Dungey (1956) has shown that the number densities of electrons and positive ions, under the action of turbulence and the magnetic field in the ionosphere, are closely equal—in other words the only fluctuations in electron density are those controlled electrostatically by the ions—and he has estimated the magnitude of the fluctuations. The present paper uses Dungey's model and results, reduces his equations to a single equation for electron density, in each of several cases, and then investigates the possible spectra of fluctuations. It is concluded that, in the circumstances that commonly arise, the spectrum on this model should be nearly isotropic, though exceptionally there could be a strong elongation of irregularities at right angles to the magnetic field. Thus some other mechanism is required to account for the elongation that is observed, parallel to the field.

Below 110 km, where the magnetic effect on the ions’ motion is small, and at wave-numbers in the inertial subrange of the turbulence, dimensional argument shows that the spectrum function (integrated over all directions) is proportional partly to κ−1 and partly to $\kappa^{-\frac{5}{3}$. Above 120 km the magnetic effect is large; a more detailed study shows that when turbulence is present, which probably is not often, the spectrum function in the inertial subrange is proportional to $\kappa {\frac{2}{3}$, with considerable anisotropy.