Streaming instabilities in solids and the role of collisions

An analysis is made of several solid-state amplifiers using streaming carriers, and the role played by collisions is discussed. In the case of an electron stream interacting with a TM wave there are found to be no "collision-induced" instabilities, in contrast to various statements in the literature; in the case of TEM waves collisions can induce instabilities under proper conditions. For TM-waves, where there is a first-order longitudinal RF electric field component interacting with the drifting carriers, collisions tend only to decrease the amplification, the instability being due to interaction between the positive-energy-carrying "circuit" wave and the negative-energy-carrying slow-space-charge wave supported by the streaming carriers. Similarly, the resistive-wall amplifier (also a TM case) is, interestingly, found to be simply a two-stream amplifier in which collisions become dominant in one of the streams. On the other hand, in the interaction with linearly polarized TEM waves, where there is no first-order RF electric field along the direction of drift, collisions can produce a proper phase for the second-order RF electric field (due to
\tilde{V}_{trans}
×
\tilde_{B}_{trans}
so that this field component interacting with the carriers can lead to amplification.