Bunching effect and cavity magnetron construction

Bunching effect

Bunching is the formation of dense groups of electrons at regular intervals in a beam. It results when electrons of different velocities (caused by an RF field) catch up with one another, as in klystrons and TWTs. In a magnetron the same grouping comes from phase focusing: electrons in the favourable RF phase stay in the interaction, and those in the unfavourable phase are removed. So the electrons form spokes, which give energy to the RF field in step with it.

Cavity magnetron

A cavity magnetron is a cross-field (M-type) high-power microwave oscillator.

Construction

        anode block with N = 8 cavities
         _/ \_/ \_/ \_/ \_
        /                  \
       |  interaction space |
       |    ( cathode )     |   B0 axial (out of page)
       |  spokes rotate ->  |   E radial
        \_/ \_/ \_/ \_/ \_/
          straps   output loop -> RF out

• A cylindrical cathode (radius a) coated with oxide, heated from inside.
• A copper anode block (radius b) with N cavities (usually 8 to 16) of hole-and-slot, vane or rising-sun shape, opening into the interaction space.
• A permanent magnet giving an axial magnetic field B₀, and a DC anode voltage V₀ giving a radial electric field.
• Straps joining alternate anode segments to hold the π-mode, and a coupling loop in one cavity to take out power.

Operational features

1. Electron paths: with E only, electrons go straight to the anode. With crossed E and B, they follow curved (cycloid-like) paths. At the Hull cut-off field they just graze the anode: B₀c = √(8mV₀/e) / [b(1 − a²/b²)]. The tube is run with B₀ slightly above this value.
2. RF field: noise excites the cavities. In the π-mode, adjacent cavities are 180° out of phase, and their fringing fields form a wave rotating around the cathode.
3. Hartree condition: V₀ and B₀ are chosen so that the electron drift speed around the cathode equals the angular phase velocity of this wave.
4. Phase focusing (bunching): electrons in a retarding tangential RF field lose energy to the wave and move outward toward the anode. Electrons in an accelerating field gain energy and are bent back to the cathode, which removes them. The useful electrons form N/2 spokes.
5. Energy transfer: each spoke passes a slot when its field is retarding, so it keeps giving energy to the cavities and the oscillation is sustained.
6. Performance: efficiency of 40–70% (high, because electrons reach the anode with little kinetic energy), pulsed peak power from kW to 10 MW, CW power up to several kW. Frequency is set mainly by cavity size. Frequency pushing (change with current) and pulling (change with load) occur.
7. Mode separation: strapping or a rising-sun anode separates the π-mode from nearby modes, so the tube does not jump modes.

Applications: radar transmitters, microwave ovens (2.45 GHz), industrial heating and medical linear accelerators.