--- title: "Cavity magnetron with 45° phase shift and applications" subject: "RF and Microwave Engineering" chapter: 5 key: "semester_7/rf_and_microwave_engineering:cavity-magnetron-45-applications" source: https://www.bctengineer.com/q/semester_7/rf_and_microwave_engineering/cavity-magnetron-45-applications site: BCT Engineering --- # Cavity magnetron with 45° phase shift and applications RF and Microwave Engineering · Chapter 5: Microwave Generators - Asked in: 2074 Magh, 8 marks - 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-45-applications - Whole chapter: https://www.bctengineer.com/md/semester_7/rf_and_microwave_engineering/chapter-5 ## Question Describe the working principle and applications of cavity magnetron having phase shift of 45° between the cavities. ## Short answer In an 8-cavity magnetron with 45° phase shift (mode n=1), crossed radial electric and axial magnetic fields cause electrons to drift synchronously with a rotating RF wave; phase-focused electrons form a spoke and transfer energy to the cavities, sustaining oscillation. Applications include pulsed radar transmitters, microwave ovens, industrial heating, and linear accelerators. ## Answer 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.) ```text 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. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. For 45° between adjacent cavities, how many spokes does an 8-cavity anode in n = 1 mode have? A. Four B. Two C. None D. One Answer: D. The pattern repeats every 8 cavities, so one rotating spoke forms (the pi-mode would give N/2 spokes). (Key point: Mode for 45 degrees) 2. What does the Hartree condition ensure? A. The magnet is switched off B. The cathode stays cold C. The electron drift around the cathode matches the angular speed of the RF wave D. The anode current is zero Answer: C. V0 and B0 are chosen so the E×B drift equals the wave's rotation speed, keeping electrons in step. (Key point: Synchronism) 3. Which electrons form the useful spoke in a magnetron? A. Those in the accelerating phase, which return to the cathode B. Those not affected by the RF field C. Those that hit the anode first D. Those in the retarding phase, which give energy to the wave and move to the anode Answer: D. Retarding-phase electrons give up energy and are kept; accelerating-phase electrons go back to the cathode and are removed. (Key point: Phase focusing) 4. Which is a typical application of the cavity magnetron? A. Low-noise receiver front end B. Microwave oven (2.45 GHz) and pulsed radar transmitters C. Audio amplification D. Wideband swept signal generator Answer: B. Magnetrons are high-power oscillators used in radar, microwave ovens, industrial heating and linacs. 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