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

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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

[EQUATION]

and, in what follows, we shall assume [FORMULA], i.e. we consider a y-invariant, potential magnetic field contained in the xz plane. Then,

[EQUATION]

i.e.

[EQUATION]

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

[EQUATION]

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

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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