Bunching effect and backward wave oscillator

Bunching effect

Bunching is the formation of dense groups (bunches) of electrons in a beam. A uniform beam passing through an RF field is velocity-modulated: some electrons are sped up and some are slowed down. As they drift on, the fast ones catch up with the slow ones, so the beam becomes density modulated. The bunches can then give kinetic energy to an RF field by passing through it during its retarding phase. Bunching is the basic mechanism of klystrons, TWTs and BWOs.

Backward wave oscillator (BWO)

A BWO (O-type carcinotron) is a slow-wave tube oscillator. Its beam interacts with a backward space harmonic of a periodic structure. The harmonic's phase velocity is in the beam direction, but its group velocity (energy flow) is opposite to the beam.

Construction

 RF out                              matched
  ^                                 termination
  |                                     |
 gun |>==== slow-wave structure ========| collector
        (helix / interdigital line)
   beam  -------------->   v0
   energy <-------------   vg (backward)
        axial focusing magnet

• An electron gun gives a beam at velocity v₀ = √(2eV₀/m), focused by an axial magnetic field.
• A periodic slow-wave structure (helix, interdigital line or folded waveguide).
• The output is taken from the gun end. The collector end is matched so no wave reflects. There is no RF input.

Working principle

1. Any noise sets up fields on the structure. The space harmonic whose phase velocity equals the beam velocity interacts with the beam.
2. The beam is velocity-modulated near the gun and bunches form as it moves toward the collector.
3. The bunches meet the retarding phase of the backward harmonic and give energy to it. This energy flows backward along the structure toward the gun end.
4. At the gun end the strengthened wave modulates the fresh, unbunched beam even more. This gives a closed feedback loop inside the tube. When the beam current exceeds the start-oscillation current, oscillations build up and power is taken out at the gun end.
5. Electronic tuning: the oscillation frequency is the one at which the backward harmonic's phase velocity equals v₀. Changing the beam voltage V₀ changes v₀, so the frequency changes. The tuning range can be up to an octave.

Features: wide voltage tuning, low to moderate power (mW to W), low efficiency (5–20%). M-type BWOs (cross-field) give more power.

Applications: swept-frequency signal generators, local oscillators in wideband receivers, broadband jamming, and mm-wave and THz sources.