Cavity magnetron with 45° phase shift and applications

A cavity magnetron is a cross-field (M-type) high-power microwave oscillator. The electrons move in a radial DC electric field and an axial DC magnetic field, and they give energy to RF fields in resonant cavities cut in the anode.

Mode for 45° phase shift

For N cavities in mode n, the phase shift between adjacent cavities is φ = 2πn/N. With 45°, N = 8n. An 8-cavity anode in mode n = 1 gives 45° and one rotating spoke. A 16-cavity anode in mode n = 2 gives two spokes. (The common π-mode has 180° and N/2 spokes.)

   8-cavity anode, cavity phases
              0°
       315° _/ \_ 45°
          /       \
    270° | (cathode) |  90°   B0 axial
          \  spoke  /        E radial
       225° \_ _/ 135°
             180°  -> output loop

Working principle

1. Construction: a heated cylindrical cathode (radius a) sits inside a copper anode block (radius b) with 8 resonant cavities that open into the interaction space. A magnet gives an axial B₀, and a DC voltage V₀ is applied between anode and cathode.
2. Cross-field motion: electrons follow cycloid-like paths under E and B. If B₀ is above the Hull cut-off, B₀c = √(8mV₀/e) / [b(1 − a²/b²)], they curve back without reaching the anode.
3. RF wave: noise excites the cavities. With 45° between neighbouring cavities, the fringing fields form a wave rotating around the cathode at angular velocity ω/n.
4. Synchronism (Hartree condition): V₀ and B₀ are set so that the electron drift speed around the cathode equals the wave's angular speed.
5. Phase focusing: electrons in the retarding RF phase give energy to the wave and drift outward to the anode. Electrons in the accelerating phase gain energy and return to the cathode. The useful electrons form a spoke that rotates with the wave.
6. Output: the spoke keeps giving energy to the cavities as it passes them, so oscillation builds up. A loop in one cavity takes out the RF power.
7. Mode control: non-π modes are close in frequency to others. The anode shape (rising-sun) or straps and coupling are designed to hold the wanted mode.

Efficiency is about 40–70%, and pulsed peak power ranges from kW to several MW.

Applications

• Radar transmitters (pulsed search and weather radar).
• Microwave ovens (2.45 GHz) and industrial heating, drying and plasma generation.
• Linear accelerators for medical radiotherapy.
• Microwave diathermy and some ECM/jamming transmitters.
• In amplifier form (cross-field amplifier), high-power radar stages.