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Visualization of cylindrical resonances

Brais Vila

TL;DR

The paper tackles the visualization gap for cylindrical resonators by introducing interactive JavaScript web applications that display both mode distributions and field distributions. It grounds the visualizations in the standard cylindrical resonance theory, including the frequency relation $f_{m,n,n_z} = \frac{c}{2} \sqrt{(\frac{n_z}{l})^2 + (\frac{\alpha_{mn}}{a})^2}$ with $\alpha_{mn}=x'_{mn}/\pi$, and demonstrates how mode feasibility is bounded by an elliptical region in the $(\alpha_{mn}, n_z)$ plane. Beyond teaching, the work provides design guidance (monomode vs multimode, coupling considerations) and extensions to other problems (parametric resonance, quantum-box analogies) via supplementary materials. The open-source apps enable rapid exploration for undergraduate labs and advanced research, potentially accelerating learning and development in areas ranging from acoustics to accelerator physics. Overall, the article offers a practical, visually intuitive toolkit that complements formal theory and enhances both pedagogy and resonator design practice.

Abstract

The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set of interactive web applications and citing potential use cases in the form of both academic courses and published research. These cover several branches of physics and engineering, showing that these materials can be useful for a broad audience.

Visualization of cylindrical resonances

TL;DR

The paper tackles the visualization gap for cylindrical resonators by introducing interactive JavaScript web applications that display both mode distributions and field distributions. It grounds the visualizations in the standard cylindrical resonance theory, including the frequency relation with , and demonstrates how mode feasibility is bounded by an elliptical region in the plane. Beyond teaching, the work provides design guidance (monomode vs multimode, coupling considerations) and extensions to other problems (parametric resonance, quantum-box analogies) via supplementary materials. The open-source apps enable rapid exploration for undergraduate labs and advanced research, potentially accelerating learning and development in areas ranging from acoustics to accelerator physics. Overall, the article offers a practical, visually intuitive toolkit that complements formal theory and enhances both pedagogy and resonator design practice.

Abstract

The analysis of cylindrical resonators is part of standard physics curricula but, unlike for their rectangular counterpart, their mode structure is hardly ever visualized. The aim of this work is to show a way of doing it, providing a set of interactive web applications and citing potential use cases in the form of both academic courses and published research. These cover several branches of physics and engineering, showing that these materials can be useful for a broad audience.
Paper Structure (7 sections, 2 equations, 7 figures)

This paper contains 7 sections, 2 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Visualizing the mode distribution
  3. Visualizing the field distribution
  4. Understanding coupling
  5. Designing the resonator
  6. Modifying the applications
  7. Conclusions

Figures (7)

  • Figure 1: Second longitudinal mode of a cylindrical resonator (supplement A).
  • Figure 2: Mode distribution of a cylindrical acoustic resonator (supplement B).
  • Figure 3: Electric field amplitude of the $TE_{113}$ mode (supplement D).
  • Figure 4: Rectangular waveguide feeding a cylindrical resonator.
  • Figure 5: Proposed dynamics for the experiments described in Ref. franke, where the jet exiting the outlet moves sideways as seen from the inlet, oscillating atfranke 990 Hz. The analytical value calculated with supplement B is 988 Hz.
  • ...and 2 more figures