Parallels Between Models of Gyrotron Physics and Some Famous Equations Used in Other Scientific Fields
Source abstract
Abstract
In this integrative review paper, we explore the parallels between the physical models of gyrotrons and some equations used in diverse and broad scientific fields. These include Adler’s famous equation, Van der Pol equation, the Lotka–Volterra equations and the Kuramoto model. The paper is written in the form of a pedagogical discourse and aims to provide additional insights into gyrotron physics through analogies and parallels to theoretical approaches used in other fields of research. For the first time, reachability analysis is used in the context of gyrotron physics as a modern tool for understanding the behavior of nonlinear dynamical systems.
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Research context
OpenAlex topics: Gyrotron and Vacuum Electronics Research · Geophysics and Sensor Technology
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Institute of Electronics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria
References (100+)
Show source-provided references
1. Maler, O. (2008). Computing Reachable Sets: An Introduction, French National Center of Scientific Research. Available online: https://www-verimag.imag.fr/~maler/Papers/reach-intro.pdf.
2. Set propagation techniques for reachability analysis10.1146/annurev-control-071420-081941 ↗
3. (2025, May 10). ReachabilityAnalysis.jl. Methods to Compute Sets of States Reachable by Dynamical Systems. Available online: https://juliareach.github.io/ReachabilityAnalysis.jl/dev/.
4. Bogomolov, S., Forets, M., Frehse, G., Potomkin, K., and Schilling, C. (2019, January 16–18). JuliaReach: A toolbox for set-based reachability. Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, Montreal, QC, Canada.10.1145/3302504.3311804 ↗
5. Review of the theory of mode interaction in gyrodevices10.1109/27.772257 ↗
6. The Progress in the Studies of Mode Interaction in Gyrotrons10.1007/s10762-022-00845-7 ↗
7. Development of terahertz gyrotrons for spectroscopy at MIT
8. A review on the sub-THz/THz gyrotrons10.1016/j.infrared.2016.01.015 ↗
9. Gyrotron-Based Technological Systems for Material Processing-Current Status and Prospects10.1007/s10762-020-00727-w ↗
10. Idehara, T., Sabchevski, S., Glyavin, M., and Mitsudo, S. (2020). The Gyrotrons as Promising Radiation Sources for THz Sensing and Imaging. Appl. Sci., 10.10.3390/app10030980 ↗
11. Novel and Emerging Applications of the Gyrotrons Worldwide: Current Status and Prospects10.1007/s10762-021-00804-8 ↗
12. Russian Gyrotrons: Achievements and Trends10.1109/JMW.2020.3030917 ↗
13. Karmakar, S., and Mudiganti, J. (2021). Gyrotron: The Most Suitable Millimeter-Wave Source for Heating of Plasma in Tokamak. Plasma Science and Technology, IntechOpen.10.5772/intechopen.98857 ↗
14. Sabchevski, S., and Glyavin, M. (2023). Development and Application of THz Gyrotrons for Advanced Spectroscopic Methods. Photonics, 10.10.3390/photonics10020189 ↗
15. Kartikeyan, M., Borie, E., and Thumm, M. (2003). GYROTRONS High Power Microwave and Millimeter Wave Technology, Springer.10.1007/978-3-662-07637-8 ↗
16. Nusinovich, G. (2004). Introduction to the Physics of Gyrotrons, The Johns Hopkins University Press.10.1353/book.62236 ↗
17. The Electron Cyclotron Maser10.1103/RevModPhys.76.489 ↗
18. Tsimring, S.E. (2007). Electron Beams and Microwave Vacuum Electronics, Wiley-Interscience.10.1002/0470053763 ↗
19. Du, H., Du, C.-H., and Liu, P.-K. (2014). Millimeter-Wave Gyrotron Traveling-Wave Tube Amplifiers, Springer.10.1007/978-3-642-54728-7 ↗
20. Gilmour, A.S. (2011). Klystrons, Traveling Wave Tubes, Magnetrons, Crossed-Field Amplifiers, and Gyrotrons, Artech House.
