The k spectrum of ionospheric irregularities

Dimensional analysis is applied to the E × B gradient drift plasma instability, which appears to be responsible for various ionospheric irregularities (e.g., type 2 irregularities in the equatorial E region) in which the perturbations first develop at long wavelengths and then cascade down to smaller scale sizes. We find that the power spectrum must be of the form f(k LN, Vd/kDa, θ)k−1 where k is the wave number, LN is the density gradient length, Vd is the electron drift velocity relative to the ions, Da is the ambipolar diffusion coefficient, and θ describes the direction of k relative to Vd. This implies, for example, that if the spectrum is proportional to Vd², as is apparently the case for the equatorial type 2 irregularities, the spectrum must decrease with k at least as fast as k−3.