Cross-field magnetron with 60° phase difference

A cross-field (cavity) magnetron is an M-type tube in which a radial DC electric field and an axial DC magnetic field act at right angles on the electrons. The electrons give their potential energy to a travelling RF wave carried by the cavities of the anode.

Mode and number of cavities for 60° phase difference

For an anode with N cavities, the phase difference between adjacent cavities in mode n is:

φ = 2πn / N
60° = 360°·n / N   =>  N = 6n
N = 6  -> n = 1  (one spoke)
N = 12 -> n = 2  (two spokes)

So a 6-cavity anode in its n = 1 mode (or a 12-cavity anode in its n = 2 mode) has 60° between adjacent cavities. The RF field pattern repeats every 360°/60° = 6 cavities. The number of electron spokes equals n. (The usual π-mode has 180° between cavities and N/2 spokes.)

   6-cavity anode, 60° between cavities
          0°
     300°  _   60°
       \ / \ /
   ----( cath )----   B0 axial (out of page)
       / \_/ \        E radial
     240°     120°
         180°
   one spoke rotating at ω (angular)

Working principle

1. The heated cathode emits electrons. The anode voltage V₀ gives a radial E field. An axial B₀ above the Hull cut-off value, B₀c = √(8mV₀/e) / [b(1 − a²/b²)], bends the electron paths so that, without RF, they curve back to the cathode.
2. Noise excites the cavities. In this mode each cavity's fringing field is 60° behind its neighbour, so the RF pattern forms a wave that rotates around the cathode at angular velocity ω/n.
3. The DC fields make electrons drift around the cathode at the E × B speed. V₀ and B₀ are chosen (Hartree condition) so that this drift matches the wave's angular velocity.
4. Phase focusing: electrons that meet a tangential retarding RF field lose energy to the wave, slow down and move outward step by step to the anode. Electrons that meet an accelerating field gain energy and are returned to the cathode, which removes them early.
5. The useful electrons form n rotating spokes (one spoke for N = 6). Each spoke passes the cavity slots in step with the retarding phase, so energy flows into the cavities every cycle. The oscillation builds up and RF is taken out with a coupling loop.

Remarks

• The different modes lie close in frequency, so mode control is needed. Strapping and the rising-sun anode are designed mainly to hold the π-mode; for the 60° mode, V₀ and B₀ are set to the Hartree condition of that mode.
• Efficiency is about 40–70%, because the electrons hit the anode with little leftover kinetic energy.
• If an RF signal is injected into the cavity chain (as in a cross-field amplifier), the same interaction amplifies it.