{
  "id": "astro-ph/0011548",
  "version": "v2",
  "published": "2000-11-29T17:28:23.000Z",
  "updated": "2001-04-23T14:32:38.000Z",
  "title": "Conservation of Magnetic Helicity and Its Constraint on $α$-Effect of Dynamo Theory",
  "authors": [
    "Hongsong Chou",
    "George B. Field"
  ],
  "comment": "31 pages, 5 figures, submitted to ApJ",
  "categories": [
    "astro-ph"
  ],
  "abstract": "Dynamical studies of MHD turbulence on the one hand, and arguments based upon magnetic helicity on the other, have yielded seemingly contradictory estimates for the $\\alpha$ parameter in turbulent dynamo theory. Here we show, with direct numerical simulation of three-dimensional magnetohydrodynamic turbulence with a mean magnetic field, $\\OB$, that the constraint on the dynamo $\\alpha$-effect set by the magnetic helicity is time-dependent. A time-scale $t_c$ is introduced such that for $t<t_c$, the $\\alpha$-coefficient calculated from the simulation is close to the result of Pouquet et al and Field et al, $-\\frac{\\tau_{cor}}{3}(< \\v \\cdot \\nabla \\times \\v > - < \\b \\cdot \\nabla \\times \\b >)$; for $t>t_c$, the classical result of the $\\alpha$-coefficient given by the Mean-Field Electrodynamics is reduced by a factor of $1/({R_m |\\OB|^2/v_{rms}^2})$, as argued by Gruzinov & Diamond, Seehafer and Cattaneo & Hughes. Here, $R_m$ is the magnetic Reynolds number, $v_{rms}$ the rms velocity of the turbulence, $\\tau_{cor}$ the correlation time of the turbulence, and $\\overline B$ is in velocity unit. The applicability of and connection between different models of dynamo theory are also discussed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-04-23T14:32:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magnetic helicity",
      "constraint",
      "conservation",
      "magnetic reynolds number",
      "turbulent dynamo theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 548858,
      "adsabs": "2000astro.ph.11548C"
    }
  }
}