This paper presents a new formalism which makes the analysis and understanding of both the relativistic klystron (RK) and the standing-wave free-electron laser (SWFEL) two-beam accelerator (TBA) available to a wide audience of accelerator physicists. A ''coupling impedance'' for both the RK and SWFEWL is introduced, which can include realistic cavity features, such as beam and vacuum ports, in a simple manner. The RK and SWFEL macroparticle equations, which govern the energy and phase evolution of successive bunches in the beam, are of identical form, differing only by multiplicative factors. Expressions are derived for the phase and amplitude sensitivities of the TBA schemes to errors (shot-to-shot jitter) in current and energy. The analysis allows, for the first time, relative comparisons of the RK and the SWFEL TBAs.
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