Magnetic induction and plasma impedance in a planar inductive discharge

For a planar inductive discharge the magnetic induction components B-r(r, z) and B-z(r, z), the electric field component E-theta(r, z) and the plasma current are calculated from first principles assuming axisymmetric geometry. The mutual inductance M between the primary and secondary circuit, the self-inductance L-2 of the plasma and the impedance of the plasma are determined theoretically and related to the properties of the plasma. A global (volume-averaged) discharge model is applied to relate the electron and ion densities and the electron temperature in an argon plasma to the neutral gas pressure and power in the pressure range 2-60 mTorr. The planar inductive discharge is medalled as a transformer with the inductive coil taken as the primary circuit and the plasma as the secondary circuit to find the impedance characteristics in the primary circuit due to the plasma load and the capacitive coupling between the coil and the plasma. The model calculations are compared to measured impedance, rf current and rf voltage, showing fair agreement.