Electrodynamics of a planar Archimedean spiral resonator

TL;DR

This paper provides a comprehensive theoretical and experimental analysis of the resonant frequencies and current distributions in a finite-length planar Archimedean spiral superconducting resonator, demonstrating simple relationships and validating with measurements.

Contribution

It introduces an analytical model for the electrodynamics of a finite-length spiral resonator, including resonance frequencies and current distributions, validated by experiments and simulations.

Findings

Resonant frequencies follow a linear relationship $f_n=f_1 n$.

Current distributions are approximately sinusoidal with respect to the squared radius.

Theoretical predictions agree well with numerical simulations and experimental measurements.

Abstract

We present a theoretical and experimental study of electrodynamics of a planar spiral superconducting resonator of a finite length. The resonator is made in the form of a monofilar Archimedean spiral. By making use of a general model of inhomogeneous alternating current flowing along the resonator and specific boundary conditions on the surface of the strip, we obtain analytically the frequencies $f_n$ of resonances which can be excited in such system. We also calculate corresponding inhomogeneous RF current distributions $\psi_n (r)$, where $r$ is the coordinate across a spiral. We show that the resonant frequencies and current distributions are well described by simple relationships $f_n=f_1 n$, and $\psi_n(r)\simeq \sin[\pi n (r/R_e)^2]$, where $n=1,2...$, and $R_e$ is the external radius of the spiral. Our analysis of electrodynamic properties of spiral resonators' is in good accord with direct numerical simulations and measurements made using specifically designed magnetic probe and laser scanning microscope.