Scientific investigation of plasma phenomena can be undertaken through either experiments, or numerical and analytical modelling, for which there are a number of well-established options. Global models are quick to implement and have low computation cost, but approximate bulk values. Fluid models can take days to solve, but provide spatial profiles.
This work details a different type of model, analytically similar to fluid models, but computationally closer to a global model, and able to give spatially resolved solutions for the challenging environment of electronegative plasmas. Equations are derived to describe the time averaged spatial profiles of densities, fluxes, and temperatures. Through extended analytical work and normalisations, the resulting differential equations can be solved with an initial value type integration scheme. This is found to be hundreds of times faster than boundary value type methods.
Results and trends are analysed for a symmetrical capacitively coupled oxygen plasma, and relationships between properties are found to conform to the existing knowledge. The behaviour of the system is found to change depending on whether or not the self-interaction of charged species is significant compared to the interaction with the neutrals.
Results from the semi-analytical model agree well with a significantly more detailed and computationally intensive fluid model. In addition to the bulk spatial profiles agreeing both qualitatively and quantitatively, the values of other measured plasma properties agree over a range of system pressures and powers. This comparison is demonstrated to be favourable when contrasted with the results of a global model.
The dynamics of the neutral gas are found to be an important consideration for plasma densities greater than around one part per million. In this model the frictional forces from fast moving ions and thermal energy transfer from hot electrons are the leading cause of disturbance to the neutral properties.
