In this paper we investigate how the parameters of the ionosphere and the low-altitude magnetosphere mediate the formation and spatiotemporal properties of small-scale, intense electromagnetic structures commonly observed by low-altitude satellites in the auroral and subauroral magnetosphere. The study is based on numerical modeling of a time-evolving, nonlinear system that describes multiscale electrodynamics of the magnetosphere-ionosphere coupled system in terms of field-aligned currents, both quasi-static and Alfv¿nic. Simulations show that intense electric fields and currents with a perpendicular size of 10--20 km at 120 km altitude can be generated by a large-scale, slowly evolving current system interacting with a weakly conducting ionosphere, even without a resonant cavity in the magnetosphere. These structures form in the strong gradient in the ionospheric conductivity that develops at the boundary between the large-scale upward and downward currents when the background ionospheric Pedersen conductivity, ΣP, is low but higher than the Alfv¿n conductivity, ΣA = 1/¿0vA, above the ionosphere. When ΣP ≈ ΣA the ionosphere can generate electromagnetic waves with perpendicular sizes less than 10 km. These waves can be trapped inside the cavity of the classical ionospheric Alfv¿n resonator, and their amplitude can be significantly amplified there by the ionospheric feedback instability.