The electromagnetic modes of a helical resonator

Abstract

The electric fields of the helical resonator, both of the fundamental frequency and the odd harmonics up to the eleventh, have been probed using metallic copper and heavily doped Si:P disks by measuring the relative frequency shift Δf/f and the change in quality factor Δ(1/Q) with a network analyzer after insertion of the disk as a probe mounted on a dielectric support rod which could be translated along the z axis of the helix with a micrometer drive. The magnetic field component Hz was probed using the paramagnetic free radical DPPH and a simple transmission electron spin resonance (ESR) spectrometer. The Δf/f results were compared with calculated results using the Bethe–Schwinger expression and the plasma result for the change in dielectric response, while the Δ(1/Q) results were compared with a standard loss expression. The results, except for the role of the short but including the metallic disk thickness and diameter dependence, agree with the fields given by Pierce for an infinite helical current sheet, when adapted to the standing wave form. The ESR results demonstrate the optimum position for a paramagnetic sample. The ESR amplitude versus probe insertion depth is in qualitative agreement with an expression by Wilmshurst et al., but also exhibits an unexplained sign change.