lines and electric field strength as time passed. The space charges are covered by a thin layer. The reasonable enhanced field is detected with this formation although the streamer begins its propagation right after the electron avalanche at the cathode. The streamers can be investigated with the interior and exterior regions which have different electron densities. The fluctuations in density can be one of the causes of the streamer formation in high pressures. The ionization takes place when there are free electrons and the electric field is higher than a limit. Ionization is explored in a moving boundary by solving velocity which is equal to electron drift velocity in larger electric fields. The new boundary conditions are adapted to solve the continuity for the interior and exterior regions. They believe that the branching of a streamer results from the Laplacian instability between those two regions. The other outcome of this prediction is that charge fluctuations does not need to be present to observe branching but a space charge layer is required. On the other hand, charge conservation and streamer width should be considered for the DBD models.
As a conclusion, this article describes the streamer formation, the regions inside and outside the thin layer of a streamer and the streamer branching. The model is revised by including a Laplacian instability and a moving ionization boundary.
Reference: Ebert, Ute, Carolynne Montijn, T. M. P. Briels, Willem Hundsdorfer, Bernard Meulenbroek, A. Rocco, and E. M. Van Veldhuizen. “The multiscale nature of streamers.” Plasma Sources Science and Technology 15, no. 2 (2006): S118.
Course: AME 60637
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