A theory is developed to describe quantitatively the idea that in an ionized gas subject to an imposed magnetic field, such as the ionosphere, the lines of magnetic flux are approximately equipotential lines. The ionosphere is assumed to be horizontally stratified, and the case in which the earth's magnetic field is vertical is considered. Small-scale electrostatic fields are studied with a view towards elucidating the phenomena of spread F and radio star scintillation.
The analysis indicates that in the ionosphere the results are strongly affected by the variation of conductivity with height, as well as by the anisotropy. For a reasonable model of the ionosphere it is shown that it is possible, under certain conditions, for a horizontal field three kilometers or larger in extent, at a height of about 120 or more kilometers, to produce a similar, localized electric field in the F region, not appreciably reduced in strength. The height of the source is the most important factor, but the temperature and ionization-density profiles are also significant. The fact that the strength of the small-scale fields in the F region could vary by one or two powers of 10 for plausible diurnal variations of the ionospheric parameters suggests that these fields could perhaps be responsible for the puzzling diurnal behavior of spread F and radio star scintillation.