21. Grigoriev, A.D., Ivanov, V., and Molokovsky, S. (2018). Microwave Electronics, Springer.10.1007/978-3-319-68891-6 ↗
22. Dattoli, G., Palma, E., Sabchevski, S., and Spassovsky, I. (2021). An overview of the gyrotron theory. High Frequency Sources of Coherent Radiation for Fusion Plasmas, IOP Publishing.10.1088/978-0-7503-2464-9ch5 ↗
23. Code KARAT Simulations Power Microw. Sources Incl. Cherenkov Plasma Devices, Vircators, Orotron, E-Field Sensor, Calorimeter Etc10.1051/epjconf/201714904024 ↗
24. User-configurable MAGIC for electromagnetic PIC calculations10.1016/0010-4655(95)00010-D ↗
25. Modeling of gyroklystrons with MAGY10.1109/27.887741 ↗
26. Design of a 60 GHz, 100 kW CW gyrotron for plasma diagnostics: GDS V.01 simulations10.2528/PIERB10061508 ↗
27. Recent evolution of the simulation tools for computer aided design of electron-optical systems for powerful gyrotrons
28. Sabchevski, S., Idehara, T., Saito, T., Ogaw, I., Mitsudo, S., and Tatematsu, Y. (2010). Physical Models and Computer Codes of the GYROSIM (GYROtron SIMulation) Software Package, IOP Publishing. FIR Center Report FIR FU-99.
29. TWANG-PIC, a novel gyro-averaged onedimensional particle-in-cell code for interpretation of gyrotron experiments10.1063/1.4923299 ↗
30. GYROCOMPU: Toolbox Designed for the Analysis of Gyrotron Resonators10.1109/TPS.2020.3013299 ↗
31. Development of the Full Package of Gyrotron Simulation Code10.3938/jkps.73.1750 ↗
32. Two-cavity CRM at harmonics of electron cyclotron frequency
33. Theory of synchronization of oscillations in a cyclotron resonance maser monotron by an external signal10.1007/BF01037666 ↗
34. Synchronization of CRM-monotron by by electron beam modulation10.1007/BF01034283 ↗
35. Efficiency of the mode nonlinear selection methods in CRM-Oscillators
36. Observations of Phase Locking in a Single-Cavity Gyrotron Oscillator10.1109/TPS.1985.4316452 ↗
37. Nonlinear theory of phase-locking gyrotron oscillators driven by an external signal10.1103/PhysRevA.39.3432 ↗
38. Phase locking and bandwidth in a gyrotron oscillator10.1007/BF02146252 ↗
39. Phase-locking of a second-harmonic gyrotron oscillator using a quasi-optical circulator to separate injection and output signals10.1109/27.473201 ↗
40. High efficiency, phase-locked operation of the harmonic-multiplying inverted gyrotwystron oscillator10.1109/27.772268 ↗
41. Experimental study of phase deviation and pushing in a frequency doubling, second harmonic gyro-amplifier10.1109/16.954489 ↗
42. Gyrotron frequency stabilization by a weak reflected wave10.1007/s11141-016-9639-0 ↗
43. Design of master oscillator for frequency locking of a complex of megawatt level microwave sources10.1002/mop.32330 ↗
44. Denisov, G., Kuftin, A., Glyavin, M., Tsvetkov, A., Golubiatnikov, G., Tai, E., Soluyanova, E., Bakulin, M., Fokin, A., and Shmelev, M. (2021, January 27–30). Experimental tests of a high-stable 170 GHz/25 kW gyrotron as a master oscillator for frequency locking of megawatt level microwave sources. Proceedings of the 2021 22nd International Vacuum Electronics Conference (IVEC), Rotterdam, The Netherlands.10.1109/IVEC51707.2021.9722456 ↗
45. Krier, L., Avramidis, K.A., Braune, H., Gantenbein, G., Illy, S., Ioannidis, Z., Jelonnek, J., Laqua, H.P., Marsen, S., and Moseev, D. (September, January 29). Frequency Stabilization of Megawatt-Class 140 GHz Gyrotrons at W7-X Using an Off-the-Shelf PLL System. Proceedings of the 2021 46th International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz), Chengdu, China.10.1109/IRMMW-THz50926.2021.9566847 ↗
