The dispersion and matching characteristics of the helical resonator plasma source

The dispersion characteristics and the fields of a helical resonator are obtained. The coil is approximated by a helical current layer with infinite conductivity along the current direction (a “sheath helix”). The plasma column is modeled as a cylindrical dielectric in which the dielectric losses can be neglected in determining the propagation properties of the resonator. Assuming the plasma losses are known, the model can be used to study the matching of the helical resonator to an external power source which is connected to the helix by a tap. The resonator is modeled as a parallel connection of two transmission line segments on each side of the tap position. We determine the efficiency of power transfer to the resonator as a function of the tap position driving frequency, and plasma loading. We find that whereas for a small plasma loading it is possible to achieve perfect matching, there exists a critical value of plasma loading beyond which a perfect match is no longer possible