Autophase stability is provided for a traveling wave device (TWD) electron beam for amplifying an RF electromagnetic wave in walls defining a waveguide for said electromagnetic wave. An off-axis electron beam is generated at a selected energy and has an energy noise inherently arising from electron gun. The off-axis electron beam is introduced into the waveguide. The off-axis electron beam is introduced into the waveguide at a second radius. The waveguide structure is designed to obtain a selected detuning of the electron beam. The off-axis electron beam has a velocity and the second radius to place the electron beam at a selected distance from the walls defining the waveguide, wherein changes in a density of the electron beam due to the RF electromagnetic wave are independent of the energy of the electron beam to provide a concomitant stable operating regime relative to the energy noise.