The Cavity Magnetron: The Spinning Electron Spokes Inside Your Microwave

The Machine: A Copper Block, a Hot Wire, and Two Ring Magnets

Pull a magnetron out of a microwave oven and the geometry inside is almost absurdly simple. A cylindrical anode block of oxygen-free copper is drilled with ten identical holes running parallel to its axis, each hole opened to the central bore by a narrow slot. The copper left standing between the slots forms ten wedge-shaped vanes pointing inward like the spokes of a wheel. Down the axis, held on ceramic insulators, runs a coiled thoriated-tungsten cathode of roughly 2 mm radius. The anode bore radius is about 4 mm, so the entire interaction region is an annular gap 2 mm wide and some 8 mm tall — smaller than a pencil eraser.

Three connections drive it. A filament transformer supplies about 3.3 V at 10 A, heating the cathode to near 2,000 K, hot enough for thermionic emission to liberate electrons in bulk. A half-wave voltage-doubler holds the anode about 4 kV positive relative to the cathode while drawing around 300 mA, so roughly 1.2 kW of DC goes in. Two black ferrite ring magnets, closed by a soft-iron yoke, drive an axial magnetic field of 0.15–0.2 T straight down the bore. Everything else — ten cavities, one wire loop, one ceramic-sealed antenna — is passive metal. There is no amplifier, no oscillator circuit, nothing that could be called electronics.

Crossed Fields: Why No Electron Can Reach the Anode

An electron leaving the cathode feels the Lorentz force F = −e(E + v × B), with E pointing radially outward and B along the axis. The two fields are at right angles — that is what crossed-field means. E alone would fling the electron across the 2 mm gap in well under a nanosecond; B alone would bend it into a circle. Together they produce something stranger: the electron traces a cycloid, the curve drawn by a chalk mark on a rolling wheel, looping outward and back while the loop centre marches sideways at the E × B drift velocity, v = E/B.

Put real numbers in. E = 4,000 V across 2 mm is 2 × 10⁶ V/m; with B = 0.18 T the drift speed is v = E/B ≈ 1.1 × 10⁷ m/s, about 3.7% of light speed — and, remarkably, independent of the electron's charge and mass. The cyclotron angular frequency is ω_c = eB/m ≈ 3.2 × 10¹⁰ rad/s (f_c ≈ 5 GHz), and the crest of each cycloid arch rises only 2mE/eB² ≈ 0.70 mm above the cathode. The gap is 2 mm. The electron turns around well short of the anode and starts again.

That is the Hull cut-off, and for coaxial geometry it has a closed form:

• V_c = (e/8m) · B² · r_a² · (1 − r_c²/r_a²)²

With B = 0.18 T, anode radius r_a = 4.0 mm and cathode radius r_c = 2.0 mm this evaluates to ≈ 6.4 kV. The tube runs at 4 kV, comfortably below cut-off. In a smooth-bore magnetron that would mean no anode current whatsoever: the electrons pile into a rotating, self-repelling sheath called Brillouin flow, a genuine non-neutral plasma whose density runs up toward the Brillouin limit ε₀B²/2m, of order 10¹⁷ m⁻³ at 0.18 T. The cavities are what finally coax energy out of that trapped cloud.

Ten LC Circuits Machined Out of Solid Copper

Each cavity is a lumped resonator hiding in plain sight. The drilled hole is a one-turn inductor — a copper loop enclosing magnetic flux — and the narrow slot between two vane tips is a parallel-plate capacitor. Shock it and it rings at f = 1/(2π√LC). Oven anode blocks are machined so that f = 2.450 GHz, a free-space wavelength of 12.24 cm. Nothing tunes it from outside; the operating frequency is cut into the copper.

Ten coupled resonators support ten normal modes, distinguished by the phase step from one cavity to the next. The one that matters is the π-mode, in which adjacent cavities ring exactly 180° apart, so the RF voltages on successive vane tips alternate + − + − around the ring. The pattern repeats every two cavities, and the whole field configuration rotates by one cavity-pair per RF cycle:

• rotation rate = 2f/N = 2 × 2.45 GHz / 10 = 4.9 × 10⁸ revolutions per second (ω ≈ 3.1 × 10⁹ rad/s);
• at the anode radius that is a tangential speed of ≈ 1.2 × 10⁷ m/s — the same as the drift speed v = E/B above. That match is the entire design.

