Astrophysics and Space Science

, Volume 145, Issue 2, pp 277–286 | Cite as

A class of semi-analytical solutions for a rotating toroidal plasma

  • A. H. Khater
  • M. G. El Sheikh
  • D. K. Callebaut


In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P s andf2 are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.


Entropy Differential Equation Partial Differential Equation Rectangular Cross Section Quadratic Polynomial 
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Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • A. H. Khater
    • 1
  • M. G. El Sheikh
    • 2
  • D. K. Callebaut
    • 3
  1. 1.Mathematics Department, Faculty of ScienceCairo UniversityBeni-SuefEgypt
  2. 2.Mathematics Department, Faculty of ScienceAin Shams UniversityCairoEgypt
  3. 3.Physics DepartmentUniversity of Antwerp (U.I.A.)AntwerpBelgium

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