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A folded waveguide (FW) is a promising slow-wave structure (SWS) for millimeter-wave traveling-wave tubes (TWTs) with the advantages of high power and considerable bandwidth. A novel rectangular groove-loaded FW SWS is analyzed for the purpose of gaining higher power with a smaller size compared with the normal circuit. The high-frequency characteristics, including dispersion properties and interaction impedance, are investigated by numerical simulation, and the nonlinear large-signal performance of such a TWT is also analyzed by a 3-D particle-in-cell code MAGIC3D. Compared with a normal circuit, larger gain and electronic efficiency together with notably higher output power at a Ka-band are predicted by the simulation. Meanwhile, the novel circuit is also much shorter than the normal circuit with good performance at the working frequencies. It, therefore, will favor the miniaturized design of a high-power millimeter-wave TWT.