Astron. Astrophys. 351, 733-740 (1999)

2. Potential magnetic field configurations

The coronal magnetic field structure is treated in Cartesian coordinates with the z-axis in the vertical direction. All physical quantities are assumed stationary and y-invariant, so they depend on the variables x and z only.

Potential magnetic fields are characterised by

and, in what follows, we shall assume , i.e. we consider a y-invariant, potential magnetic field contained in the x, z plane. Then,

i.e.

This is just a particular case of the more general force-free solution and the expression for can be obtained from the Grad-Shafranov equation with ,

To determine the flux function in the corona () one must integrate this partial differential equation, imposing some boundary conditions. We prescribe the value of the flux function at the photospheric level, , and assume that A does not diverge as .

© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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