{
  "id": "1907.06403",
  "version": "v1",
  "published": "2019-07-15T09:54:59.000Z",
  "updated": "2019-07-15T09:54:59.000Z",
  "title": "Optimal Control of a Hot Plasma",
  "authors": [
    "Jörg Weber"
  ],
  "categories": [
    "math-ph",
    "math.MP",
    "math.OC",
    "physics.plasm-ph"
  ],
  "abstract": "The time evolution of a collisionless plasma is modeled by the relativistic Vlasov-Maxwell system which couples the Vlasov equation (the transport equation) with the Maxwell equations of electrodynamics. We consider the case that the plasma is located in a bounded container $\\Omega\\subset\\mathbb R^3$, for example a fusion reactor. Furthermore, there are external currents, typically in the exterior of the container, that may serve as a control of the plasma if adjusted suitably. We model objects, that are placed in space, via given matrix-valued functions $\\varepsilon$ (the permittivity) and $\\mu$ (the permeability). A typical aim in fusion plasma physics is to keep the amount of particles hitting $\\partial\\Omega$ as small as possible (since they damage the reactor wall), while the control costs should not be too exhaustive (to ensure efficiency). This leads to a minimizing problem with a PDE constraint. This problem is analyzed in detail. In particular, we prove existence of minimizers and establish an approach to derive first order optimality conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-15T09:54:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q61",
      "35Q83",
      "49J20",
      "82D10"
    ],
    "keywords": [
      "optimal control",
      "hot plasma",
      "derive first order optimality conditions",
      "fusion plasma physics",
      "relativistic vlasov-maxwell system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}