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

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3. Boundary conditions and solutions

To solve Eq. [FORMULA], we first Fourier transform it in x, which gives

[EQUATION]

where the Fourier transform [FORMULA] is defined by

[EQUATION]

The solution to Eq. [FORMULA] that satisfies the mentioned boundary conditions now follows as

[EQUATION]

where [FORMULA] is the Fourier transform of the boundary condition [FORMULA],

[EQUATION]

Finally, [FORMULA] is obtained by applying the inverse Fourier transform to [FORMULA] given by Eq. [FORMULA],

[EQUATION]

The magnetic field components [FORMULA] and [FORMULA] easily follow from this expression and Eq. [FORMULA],

[EQUATION]

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© European Southern Observatory (ESO) 1999

Online publication: November 3, 1999
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