The π-mode is also the most fragile, sitting closest in frequency to its neighbours, and a tube that jumps modes goes off-frequency and off-power. James Sayers, at Birmingham in 1941, fixed this by soldering two concentric strapping rings across alternate vanes: in π-mode those vanes are already at equal potential, so the straps carry no current and barely shift the frequency, while in every competing mode they short part of the field and shove its frequency far away. Tubes above roughly 10 GHz use the rising-sun alternative — cavities alternating between two depths — because straps become impractically small. At 2.45 GHz the skin depth in copper is only about 1.3 μm, so the RF current flows in a layer thinner than a red blood cell; hence oxygen-free copper, a good surface finish, and an unloaded Q of several hundred.

Spokes: How the Cloud Bunches Itself, and Where the Energy Comes From

Now the two halves meet. The rotating cloud sweeps past the vane tips, and the fringing RF field leaking from each cavity reaches a fraction of a millimetre into the gap, giving each drifting electron a small azimuthal push — forward or backward, depending on where it sits in the RF cycle. Crossed with the axial B, an azimuthal force produces a radial drift, and this is the trick on which everything turns:

• an electron in the retarding phase — moving against the RF field, and so giving energy to it — drifts outward, toward the anode;
• an electron in the accelerating phase — stealing energy from the field — drifts inward, back to the cathode, where it is absorbed.

Electrons that help are promoted; electrons that steal are removed. The bunching is self-reinforcing in azimuth too, since outward-drifting electrons lag while inward-drifting ones run ahead. Within nanoseconds of switch-on the smooth sheath collapses into N/2 = 5 space-charge spokes: a rotating five-armed pinwheel of charge locked in step with the π-mode field, invisible from outside a sealed tube, but reproduced in detail by particle-in-cell simulation.

The energy bookkeeping is what surprises people. The electron does not slow down and surrender kinetic energy; its speed stays pinned near v = E/B the whole way across, worth only ½mv² ≈ 340 eV. Having fallen through 4,000 V, it lands on the anode carrying about 340 eV instead of 4,000 eV, and the missing ~3,660 eV went into the cavity field en route. A magnetron converts DC potential energy into microwaves, using the electron only as a courier. Ideally that is ~91% efficient; real tubes reach 65–75%, losing the balance to returning electrons, to cathode back-bombardment (several percent of input power, enough that some designs cut filament drive once running), and to I²R heating of the copper.

Oscillation has a lower bound too — the Hartree voltage, below which electrons cannot stay synchronous with the rotating pattern, near 2.9 kV for these dimensions. The 4 kV operating point therefore sits inside the only window where the tube oscillates at all: above Hartree, below Hull cut-off.

Getting the Power Out — and Measuring It

One cavity, and only one, has a wire loop threaded through it. The current induced in that loop runs up a copper stalk, through a ceramic vacuum seal, to a short antenna dome radiating into a rectangular waveguide launcher; at 2.45 GHz the standard guide is WR-340 (86.4 × 43.2 mm, TE₁₀ cutoff 1.736 GHz). Coupling the loop loads the resonator, dropping its Q from several hundred unloaded to roughly 100–200 loaded: tighter coupling extracts more power but makes the tube more sensitive to whatever sits at the far end of the guide.

Because there is no input signal, a magnetron's frequency is never commanded, only influenced — and the two influences have names. Pushing is the frequency shift with anode current; pulling is the shift with load impedance, and a typical oven tube's pulling figure is around 10 MHz as a 1.5:1 mismatch is rotated through all phases. Manufacturers characterise both on a Rieke diagram — contours of output power and frequency plotted onto a Smith chart of the load reflection coefficient, still the standard measurement for any oscillator tube.

Output power itself is measured calorimetrically. IEC 60705, the international oven test method, specifies heating 1,000 ± 5 g of water in a standard vessel and computing power from the temperature rise over a timed run; the wattage printed on an oven door comes from that thermometer, not a wattmeter. A spectrum analyser shows why RF measurement is awkward: fed by an unfiltered half-wave supply, an oven magnetron oscillates only during part of each mains cycle and chirps as the anode voltage swings, smearing its emission across tens of megahertz inside the 2.400–2.500 GHz band — harmless in a shielded cavity, notorious for Wi-Fi interference outside one.

Birmingham, 21 February 1940

Albert W. Hull at General Electric coined the name magnetron and published the cut-off condition in 1921, but his smooth-bore tube was conceived as a magnetically controlled switch, not an oscillator. Split-anode versions came quickly: August Žáček in Prague and Erich Habann in Jena, both working in 1924, got split-anode tubes oscillating from around 100 MHz (Habann) up to about 1 GHz (Žáček), and Kinjirō Okabe at Tōhoku pushed into centimetre waves by 1929. Multi-cavity designs were patented by Hans Hollmann in 1935; Nikolay Alekseev and Dmitry Malyarov reported some 300 W at 9 cm in the Soviet Union.

