Reformulation of gas discharge theory using data from ICPS and helicons

Summary form only given. Experimental data from Inductively Coupled Plasmas (ICPs) have shown that uniform or centrally peaked density profiles n(r) can be produced with antennas on the circumference with no elements near the axis, even though the skin depth is much smaller than the discharge radius. Many attempts to explain this Anomalous Skin Effect using kinetic theory for electron thermal penetration have failed to reproduce the data. We have previously suggested that the nonlinear Lorentz force, coupled with cylindrical walls, can explain this¹. Here we find an even simpler mechanism occurring in steady-state equilibrium. The key is to implement the Simon short-circuit effect2, which, in discharges with intermediate length-to-radius ratios, causes the electrons to follow the Boltzmann relation relating the potential to the logarithm of n(r). We show that this happens even in a magnetic field, which is why hollow n(r)´s are not observed in helicon discharges. The resulting radial electric field drives ions to the cylindrical wall, while the electrons escape through the sheaths at the end walls. Surprisingly, with proper scaling, the n(r)´s in all discharges are self-similar: flat or centrally peaked. Discharges differ only in the nonlinear v-Vv term in the ion fluid equation of motion, a term depending only on the ratio of charge exchange collision to ionization probabilities. A program EQM has been made to calculate profiles including neutral depletion and ionization balance. The presheath is automatically calculated. For helicon discharges the HELIC program³ calculates the power absorption profile for given n, Te, and neutral profiles. EQM and HELIC are then iterated to give exact solutions with consistent profiles. Power balance using the Vahedi curve⁴ yields the absolute value of n, in agreement with measurements, with no adjustable parameters. This work has been submitted .