Bunching, field effect and high power oscillator

Bunching effect

Bunching is the grouping of electrons in a beam into dense packets (bunches) at regular time intervals. A uniform beam passes an RF gap and is velocity-modulated: electrons crossing during the positive half-cycle speed up and those crossing during the negative half-cycle slow down. In the following drift space the faster electrons catch up with the slower ones, so the current becomes density-modulated at the RF frequency. Bunches give energy to an RF field when they pass through a retarding field. This is the basis of klystrons and TWTs (O-type tubes).

Field effect (cross-field effect)

The cross-field effect is the motion of electrons under a DC electric field E and a DC magnetic field B that are perpendicular to each other. The Lorentz force F = −e(E + v × B) makes the electrons move in cycloidal paths that drift at velocity E/B, perpendicular to both fields. The electrons interact with an RF wave moving at that drift speed and give it their potential energy. This is used in magnetrons and cross-field amplifiers (M-type tubes).

Cavity magnetron: a high-power oscillator using both effects

The cavity magnetron uses the cross-field effect (radial E, axial B) to move electrons around the cathode. Phase focusing then groups them into spokes, which is a form of bunching.

       anode with N cavities (N = 8)
       _/ \_/ \_/ \_/ \_
      /    \ spoke  /    \
     |   --( cathode )--   |   B0 axial
     |    /  spoke   \     |   E radial
      \_/ \_/ \_/ \_/ \_/
         output loop -> RF

Working

1. The heated cathode emits electrons. The DC anode voltage V₀ gives a radial E field, and the magnet gives an axial B₀ field above the Hull cut-off value B₀c = √(8mV₀/e) / [b(1 − a²/b²)]. Without RF, electrons curve back to the cathode.
2. Noise excites the cavities. In the π-mode, adjacent cavities are 180° out of phase, and the fringing RF fields across the slots form a wave rotating around the interaction space.
3. Field effect: electrons move around the cathode at the E × B drift speed. When this matches the angular velocity of the RF wave (Hartree condition), the electrons keep a constant phase relative to the wave.
4. Bunching (phase focusing): electrons in a retarding RF field lose energy, move outward and give energy to the cavities. Electrons in an accelerating field gain energy and are sent back to the cathode. So the useful electrons gather into N/2 rotating spokes.
5. Each spoke passes a slot just when its field is retarding, so energy is fed to the cavities every cycle and the oscillation is sustained. Power is taken out with a coupling loop. Strapping keeps the π-mode separate from other modes.

Features: efficiency of about 40–70%, kW to MW pulsed power. Used in radar transmitters and microwave ovens.