{
  "abstract": "Accurate magnetic-field evaluation on and near current-carrying surfaces is a recurring computational bottleneck in magnetic-confinement fusion. As targets approach the source surface, Biot--Savart and virtual-casing kernels become singular, causing standard Gauss--Legendre and upsampled trapezoidal quadratures to lose accuracy. We introduce AMPERe, a quadrature-by-expansion (QBX) evaluator for vector magnetostatic kernels on general three-dimensional, non-axisymmetric tokamak and stellarator geometries. The method develops a spherical-harmonic QBX formulation for the vector Biot--Savart and virtual-casing (Stratton--Chu) fields and expresses the resulting magnetic field as the analytic curl of a regular-solid-harmonic vector potential. This construction yields a divergence-free discrete field at every expansion order, provides analytic derivatives, and enables an a priori separation of truncation, quadrature, and geometric errors. On the rotating-ellipse benchmark of Malhotra et al. [1], QBX maintains a relative error of 2--5 x 10^{-6} throughout the near-surface regime at distance-independent cost, whereas upsampled trapezoidal quadrature exhibits O(1) errors and requires node counts scaling as (h/d)^2. AMPERe is implemented as a header-only, performance-portable Kokkos library supporting CPU and GPU backends, with target-specific and local-correction accelerations validated against the baseline. The method is further demonstrated on realistic Wendelstein 7-X configurations, including sheet-current and virtual-casing field evaluations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41544",
  "author_total": 4,
  "authors": [
    {
      "name": "H. Betar"
    },
    {
      "name": "Y. Sarazin"
    },
    {
      "name": "V. Grandgirard"
    },
    {
      "name": "D. Zarzoso"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/74brfvpp6gpha.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41544",
  "fulltext_url": null,
  "id": "74brfvpp6gpha",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41544",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.plasm-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41544",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/74brfvpp6gpha.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41544",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41544"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.plasm-ph",
      "subfield": "plasma"
    }
  ],
  "title": "AMPERe: an exactly divergence-free quadrature-by-expansion evaluator for near-surface Biot--Savart and virtual-casing fields in fusion geometries",
  "title_text": "AMPERe: an exactly divergence-free quadrature-by-expansion evaluator for near-surface Biot--Savart and virtual-casing fields in fusion geometries",
  "type": "preprint",
  "updated_at": "2026-11-03T12:20:36Z",
  "url": "https://research.draconitic.com/paper/74brfvpp6gpha",
  "venue": "arXiv",
  "versions": []
}