Chaos Theory and Klystrons

       Is it possible that klystrons, traveling wave tubes, and all velocity modulation amplifiers are an expression of one of the central elements of chaos theory? These devices  are simply tubes wherein a beam of electrons flowing down the length of the tube interacts with with a tiny e.m.f. introduced by a small antenna at the upstream end.  The signal to be amplified is "broadcast" into the tube, and the individual electrons in the beam are either accelerated or decelerated as they past through the radio wave, depending on the phase of the wave at the instant they encounter it. This change in velocity is extremely minute, but with the passage of time, the electrons which were accelerated drift further and further ahead of the others, and those which were decelerated get further and further behind.  By the time they get to the antenna at the downstream end, there is a pronounced "bunching" effect.  As these grouped electrons strike the antenna, they induce an alternating current waveform identical to the tiny current introduced at the upstream end, only a thousand times greater in amplitude.  But for the process to work, time must be allowed to do its work.  In chaos theory, time is also a central element.  The idea  is not that a butterfly flapping its wings in Tibet might cause a stock market crash in London. It's that a butterfly flapping its wings in Tibet might, after the passage of sufficient time---cause a crash.   Of course, in chaos theory, the idea is that the ultimate results of an action can eventually get so complex that no prediction of that result is possible. Whereas a well designed klystron is quite predictable.