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Nonlinear periodic solutions for isothermal magnetostatic atmospheres

Published online by Cambridge University Press:  01 November 2006

A. H. Khater
Affiliation:
Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt email: [email protected] Departement Natuurkunde, CGB, University of Antwerp (UA), B-2020 Antwerp, Belgium email: [email protected]
D. K. Callebaut
Affiliation:
Departement Natuurkunde, CGB, University of Antwerp (UA), B-2020 Antwerp, Belgium email: [email protected]
E. S. Kamel
Affiliation:
Mathematics Department, Faculty of Science, Fayoum University, Fayoum, Egypt
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Abstract

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Magnetohydrodynamic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic partial differential equation for the magnetic potential A, known as the Grad-Shafranov equation. Specifying the arbitrary functions in the latter equation, one gets a nonlinear elliptic partial differential equation (the sinh Poisson equation). Analytical solutions of this equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained by using the tanh method, and are adequate for describing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium in a uniform gravitational field.

Type
Contributed Papers
Copyright
© 2006 International Astronomical Union