46. A study of gyrotron synchronization in the hard-excitation regime on the basis of the modified quasilinear model10.1007/s11141-023-10220-8 ↗
47. Adilova, A.B., and Ryskin, N.M. (2022, January 23–25). The phase-locking of high-power delay-coupled gyrotron oscillators with hard excitation. Proceedings of the 2022 IEEE 8th All-Russian Microwave Conference (RMC), Moscow, Russia.10.1109/RMC55984.2022.10079402 ↗
48. Phase-Locking of Second-Harmonic Gyrotrons for Providing MW-Level Output Power10.1109/TED.2021.3134187 ↗
49. Concept of Gyrotron Complexes With Serial Phase and Frequency Locking10.1109/TED.2023.3247368 ↗
50. Fokin, A.P., Kuftin, A.N., Belousov, V.I., Chirkov, A.V., Shmelev, M.Y., Golubiatnikov, G.Y., Movshevich, B.Z., Tai, E.M., Glyavin, M.Y., and Denisov, G.G. (2024, January 21–25). First Experiments on Frequency Locked Operation of the 170 GHz/1 MW Gyrotron. Proceedings of the 2024 Photonics and Electromagnetics Research Symposium (PIERS), Chengdu, China.10.1109/PIERS62282.2024.10618801 ↗
51. The Remote Control and Beyond: The Legacy of Robert Adler
52. A Study of Locking Phenomena in Oscillators10.1109/JRPROC.1946.229930 ↗
53. Lai, X., and Roychowdhury, J. (2005, January 21). Analytical equations for predicting injection locking in LC and ring oscillators. Proceedings of the IEEE 2005 Custom Integrated Circuits Conference, San Jose, CA, USA.
54. Razavi, B. (2003, January 24). A study of injection pulling and locking in oscillators. Proceedings of the IEEE 2003 Custom Integrated Circuits Conference, San Jose, CA, USA.
55. Technical noise in gyroklystrons and phase-locked gyrotron oscillators10.1063/1.872317 ↗
56. Phase locking of a gyrotron with low-frequency voltage and current fluctuations by an external monochromatic signal10.1007/s11141-021-10064-0 ↗
57. Stabilization of the radiation frequency of a gyrotron with a remote reflector under the conditions of interaction of the equidistant-spectrum modes10.1007/s11141-023-10237-z ↗
58. Adilova, A.B., and Ryskin, N.M. (2022). Theory of Peer-to-Peer Locking of High-Power Gyrotron Oscillators Coupled with Delay. Electronics, 11.10.3390/electronics11050811 ↗
59. Experimental Study of Extended Operating Zone of a 170-GHz/1-MW Gyrotron Locked by a Narrowband External Signal10.1109/TED.2024.3457568 ↗
60. L. I. Mandel’shtam and the modern theory of nonlinear oscillations and waves10.1070/PU1979v022n08ABEH005590 ↗
61. To the theory of gyrotrons with confocal resonators10.1063/1.5099909 ↗
62. Cavity Excitation Described by the van der Pol Equation in Transit-Time Tubes10.1109/TED.2007.907144 ↗
63. Complex dynamics of a simple distributed self-oscillatory model system with delay10.1134/1.1495037 ↗
64. Transient Processes in the Distributed Active Medium “Helical Electron Beam–Counterpropagating Electromagnetic Wave”10.1023/B:RAQE.0000046308.77565.8f ↗
65. (2025, May 10). Reachability Computations for Dynamical Systems in Julia. Available online: https://github.com/juliareach.
66. (2025, May 10). Mathematica Tutorial for the Second Course. Part III: Van der Pol Equations. Available online: https://www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch3/pol.html.
