We describe a high-power, annular beam klystron, the Triaxial Klystron, that promises high efficiency at GW power levels and frequencies up to X band. Higher frequency operation should be possible at reduced power levels. The device consists of a thin annular electron beam propagating in an annular drift region, with cavity structures located inside and outside the beam. So long as the width of the drift region is less than half a wavelength (to cut off TM modes), the beam diameter can be as large as necessary to accommodate the required current and to reduce the RF surface fields to tolerable levels. Beam transport and stability are also facilitated in the annular channel. Simulations at X-band (using MRC’s particle-in-cell code, MAGIC) show strong beam bunching and efficient energy extraction from specially designed radial cavity structures. Initial experiments at the Naval Research Laboratory have demonstrated transport of a 16-kA, 400-keV beam over a distance of ∼1 m with no evidence of instability or...