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An experimental research is being conducted at the Yale University Beam Physics Laboratory, aiming to confirm fundamental aspects of an as-yet untested two-beam collinear electron accelerator concept employing a detuned bimodal cavity structure. The features of this novel beam-driven accelerator concept include (i) interleaving of bunches of the low-current accelerated beam with bunches of the high-current drive beam, while both beams move along the same central axis in the structure; (ii) excitation by the drive beam of two modes of each cavity in the structure, with the frequency of the higher mode equal to three times the frequency of the fundamental TM010mode; and (iii) detuning of the cavity modes away from the frequency of the accelerated and drive beam bunches, and their third harmonic. Advantages that are anticipated from this approach include (a) operation at higher acceleration gradient with lower breakdown and pulsed heating rates than for a structure of single-mode cavities at the same acceleration gradient, due to the unconventional spatiotemporal field distributions in the bimodal cavities; (b) realization of a transformer ratio well above two, due to the detuning of the cavity modes; and (c) greater system simplicity and lower cost than for a two-beam accelerator with separate drive and accelerated beam-lines. The recent R&D; progress is presented.