Resonant absorption instability: Acceleration and radiation amplification

A new type of instability is demonstrated. It occurs when a space-change wave that oscillates at a frequency close to the resonance of the medium in which the electron beam propagates. The space-charge wave grows in space according to the loss associated with the resonance namely, it is directly related to the attenuation of a pure electromagnetic mode in the medium. The spatial growth is proportional to the square root of the current density and for a given current, it is inverse proportional to the normalized momentum to the power of 1.5 i.e. (γβ)-3/2. We briefly discuss possible application to particles acceleration and millimeter wave amplification