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Astron. Astrophys. 318, 947-956 (1997)

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2. DC electric current generation

In a non axially symmetrical geometry, electric currents can be generated in separatrices or separators of the coronal magnetic field, for example, by shear motions either parallel or perpendicular to the photospheric neutral line. For axially symmetrical magnetic fields, steady azimuthal motions can generate currents. In this case, two models of current generation are distinguished.

The first one assumes the plasma is fully ionized with infinite conductivity. Hence, the magnetic field is frozen and moves with the plasma. Consequently, the generation of an azimuthal component of the field, and subsequently of a current along the flux tube, requires a variation of the angular velocity [FORMULA] in the azimuthal plasma velocity [FORMULA] along s, the flux tube length, i.e. [FORMULA] (see Ch. 11 in Somov (1994) for a review). The current density is just derived from Ampère's law, [FORMULA]. The most acceptable location for this mechanism is below the photosphere where the plasma kinetic energy dominates over the magnetic energy. This model is widely used to explain qualitatively the generation of currents by twisting the photospheric part of magnetic loops where both feet are anchored in the deep and dense photosphere. However, it is difficult to conceive how this mechanism could generate currents in open flux tubes where the rotation of the upper part of the structure cannot be controlled by the rarified upper atmosphere. Moreover, no steady-state situation is obtained since a continuous twisting of the lines of force in the very deep photosphere leads to a continuous increase of the azimuthal [FORMULA] component of the field (Steinolfsen 1991).

In the second model presented in this paper, where currents are generated by azimuthal motions in a partially ionized atmosphere, the azimuthal velocities may be constant along the loop length. Since it is the relative azimuthal velocity between the magnetic field lines and the partially ionized atmosphere that generates currents, these currents can result either from azimuthal motions of the gas around a fixed magnetic field or from the rotation around the flux tube axis of the magnetic field imbedded in a static partially ionized atmosphere.

Assuming steady state, the azimuthal and radial components of the current density can be derived from the steady equation of fluid dynamics


The corresponding equation for the horizontal components of the forces and velocities, in a thin flux tube of constant cross section, leads to the following expressions for the azimuthal and radial current densities


where the contribution of the terms of inertia is neglected, and


Eq. (3) shows that radial current generation requires an influx of matter and angular momentum inside the flux tube. The radial current density cannot be computed without knowing the plasma radial velocity [FORMULA].

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998