Working principle of a cavity magnetron

A cavity magnetron is a cross-field (M-type) high-power microwave oscillator. Electrons move under a radial DC electric field and an axial DC magnetic field that is perpendicular to it, and give their energy to the RF fields of resonant cavities.

Construction

• A cylindrical, heated cathode sits at the centre.
• Around it is a copper anode block with N cavities (for example 8), cut as hole-and-slot, vane or rising-sun shapes. The cavities open into the cathode–anode interaction space.
• A strong permanent magnet gives an axial magnetic field B₀. A DC voltage V₀ is applied between anode and cathode.
• Straps join alternate segments to keep the oscillation in the π-mode. A loop in one cavity couples out the power.

          anode block, N cavities
        ___   ___   ___   ___
       /   \_/   \_/   \_/   \
      |   interaction  space   |
      |       ( cathode )      |  B0 axial
      |   spokes rotate  ->    |  (out of page)
       \___/ \___/ \___/ \___/
              output loop -> RF out

Working principle

1. Without B: electrons go straight from cathode to anode.
2. With B: the force F = −e(E + v × B) bends their paths into cycloid-like curves. At the Hull cut-off field, electrons just graze the anode and return: B₀c = √(8mV₀/e) / [b(1 − a²/b²)], where a = cathode radius and b = anode radius. The magnetron is run slightly above this field.
3. Any noise excites the cavities. The RF field fringing across the slots forms a wave that travels around the interaction space.
4. Phase focusing: electrons that meet a retarding RF field give energy to the wave, move outward and finally reach the anode. Electrons that meet an accelerating field gain energy and return quickly to the cathode, which removes them from the interaction. This sorting groups the useful electrons into spokes (like a wheel), which rotate in step with the RF field (Hartree condition).
5. In the π-mode, adjacent cavities are 180° apart and there are N/2 spokes. Each spoke passes a slot when the field there is retarding, so energy is fed to the cavities each cycle and oscillations are sustained.

Features: efficiency of about 40–70%, peak powers of kW to several MW in pulsed operation, compact, frequency fixed mainly by the cavity size.

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