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Astron. Astrophys. 330, 726-738 (1998)

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2. Physical model

A plasma generally exhibits both collective (fluid-like) and individual (particle-like) behaviour. In the MHD model, the plasma is treated as a conducting fluid having macroscopic parameters that accurately describe its particle-like interactions. The magnetohydrodynamic equations represent the coupling of the fluid dynamic equations with Maxwell's equations of electrodynamics with the displacement current and the separation between ions and electrons being neglected.

In the solar corona the plasma- [FORMULA] is much smaller than unity. Consequently, the gas pressure term can be neglected and the coronal plasma can be described by a simpler form of the MHD equations, which comprise the mass continuity equation,

[EQUATION]

the momentum equation,

[EQUATION]

the induction equation,

[EQUATION]

and the divergence-free equation,

[EQUATION]

Here [FORMULA] is the gas density, [FORMULA] is the plasma velocity, [FORMULA] is the magnetic field, and [FORMULA] is the permeability of the plasma.

The above equations are solved in a cartesian coordinate system [FORMULA] in which the x -axis is directed horizontally along the solar surface and the z -axis is vertical. In what follows, we assume that y is an ignorable coordinate, i. e. [FORMULA], and that the y -component of the flow ([FORMULA]) and the magnetic field ([FORMULA]) are identically zero. This assumption removes the Alfvén wave from the system. Moreover, as the cold plasma approximation removes the slow wave, the system (1)-(4) then describes fast magnetosonic waves.

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© European Southern Observatory (ESO) 1998

Online publication: January 16, 1998
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