Astron. Astrophys. 337, 887-896 (1998)

2. Model

To search the properties of an equivalent LRC-circuit of a current-carrying magnetic loop we consider a coronal loop with footpoits imbedded into the photosphere and formed by the converging flow of photospheric plasma. Such a situation can arise, for instance, when the loop footpoints are located in the nodes of several supergranulation cells. An electric circuit analog of such a loop consists of three main domains (Fig. 1).

Fig. 1. An electric circuit analog of current-carrying loop. The loop legs locate at the nodes of several supergranulation cells. In region 1, located in the photosphere, electron-atom collision frequency is less compared to the electron gyrofrequency whereas ion-atom collision frequency prevails over the ion gyrofrequency. Both the electric current and the magnetic field grow here, caused by the converging flows of photospheric plasma. Region 2 is the coronal part of a loop. Here 1 and the electric current flows along the magnetic field lines. We suppose that deep in the photosphere (region 3) where 1 the current flowing through the coronal part of a loop closes between legs

In region 1, located in the photosphere, the magnetic field and therefore the electric current are generated. In this region the following inequalities are satisfied:

where and are the electron and ion gyrofrequencies, and are `effective' frequencies for electron-atom and ion-atom collisions, respectively, related with collision frequencies (index o) by

Such conditions are thought to excite the radial electric field due to the charge imbalance, which together with the initial magnetic field generates the Hall current in the azimuthal direction and which, in turn, leads to the increase of (Sen & White 1972). The magnetic field grows up to the value when the field enhancement caused by the converging flow is compensated by the magnetic field diffusion due to the plasma conductivity. As a result a steady-state flux tube is formed with the magnetic field determined by the total energy input of the convective flux during the time of tube formation (of the order /, where is the supergranular scale and is the horizontal velocity of a convective flux). The radius of the flux tube depends on the magnetic field diffusion rate which is due to the conductivity.

Region 2 presents the coronal part of the magnetic loop. Plasma has here , and the magnetic field is force-free, e.g., the electric currents are parallel to the magnetic field lines.

Region 3 is located probably in the photosphere between the loop footpoints. This is the region of the current closure in an equivalent electric circuit. The photospheric current distribution derived from the magnetograph measurements (see, e.g., Hagyard 1989, Leka et al. 1993) favours an interpretation in terms of an un-neutralized coronal current pattern (Melrose 1991). These data suggest that the magnetic flux tubes carry a current that flows through the coronal part of a loop from one footpoint to the other with no evidence for a return current through the corona. This current must be close along a return path below the photosphere where the magnetic field is not necessarily force-free, and cross-field current can flow along a path of minimum electric resistance, rather that along the magnetic field lines (Hudson 1987, Melrose 1991). There appears to be no theory for how such an un-neutralized current closes below the photosphere.

However, as a first approximation we can assume that the region in the photosphere where this current closes, corresponds to the condition /8. The last condition is satisfied by a tube with a magnetic field B = 1000 G, and temperature T = 610³ K if the number density n = 510¹⁶ cm^-3, which corresponds to the level 1.

© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998
helpdesk.link@springer.de