Electromagnetism in a strongly stratified plasma showing an unexpected effect of the Debye shielding

In the literature, we found 15 references showing, without exception, that the sunspot photospheric magnetic field vertical gradient is on the order of 3–4 G/km, with field strength decreasing with height, whereas the horizontal gradient is nine times weaker, on the order of 0.4–0.5 G/km. This is confirmed by our recent THÉMIS observations. As a consequence, the vanishing of div B → is not realized, and the present paper is devoted to the investigation of this problem. We point out that the photosphere is a strongly stratified plasma, having different horizontal and vertical characteristic lengths of aspect ratio 1/9 as the different terms contributing to the observed div B → . The velocities are also anisotropic under the stratification effect. As a consequence, the Debye volume is a flattened sphere. We show that in this case div B → may mathematically depart from zero. Anisotropic shielding constitutes an alternative to the existence of monopoles for being responsible for non-zero div B → . We evaluate that the solar corona is conversely not a strongly stratified plasma, so that the conditions are very different there.