{
  "id": "oai:papers.qnfo.org:geometric-selection-of-stable-helical-wave-modes-on-a-toroidal-domain",
  "slug": "geometric-selection-of-stable-helical-wave-modes-on-a-toroidal-domain",
  "title": "Geometric Selection of Stable Helical Wave Modes on a Toroidal Domain",
  "authors": [
    "Rowan Brad Quni-Gudzinas"
  ],
  "abstract": "Tokamak magnetic field lines, toroidal microwave resonators, and toroidal waveguides all suffer from mode instability that forces costly redesigns or limits operational performance. Existing stability criteria rely on material parameters, plasma profiles, or detailed numerical eigenmode simulations, and no purely geometric predictor of which helical modes persist has been established. We derive a quantization condition for scalar and electromagnetic waves confined to a toroidal boundary by enforcing constructive interference separately around the toroidal (major) and poloidal (minor) cycles. The condition reduces to a rational winding requirement, $R/a = m/n$, where R and a are the major and minor radii and (m,n) are positive integers. For an assumed torus with R = 0.50 m and a = 0.10 m the smallest admissible pair is $(m,n) = (5,1)$, giving wavenumber k = 10 rad·m^-1 and electromagnetic frequency f ≈ 4.77 × 10⁸ Hz. With an assumed manufacturing tolerance of ± 0.5\\% on both radii, the projected frequency uncertainty is Δ f ≈ 2.4 × 10⁶ Hz. If validated, the rule lets designers of fusion devices, resonators, and waveguides guarantee mode stability from geometry alone, before any material-specific simulation or prototype is committed.",
  "abstract_markdown": "Tokamak magnetic field lines, toroidal microwave resonators, and toroidal waveguides all suffer from mode instability that forces costly redesigns or limits operational performance. Existing stability criteria rely on material parameters, plasma profiles, or detailed numerical eigenmode simulations, and no purely geometric predictor of which helical modes persist has been established. We derive a quantization condition for scalar and electromagnetic waves confined to a toroidal boundary by enforcing constructive interference separately around the toroidal (major) and poloidal (minor) cycles. The condition reduces to a rational winding requirement, $R/a = m/n$, where $R$ and $a$ are the major and minor radii and $(m,n)$ are positive integers. For an assumed torus with $R = 0.50\\;\\text{m}$ and $a = 0.10\\;\\text{m}$ the smallest admissible pair is $(m,n) = (5,1)$, giving wavenumber $k = 10\\;\\text{rad·m}^{-1}$ and electromagnetic frequency $f \\approx 4.77 \\times 10^{8}\\;\\text{Hz}$. With an assumed manufacturing tolerance of $\\pm 0.5\\%$ on both radii, the projected frequency uncertainty is $\\Delta f \\approx 2.4 \\times 10^{6}\\;\\text{Hz}$. If validated, the rule lets designers of fusion devices, resonators, and waveguides guarantee mode stability from geometry alone, before any material-specific simulation or prototype is committed.",
  "date": "2026-11-02",
  "first_published": "2026-11-02",
  "last_revised": "2026-11-02T00:00:00Z",
  "modified": "2026-11-02T00:00:00Z",
  "version": "1.0.0",
  "version_count": 1,
  "language": "en",
  "keywords": [],
  "quality_tags": [
    "High-quality scholarly research",
    "open-access scholarly work",
    "versioned research publication"
  ],
  "quality_label": "High-quality scholarly research",
  "quality_basis": "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
  "quality_evidence_url": "https://qnfo.org/about",
  "peer_review_status": "Not independently peer-reviewed",
  "resource_type": "ScholarlyArticle",
  "doi": null,
  "doi_url": null,
  "url": "https://papers.qnfo.org/papers/geometric-selection-of-stable-helical-wave-modes-on-a-toroidal-domain",
  "license_url": "https://legal.qnfo.org/",
  "license_spdx": null,
  "sha256": "f7476c773dcfdf991556da0c6bcb49cfa50a2c22433eebfa6c1cd51d1c526f02",
  "version_url": "https://papers.qnfo.org/papers/geometric-selection-of-stable-helical-wave-modes-on-a-toroidal-domain/v/1.0.0",
  "datacite": {
    "schemaVersion": "http://datacite.org/schema/kernel-4",
    "identifiers": [
      {
        "identifier": "https://papers.qnfo.org/papers/geometric-selection-of-stable-helical-wave-modes-on-a-toroidal-domain",
        "identifierType": "URL"
      }
    ],
    "creators": [
      {
        "name": "Rowan Brad Quni-Gudzinas",
        "nameType": "Personal",
        "nameIdentifiers": [
          {
            "nameIdentifier": "https://orcid.org/0009-0002-4317-5604",
            "nameIdentifierScheme": "ORCID",
            "schemeUri": "https://orcid.org"
          }
        ]
      }
    ],
    "titles": [
      {
        "title": "Geometric Selection of Stable Helical Wave Modes on a Toroidal Domain"
      }
    ],
    "publisher": "QNFO",
    "publicationYear": "2026",
    "resourceType": {
      "resourceTypeGeneral": "Text",
      "resourceType": "ScholarlyArticle"
    },
    "subjects": [
      {
        "subject": "High-quality scholarly research",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "open-access scholarly work",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      },
      {
        "subject": "versioned research publication",
        "subjectScheme": "QNFO publisher classification",
        "schemeUri": "https://qnfo.org/about"
      }
    ],
    "dates": [
      {
        "date": "2026-11-02",
        "dateType": "Issued"
      },
      {
        "date": "2026-11-02",
        "dateType": "Updated"
      }
    ],
    "language": "en",
    "version": "1.0.0",
    "rightsList": [
      {
        "rightsUri": "https://legal.qnfo.org/"
      }
    ],
    "descriptions": [
      {
        "description": "Tokamak magnetic field lines, toroidal microwave resonators, and toroidal waveguides all suffer from mode instability that forces costly redesigns or limits operational performance. Existing stability criteria rely on material parameters, plasma profiles, or detailed numerical eigenmode simulations, and no purely geometric predictor of which helical modes persist has been established. We derive a quantization condition for scalar and electromagnetic waves confined to a toroidal boundary by enforcing constructive interference separately around the toroidal (major) and poloidal (minor) cycles. The condition reduces to a rational winding requirement, $R/a = m/n$, where R and a are the major and minor radii and (m,n) are positive integers. For an assumed torus with R = 0.50 m and a = 0.10 m the smallest admissible pair is $(m,n) = (5,1)$, giving wavenumber k = 10 rad·m^-1 and electromagnetic frequency f ≈ 4.77 × 10⁸ Hz. With an assumed manufacturing tolerance of ± 0.5\\% on both radii, the projected frequency uncertainty is Δ f ≈ 2.4 × 10⁶ Hz. If validated, the rule lets designers of fusion devices, resonators, and waveguides guarantee mode stability from geometry alone, before any material-specific simulation or prototype is committed.",
        "descriptionType": "Abstract"
      },
      {
        "description": "Publisher quality classification: High-quality scholarly research. QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review.",
        "descriptionType": "Other"
      },
      {
        "description": "Peer review status: Not independently peer-reviewed",
        "descriptionType": "Other"
      }
    ],
    "formats": [
      "text/html"
    ]
  }
}