The decisive machine was built by John Randall and Harry Boot at the University of Birmingham. Their six-cavity copper block — end plates sealed with wax, the vacuum held by a pump running continuously — first oscillated on 21 February 1940. They had no instrument capable of reading it, so they estimated roughly 400 W at 9.8 cm by counting how many car headlamp bulbs it could light. Eric Megaw at GEC Wembley turned the curiosity into the manufacturable eight-cavity E1189 by that August.

In September 1940 the Tizard Mission carried magnetron serial No. 12 to Washington in a black metal deed box; the historian James Phinney Baxter III later called it the most valuable cargo ever brought to American shores. Bell Labs promptly noticed the tube had eight cavities although the accompanying drawings showed six. The MIT Radiation Laboratory opened that November, and at Raytheon Percy Spencer replaced machined anode blocks with punched, stacked laminations, lifting output from dozens of tubes a day into the thousands; roughly a million were built during the war, feeding centimetric radar sets such as H2S and ASV Mk III. In 1945 Spencer noticed a sweet melting in his pocket beside a running tube; the 1947 Raytheon Radarange that resulted weighed some 340 kg and was water-cooled, and Amana's countertop model finally reached kitchens in 1967.

Look-Alikes, Myths, and What Is Still Unsolved

The magnetron is routinely confused with the klystron, and the difference is structural. A klystron is a linear-beam tube: an input signal velocity-modulates a straight beam at one cavity, the electrons bunch during a field-free drift, and the bunches excite a second cavity. It is an amplifier, and its frequency is whatever you feed it. The magnetron has no input port, no drift tube and no straight beam; it self-oscillates at a frequency machined into its anode. The travelling-wave tube (Rudolf Kompfner, 1943) is another linear-beam amplifier, and the gyrotron uses relativistic cyclotron resonance to reach megawatts at 170 GHz for tokamak heating. A crossed-field amplifier does exist — William C. Brown's Amplitron at Raytheon in the mid-1950s — but it is a separate tube. And magnetron sputtering, despite the shared name and the shared E × B trapping, deposits thin films and emits no useful microwaves.

Two myths deserve killing. First, 2.45 GHz is not a resonance of water. It is an ISM allocation — the 2.400–2.500 GHz band reserved internationally for industrial, scientific and medical use — so ovens can radiate there unlicensed. Liquid water has no sharp microwave resonance at all, only a broad Debye relaxation peaking near 20 GHz at room temperature, and 2.45 GHz sits well down its low-frequency flank. That is deliberate: weaker absorption buys a penetration depth of roughly 1.4 cm rather than a couple of millimetres, so food cooks through instead of searing. Second, running an oven empty reflects nearly all the RF back down the waveguide into the tube, driving it into a pulling region where it can mode-jump and arc across the antenna dome — which, with cathode erosion from back-bombardment, is why oven magnetrons last only about 2,000 hours.

Open problems remain. Magnetron start-up from noise and mode competition still lack a complete analytic theory; designs are validated with particle-in-cell codes such as MAGIC and ICEPIC. Injection phase-locking is pursued at Fermilab and elsewhere as a way to replace klystrons in accelerator RF at a fraction of the cost per watt. And solid-state GaN sources at 2.45 GHz now reach a few hundred watts per module with far better spectral purity — yet still cost on the order of a dollar per watt, against a kilowatt magnetron that sells for about the price of a sandwich.

The magnetron against the vacuum tubes it is most often mistaken for — and one device that merely shares its name.

Device	Beam and field geometry	Frequency set by	Role and typical efficiency
Cavity magnetron	Crossed fields: radial E, axial B, cylindrical electron cloud	Cavities machined into the anode (π-mode)	Self-oscillator; 65–75%
Klystron	Linear beam; axial B used only to focus it	The injected input signal; cavities tuned to it	Amplifier (the reflex klystron oscillates); ~40–70%
Travelling-wave tube	Linear beam threading a helix slow-wave structure	The input signal — bandwidth over an octave	Wideband amplifier; ~20–50%
Gyrotron	Hollow, gyrating (helical) beam in a very strong axial B — a fast-wave device, not a linear-beam one	Cyclotron frequency eB/2πγm	Oscillator, MW-class at 28–170 GHz; ~30–50%
Magnetron sputtering source	Crossed E × B over a solid target, in a process chamber	Nothing resonant — a DC or 13.56 MHz supply	Deposits thin films; emits no useful microwaves