--- title: "Working principle of a cavity magnetron" subject: "RF and Microwave Engineering" chapter: 5 key: "semester_7/rf_and_microwave_engineering:cavity-magnetron-working" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/cavity-magnetron-working site: BCT Engineering --- # Working principle of a cavity magnetron RF and Microwave Engineering · Chapter 5: Microwave Generators - Asked in: 2079 Chaitra, 5 marks; 2071 Magh, 10 marks (asked 2 times) - Video: [Cavity Magnetron - Cylindrical Magnetron - Operation and Analysis](https://www.youtube.com/watch?v=sx3_zyteU6w) — Padmasri Naban - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/cavity-magnetron-working - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-5 ## Question Describe the working principle of a cavity magnetron. ## Short answer The cavity magnetron is a cross-field oscillator where electrons from a central cathode move in crossed DC electric and axial magnetic fields. The magnetic field bends electron paths, forming rotating spokes that synchronously interact with the π-mode resonant cavities, delivering power. It provides high pulsed power (kW–MW) for radar and heating. ## Answer 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. ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In a cavity magnetron the DC electric and magnetic fields are: A. Both radial B. Radial E and axial B, perpendicular to each other C. Both axial D. Parallel Answer: B. Cross fields force electrons into cycloidal paths around the cathode. (Key point: Cross fields) 2. What is the Hull cut-off condition? A. B at which electrons just graze the anode and return; the tube is run slightly above it B. B at which the current is largest C. B = 0 D. Voltage at which the cathode melts Answer: A. Above it electrons curve back without reaching the anode unless RF interacts. (Key point: Hull cut-off) 3. What is phase focusing? A. Electrons in retarding RF fields give energy and reach the anode, while those in accelerating fields return to the cathode, forming spokes B. All electrons reach the anode C. Random scattering D. Focusing by a lens Answer: A. This selection groups useful electrons into spokes in step with the RF wave. (Key point: Phase focusing) 4. In the π-mode of an N-cavity magnetron: A. Adjacent cavities are 0° apart B. Adjacent cavities are 180° apart and there are N/2 spokes C. There are N spokes D. Phase is 60° Answer: B. Straps keep the π-mode, with N/2 rotating spokes. (Key point: π-mode) 5. Why are straps used in the anode? A. To cool the anode B. To join alternate segments and hold π-mode C. To increase voltage D. To couple the loop Answer: B. Strapping separates the π-mode from nearby modes. 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