Electronegative plasma equilibria with spatially varying ionization

Electronegative inductive discharges in higher pressure ranges typically exhibit strongly localized ionization near the coil structure, with decay of the electron temperature and ionization into the central discharge region. We use a two-dimensional (2D) fluid code with a chlorine feedstock gas to determine the spatial profiles of the particle densities and electron temperature in a cylindrical transformer-coupled plasma device excited by a stove-top coil on top of the plasma chamber. To compare with one-dimensional (1D) analytical models, the 2D results are area-averaged over the radius. The area-averaged ionization frequency νiz is found to decay exponentially away from the coils, allowing the ansatz of an exponentially decaying axial variation for νiz to be used in a 1D numerical model. The 1D model captures the main features of the axial variations of the area-averaged 2D fluid simulation, indicating that the main diffusion mechanisms act along the axial direction. A simple analytical global discharge model is also developed, accounting for the asymmetric density and ionization profiles. The global model gives the scalings of the ion densities and electron temperature with power and pressure. The 1D and global models are compared with the 2D fluid simulations, showing reasonable agreement.