# How does bunching in a travelling wave tube amplifier result in amplification?

I'm having a bit of trouble finding a good source to understand how exactly a traveling wave tube amplifier works. I understand the basic premise that the electron beam gives up kinetic energy to the traveling wave, but I'm having a bit of trouble understanding how this actually happens.

The first type of explanation (such as this one) that I've found indicates that the electric field of the wave causes the electrons to bunch up and this results in the amplification of the signal. I'm unsure about two things here:

1. In order for kinetic energy to be on average lost by the beam, the electrons must be slowed down more than they speed up. If I use the beam as my reference point (i.e, set its velocity to zero), the electrons are effectively just moving over a non-uniform electric field. What would cause them to loose kinetic energy in this case?
2. The electrons would be attracted to the positive region of the E field and repelled from the negative one. Wouldn't this cancel the E field rather than amplifying it?

The second explanation that I found (on Wikipedia) indicates that the magnetic field instead is responsible for the bunching and energy transfer. This seems to make more sense since the Lorentz force from a magnetic field depends on velocity, which I suppose could force the electrons' velocity to become matched.

Which of these explanations is correct? Or is it something else? Finally, what role (if any) does the attenuator play other than suppressing backwards oscillations? Please include the relevant mathematics (i.e, show mathematically (if possible) that the beam velocity decreases and the wave becomes amplified because of it).

• First, consider what the output from the rf coil would look like if you were to inject a pre-bunched beam into the tube (no input on the rf coil). It should be clear that the bunched beam will induce a varying signal on the coil. No consider what happens when an input signal on the rf coil starts perturbing an initially cw electron beam. What you get is positive feedback resulting in amplification. Commented May 27, 2021 at 18:58
• That makes sense, I suppose I should rephrase my question to ask how this actually results in that positive feedback. So far I don't understand why the perturbations in the beam would do anything other than just travel down the beam without growing. Commented May 29, 2021 at 0:53