Townsand had described the DC discharge characteristics which follow well in low pressure system. Few publications are also there for dynamic modelling of this discharge at low pressure. I mean voltage dynamics with change in current. However, I didn't have any information about such modelling done for atmospheric pressure DBD in air.
There are some papers by Panousis (J. Phys. D: Appl. Phys. 39 (2006) 2140–2150) where a model is described.
The DBD model is not very complex and reproduces quite well experimental values. From electrical point of view, the DBD can be considered the combination of two elements, the plasma and a parallel capacitor. Therefore what you can do is to model a 0D plasma with an equation for a circuit including a power supply, an optional resistance, a capacitor and the plasma current. The plasma current should be determined considering the chemical kinetics to calculate electron density, and the Boltzmann equation (or simplified approaches) to calculate the electron mobility.
This simple model is quite accurate and can describe the features of the DBD in different conditions, depending on how much the electric field is above the breakdown threshold.
What do you mean by dynamic model? In my opinion dynamic model means the description of the time evolution of plasma current and voltage. In this sense the model is dynamic. Together with a time dependent circuit equation, you have a time dependent kinetic equation of the plasma. In any time step you can calculate I(t), V(t) or better E(T) and so on.
There are other possibilities, such as using a Particle in Cell code to model DBD, describing the variation of the charge density in time. In this case the plasma chemistry is considered a secondary effect.
In principle I agree with an answer of Gianpiero Colonna, DBD is not a too complex phenomenon, but in fact, in is not so easy, because apriori you do not know plasma extension and its density to estimate its resistance and capacity. To do this one have to model the dynamics of DBD evolution, and you can find this procedure in out works
1. Soloviev V R, Konchakov A M, Krivtsov V M, Aleksandrov N L, 2008, Numerical Simulation of a Surface Barrier Discharge in Air Plasma Physics Reports, 34, 594-608
2.Soloviev V R, Krivtsov V M, 2009, Surface barrier discharge modeling for aerodynamic applications J. Phys. D: Appl. Phys 42 125208
Thanks Soloviev for the references. I will go through it and get back to you.
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