{
  "annotation_id": "0f0f9cd7-00fd-4b23-a94f-02af35f63d3d",
  "date_created": "2026-03-02T18:01:03.476000Z",
  "date_modified": "2026-03-02T18:01:03.476000Z",
  "file_hash": "b72ea37346f2423972e5b53e6bcfca852e5d2a95481ac91a8c43d52384e1483d",
  "private": false,
  "record": {
    "abstract": "The calculation of both resistive and ideal plasma equilibria amounts to\nsolving a number of magnetic differential equations which are of the type $\\vec\n{B}\\cdot \\nabla \\Phi =s$. We apply the necessary and sufficient criterion for\nthe existence of the potential $\\Phi$ and find that a static equilibrium\nconfiguration of a magnetically confined plasma does not exist in axi-symmetric\ntoroidal geometry.",
    "arxiv_id": "physics/0510140",
    "authors": [
      "Wolfgang Engelhardt"
    ],
    "categories": [
      "physics.plasm-ph",
      "physics.class-ph"
    ],
    "title": "On the Solvability of Magnetic Differential Equations",
    "url": "https://arxiv.org/abs/physics/0510140"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "493fbc3d-6400-4899-af4e-b102449d6a6a",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}