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A theoretical and experimental investigation is made of a wave resonator based on the concept of wave reflection along the confinement magnetic field at a spatial location where the wave frequency matches the local value of the ion-ion hybrid frequency. Such a situation can be realized by shear Alfvén waves in a magnetized plasma with two ion species because this mode has zero parallel group velocity and experiences a cut-off at the ion-ion hybrid frequency. Since the ion-ion hybrid frequency is proportional to the magnetic field, it is expected that a magnetic well configuration in a two-ion plasma can result in an Alfvén wave resonator. Such a concept has been proposed in various space plasma studies and could have relevance to mirror and tokamak fusion devices. This study demonstrates such a resonator in a controlled laboratory experiment using a H+-He+ mixture. The resonator response is investigated by launching monochromatic waves and impulses from a magnetic loop antenna. The observed frequency spectra are found to agree with predictions of a theoretical model of trapped eigenmodes. [ABSTRACT FROM AUTHOR]