Nonlinear periodic solutions for isothermal magnetostatic atmospheres

Khater, A. H.; Callebaut, D. K.; Kamel, E. S.
December 2008
Physics of Plasmas;Dec2008, Vol. 15 Issue 12, p122903
Academic Journal
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 equation for the magnetic potential A, known as the Grad–Shafranov equation. Specifying the arbitrary functions in the latter equation, one obtains three types of nonlinear elliptic equations (a Liouville equation, a sinh Poisson equation, and a generalization of those with a sum of exponentials). Analytical solutions are obtained using the tanh method; this is elaborated in the Appendix. The solutions are adequate to describe an isothermal atmosphere in a uniform gravitational field showing parallel filaments of diffuse, magnetized plasma suspended horizontally in equilibrium.


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