A k‐space integral equation is derived that describes the propagation of electromagnetic waves induced by an external source of charge or current in a magnetized plasma (B=B0ẑ) having an arbitrary density variation in the x̂ direction. The nonlocal k‐space dielectric tensor kernel is derived keeping finite ion Larmor radius ρi corrections to all orders without the use of an expansion in the inverse density gradient scale length LN so that the effect of a strongly inhomogeneous plasma density profile (LN≊ρi) on wave propagation in the ion cyclotron range of frequencies can be studied. The integral equation is solved numerically in the electrostatic limit to study the capacitive excitation of ion Bernstein waves for frequencies near the second harmonic of the ion cyclotron frequency (ω≊2Ωi). The spectrum of weakly damped eigenmodes for a plasma having a large region of uniform density and a highly nonuniform edge is found to consist of numerous ‘‘uniform plasma’’ modes and an electrostatic drift mode that propagates only in the edge region. Asymmetries in the radial structure of these modes, which arise from the diamagnetic drift of particles in the plasma edge, result in an asymmetric distribution of wave energy launched in the directions parallel and antiparallel to the diamagnetic current. The surface electrostatic drift mode is found to be the dominant mode of oscillation as the wave frequency approaches the second harmonic of the ion cyclotron frequency.

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