Abstract We investigate the ionospheric feedback instability (IFI) driven by a finite‐duration localized source of inertial Alfvén waves. Wave‐excited conductance perturbations undergo Pedersen mobility drift in the convection and wave electric fields and are amplified. A causal Green’s‐function formulation is derived for a height‐integrated ionospheric sheet coupled to an inertial Alfvén cavity with upper‐boundary reflection. For a finite‐width source, temporal growth becomes convective amplification. The relative phase slip between the returning wave and conductance perturbation provides an a posteriori coherence timescale for evaluating the finite‐source gain. The gain is controlled by time‐integrated feedback drive minus upper‐boundary leakage and ionospheric relaxation. The complex root of the closed dispersion relation determines the wave frequency, growth rate, and packet speed. In one example, the peak field‐aligned current is several times the forced‐only value. Observability depends on phase coherence, losses, transverse escape, and instrumental sampling.