67. Van der Pol oscillator
68. Stability of mode locked states of coupled oscillator arrays10.1109/81.404045 ↗
69. The Dynamics of Two Coupled van der Pol Oscillators with Delay Coupling10.1023/A:1020536525009 ↗
70. Bifurcational mechanism of formation of developed multistability in a van der Pol oscillator with time-delayed feedback10.20537/nd1702001 ↗
71. Multistability and complex oscillatory regimes in a microwave generator with delayed reflection from the load10.1134/S1063785019030209 ↗
72. Coupled Van der Pol and Van der Pol–Duffing oscillators: Dynamics of Phase and Computer Simulation
73. Korsch, H.J., Jodl, H.J., and Hartmann, T. (2008). The duffing oscillator. Chaos, Springer.10.1007/978-3-540-74867-0_8 ↗
74. Mode competition in a high harmonic gyrotron10.1080/00207219208925612 ↗
75. Dumbrajs, O., Idehara, T., Iwata, Y., Mitsudo, S., Ogawa, I., and Piosczyk, B. (2002, January 26). Hysteresis in gyrotrons. Proceedings of the Twenty Seventh International Conference on Infrared and Millimeter Waves, San Diego, CA, USA.
76. Hysteresis-like effects in gyrotron oscillators10.1063/1.1561277 ↗
77. Hysteresis and frequency tunability of gyrotrons10.1007/s10762-015-0240-y ↗
78. Chaos and hyperchaos in a gyrotron10.1007/s11141-006-0115-0 ↗
79. Interpretation of the nonlinear mode excitation in the ITER gyrotron10.1063/1.2802076 ↗
80. High-Dimensional Chaos in a Gyrotron10.1109/TED.2006.888757 ↗
81. Chaos and Hyperchaos in a Ka-Band Gyrotron10.1109/LED.2021.3078761 ↗
82. Theory of locking of a Van der Pol oscillator by delayed reflection from a resonant load10.1007/s11141-006-0081-6 ↗
83. Phase locking of two limit cycle oscillators with delay coupling10.1063/1.4881837 ↗
84. Mutual synchronization of weakly coupled gyrotrons10.1063/1.4931746 ↗
85. Kuramoto, Y. (1975). Self-entrainment of a population of coupled non-linear oscillators. International Symposium on Mathematical Problems in Theoretical Physics, Springer.10.1007/BFb0013365 ↗
86. Phase- and Center-Manifold Reductions for Large Populations of Coupled Oscillators with Application to Non-Locally Coupled Systems10.1142/S0218127497000595 ↗
87. Strogatz, S.H. (2003). Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life, Hyperion. [1st ed.].
88. The Kuramoto model: A simple paradigm for synchronization phenomena10.1103/RevModPhys.77.137 ↗
89. Synchronization: From pendulum clocks to chaotic lasers and chemical oscillators10.1080/00107510310001603129 ↗
90. (2025, May 10). Dirk Brockman and Steven Strogatz, “Ride My Kuramoto Cycle”. Available online: https://www.complexity-explorables.org/explorables/ride-my-kuramotocycle.
91. Computer simulation of gyrophase self-organisation in a magnetoplasma10.1016/j.cpc.2004.06.065 ↗
92. The theory of amplitude-phase mode interactions in electron masers10.1007/BF01038938 ↗
93. Bifurcation analysis of multistability of synchronous states in the system of two delay-coupled oscillators10.1063/5.0065670 ↗
94. Bénard-von Kármán instability: Transient and forced regimes10.1017/S0022112087002222 ↗
95. Amplitude and phase effects on the synchronization of delay-coupled oscillators10.1063/1.3518363 ↗
96. Mode interaction in gyrotrons10.1080/00207218108901349 ↗
97. Interaction of modes in gyrotrons with a high-frequency field whose longitudinal structure is variable10.1007/BF01048496 ↗
98. Lotka-Volterra Population Models10.1146/annurev.es.09.110178.001201 ↗
99. The Orgins and Evolution of Predator-Prey Theory10.2307/1940005 ↗
100. Mode competition in a gyromonotron with a distorted axial symmetry