Numerical model for the determination of the reduced electric field in a CO₂ microwave plasma derived by the principle of impedance matching

Three dimensional electromagnetic modelling of a free-standing CO₂ microwave plasma has been performed, by describing the plasma as a dielectric medium. The relative permittivity and conductivity of the medium are parametrised. The waveguide geometry from the experiment, including the tuner, is put into the model, knowing that this corresponds to maximum power transfer of the microwave generator to the plasma under plasma impedance matching conditions. Two CO₂ plasma discharge regimes, differing mainly in pressure, input power and temperature, have been studied. The model's validity has been checked through study of materials of known conductivity. From measurements of the neutral gas temperature and the plasma electron density profile, the reduced electric field is determined. From the parametrisation of the dielectric properties, a range for the effective electron-neutral collision frequency for momentum transfer is estimated. The results for the reduced electric field and the range of the electron neutral collision frequency obtained, are consistent as verified by simulations using BOLSIG+. In addition, from this comparison it is possible to narrow down the range of the collision frequencies, and to estimate the electron temperature. The reduced electric field lies between 80 and 180 Td for the relatively low pressure, low input power, the so-called 'diffuse' regime. For the relatively high pressure, high input power ('contracted') regime it lies between 10 and 60 Td. The normalised collision frequency lies between 1.6 and 2.3 for the diffuse regime, while for the contracted regime it lies between 2 and 3. The electron temperature ranges from 2 to 3 eV for the diffuse regime, and from 0.5 to 1 eV for the contracted regime.