The magnetosphere and ionosphere are coupled by field-aligned currents that remove or deposit E-region electrons. Changes in electron number density modify ionospheric reflectivity, hence altering the magnetospheric current. Thus, self-consistent solutions are nontrivial. In this paper, we present 1-D steady states that self-consistently model modifications of ionospheric plasma density by field-aligned currents. These are used to investigate the width broadening and minimum plasma density of E-region plasma density cavities and the origin of small-scale features observed in downward current channels. A plasma density cavity forms and broadens if the maximum initial current density j parallel to(0) exceeds j(c) = alpha n(e)(2)he/(1 + 1/beta), where alpha is the recombination coefficient, n(e) is the equilibrium E-region number density in the absence of currents, h is the E-region thickness, and beta = Sigma(P0)/Sigma(A) is the initial ratio of Pedersen to magnetospheric Alfven conductivities. If a plasma density cavity forms, its final width increases monotonically with W = 2B(0)/mu(0)V(A)alpha(e)(n)2he, where B(0) is the background magnetic field strength and V(A) is the magnetospheric Alfven speed. The minimum E-region number density, and the finest length scale present in the steady state, both scale as 1/b. For typical ionospheric parameters and j(parallel to 0) = 5 mu Am(-2), the fine scale is comparable to or less than 6 lambda(e) for beta greater than or similar to 2, where lambda(e) is the electron inertial length. This suggests that electron inertial effects may become significant and introduce small-scale features, following the production of a single fine scale by depletion and broadening.