A New Approach to the Force-Free Field and Its Application to the Mag- netic Field of Solar Active Regions
Abstract
We study the force-free magnetic field which defines the equilibrium of a magnetoplasma through the equation rot B = α(x)B when the magnetic force dominates other forces. The implication of current-free and force-free magnetic fields is re-discussed in terms of the variational principles, and a correct variational problem suitable for the force-free field is set up and solved by a direct method known as the finite-element method. Examples of calculation show that the motion of the footpoints of the field lines feeds the energy into the tube of force. The stored amount of energy, however, depends on whether or not the magnetic field is strong enough at its weakest part along the tube so that the work done against the magnetic force by the motion of footpoints can become large. The value of α(x) calculated in our solution varies in space and even changes its sign from place to place even in a simple geometry. The conventional constant-α model is thus found to be a very particular model which is very unlikely to be realized in an active region. The possibility of applying the present method to the energy build-up process of solar flares is discussed.
- Publication:
-
Publications of the Astronomical Society of Japan
- Pub Date:
- 1979
- Bibcode:
- 1979PASJ...31..209S