In this paper the problem of ideal magnetohydrodynamic equilibria with mass flow is treated. Under the assumption of general symmetry (i.e. one ignorable spatial coordinate) we derive a generalized Grad-Shafranov equation in an unspecified curvilinear coordinate system. If incompressibility is assumed an elliptical equation is derived and a new, totally analytical method of solution is proposed. This is based on a particular selfsimilar separation of the variables in the unknown flux function and leads to an ordinary, non-linear differential equation for the profile of the magnetic and flow surfaces. Three novel classes of solutions are derived in different geometries, all being flexible (they contain a minimum of three free functions) and regular, which makes them suitable for astrophysical applications. These are flows in magnetic flux tubes with non-circular section, flows in magnetic arcades above the solar surface and collimated, axisymmetric outflows.
Exact solutions for symmetric magnetohydrodynamic equilibria with mass flow / L. DEL ZANNA; C. CHIUDERI. - In: ASTRONOMY & ASTROPHYSICS. - ISSN 0004-6361. - STAMPA. - 310:(1996), pp. 341-350. [2-s2.0-0001045644]
Exact solutions for symmetric magnetohydrodynamic equilibria with mass flow
DEL ZANNA, LUCA;CHIUDERI, CLAUDIO
1996
Abstract
In this paper the problem of ideal magnetohydrodynamic equilibria with mass flow is treated. Under the assumption of general symmetry (i.e. one ignorable spatial coordinate) we derive a generalized Grad-Shafranov equation in an unspecified curvilinear coordinate system. If incompressibility is assumed an elliptical equation is derived and a new, totally analytical method of solution is proposed. This is based on a particular selfsimilar separation of the variables in the unknown flux function and leads to an ordinary, non-linear differential equation for the profile of the magnetic and flow surfaces. Three novel classes of solutions are derived in different geometries, all being flexible (they contain a minimum of three free functions) and regular, which makes them suitable for astrophysical applications. These are flows in magnetic flux tubes with non-circular section, flows in magnetic arcades above the solar surface and collimated, axisymmetric outflows.File | Dimensione | Formato | |
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