Phase distortion mechanisms in linear beam vacuum devices

The mechanism for phase distortion in linear beam vacuum devices is identified in the simplest system that pertains to such devices, the force-free drifting electron beam. We show that the dominant cause of phase distortion in a force-free drifting beam is the inverse dependence of arrival time on velocity for an electron, i.e., the ``$1/u$ nonlinearity,'' and that a secondary cause of phase distortion is the nonlinearity of the velocity modulation. We claim that this is the mechanism for phase distortion in all linear beam vacuum devices, and provide evidence from a traveling wave tube calculation. Finally, we discuss the force-free drifting beam example in the context of the "self-intermodulation" description of phase distortion recently described in Refs. [J. W\"ohlbier and J. Booske, Phys. Rev. E, vol. 69, 2004, 066502], [J. W\"ohlbier and J. Booske, IEEE Trans. Elec. Devices, To appear.]