A force-free magnetic field configuration is a state of minimum energy under the constraint of magnetic helicity conservation. It is shown here that force-free magnetic field configurations that can be used for ball lightening can have alpha in the force-free field equation a scalar function rather than a simple constant. Such fields have been proposed to contain the plasma of ball lightning.
BALL LIGHTNING AS A NON-CONSTANT ALPHA SPHERICAL FORCE-FREE MAGNETIC FIELD PLASMOID