A free-electron laser (FEL) two-beam accelerator (TBA) is proposed, in which the FEL interaction takes place in a series of drive cavities, rather than in a waveguide. Each drive cavity is "beat-coupled" to a section of the accelerating structure. This standing-wave TBA is investigated theoretically and numerically, with analyses included of microwave extraction, growth of the FEL signal through saturation, equilibrium longitudinal beam dynamics following saturation, and sensitivity of the microwave amplitude and phase to errors in current and energy. It is found that phase errors due to current jitter are substantially reduced from previous versions of the TBA. Analytic scalings and numerical simulations are used to obtain an illustrative TBA parameter set.