{
  "abstract": "We develop a fully relativistic extension of the energy-conserving, unstaggered electromagnetic-potential particle-in-cell method introduced in our earlier nonrelativistic work. As in the nonrelativistic generalized-momentum formulation, the fields are advanced by a Crank--Nicolson discretization of the Lorenz-gauge potential equations, the current is deposited from particle orbits, and charge is advanced through the discrete continuity equation. The new ingredient is a generalized-momentum adaptation of the Higuera--Cary relativistic particle pusher. The vector-potential force is decomposed into an orbit-discrete-gradient part, which enforces the same finite-difference chain rule used in our earlier nonrelativistic formulation, and a skew part, which generates a Higuera--Cary magnetic rotation in mechanical momentum. For prescribed fields and frozen orbit data, this generalized-momentum Higuera--Cary map is a unit-Jacobian conjugacy of the mechanical Higuera--Cary map and preserves particle phase volume in $(\\xx,\\PP)$. For the fully coupled implicit step, the same orbit data define the current deposit, mesh-to-particle gather, vector-potential chain rule, and relativistic kinetic-energy secant velocity. The resulting particle work cancels the Crank--Nicolson field-energy balance, yielding exact relativistic total-energy conservation up to nonlinear solver tolerance, orbit-quadrature error, and roundoff. A self-adjoint Fourier projection removes modes on even-grid Nyquist planes while preserving the particle--grid work identity. Numerical tests are organized around cold relativistic two-stream and Weibel/filamentation instabilities, with diagnostics for energy drift, Gauss's law, the Lorenz gauge, particle--grid work, and the orbit chain rule.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36383",
  "author_total": 3,
  "authors": [
    {
      "name": "Andrew Christlieb"
    },
    {
      "name": "Luis Chacon"
    },
    {
      "name": "Sining Gong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57d9smff6gmeh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36383",
  "fulltext_url": null,
  "id": "57d9smff6gmeh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36383",
  "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",
      "astro-ph.HE"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7214989890",
  "pdf_url": "https://arxiv.org/pdf/2609.36383",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57d9smff6gmeh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36383",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36383"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An Energy-Conserving Unstaggered Electromagnetic-Potential Particle-in-Cell Method, Part II: Fully Relativistic Formulation with an Adapted Higuera--Cary Pusher",
  "title_text": "An Energy-Conserving Unstaggered Electromagnetic-Potential Particle-in-Cell Method, Part II: Fully Relativistic Formulation with an Adapted Higuera--Cary Pusher",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/57d9smff6gmeh",
  "venue": "arXiv",
  "versions": []
}