We consider the electromagnetic field produced by an azimuthal current of arbitrary shape, external to a plasma. In particular, we study absorption of the field energy by a radially inhomogeneous plasma cylinder with double ioncyclotron resonance. We calculate the power absorbed by plasma ions for an arbitrary ion distribution function. We show that, in some regions of the plasma it is possible for the work done by the field on the currents to be negative. We also show that, if the plasma has regions with a large density gradient (e.g. a narrow transitional plasma-vacuum layer), power absorption increases sharply. We consider, too, the exciting of the natural oscillations of the cylinder by external currents. In this case, power absorption is independant of the dissipative properties of the plasma.