Izvestiya of Saratov University.

Physics

ISSN 1817-3020 (Print)
ISSN 2542-193X (Online)

For citation:

Glukhova O. E., Krachkovskaya T. M., Petrunin A. А. Predictive evaluation of barium evaporation ratefrom the surface of a porous metal thermionic cathode: A mathematical model based on experimental data for B- and M-type cathodes. Izvestiya of Saratov University. Physics , 2026, vol. 26, iss. 2, pp. 175-184. DOI: 10.18500/1817-3020-2026-26-2-175-184, EDN: QYOLXM

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
30.06.2026
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Language: 
Russian
Heading: 
Solid-state electronics, micro and nanoelectronics
Article type: 
Article
UDC: 
621.3.032.213
DOI: 
10.18500/1817-3020-2026-26-2-175-184
EDN: 
QYOLXM

Predictive evaluation of barium evaporation ratefrom the surface of a porous metal thermionic cathode: A mathematical model based on experimental data for B- and M-type cathodes

Autors: 
Glukhova Olga E., Saratov State University
Krachkovskaya Tatiyana M., Joint Stock Company Research and Production Enterprise Almaz
Petrunin Alexander А., Saratov State University
Abstract: 

Background and Objectives: Based on the analysis of experimental studies regarding the evaporation rate patterns of the main component of the active substance – barium – from the surface of B- and M-type cathodes, a methodology for the predictive evaluation of its evaporation rate has been developed. Materials and Methods: The theoretical foundation of this methodology comprises the Langmuir formula for the rate of mass loss and the Clausius-Clapeyron equation. Results: The methodology yields a characteristic set of parameters for a given cathode type: p’0 (pressure), T0 (temperature), and q (activation energy). The effectiveness of the methodology has been demonstrated by predicting the temperature dependence of the barium evaporation rate for several B- and M-type cathodes, with the error in reproducing experimental data not exceeding 15%. New dependencies for the barium evaporation rate G(T) have been obtained for M-type cathodes containing ugleron (a sulfo-adduct of carbon nanoclusters) within the active substance in the concentration range of 0–0.4 wt%. It has been established that the evaporation rate of the active substance decreases with an increase in ugleron concentration. Conclusion: The developed methodology is promising for predicting the application of new nanomaterials in the composition of active substances for various types of thermionic cathodes.

Key words: 
porous metal cathode
evaporation rate
barium active substance
ugleron
differential evolution method
Acknowledgments: 
The work was supported the Ministry of Science and Higher Education of the Russian Federation within the framework of the State Assignment (project No. FSRR-2026-0006).
Reference: 
  1. Roy A. From radar to high-power weapons: Microwave tubes power modern warfare. Microwave Journal, 2024, vol. 67, no. 9, pp. 124–128.
  2. Litvak A. G., Denisov G. G., Glyavin M. Y. Russian Gyrotrons: Achievements and Trends. IEEE Journal of Microwaves, 2021, vol. 1, iss. 1, pp. 260–268. https://doi.org/10.1109/JMW.2020.3030917
  3. Gärtner G., Knapp W., Forbes R. G., eds. Modern Developments in Vacuum Electron Sources. Topics in Applied Physics. Springer, Cham, 2020, vol. 135. XVIII+597 p. https://doi.org/10.1007/978-3-030-47291-7
  4. Dubois B. Ch., Korolev A. N. Modern efficient cathodes. Elektronnaya tekhnika. Ser. 1. SVCh-tekhnika [Electronic Engineering. Ser. 1. Microwave Engineering], 2011, iss. 1 (508), pp. 5–24 (in Russian).
  5. Krachkovskaya T. M., Sahadji G. V., Zhuravlev S. D. Modern electron sources for TWTs in millimeter and submillimeter ranges. Zhurnal Radioelektroniki [Journal of Radio Electronics], 2017, no. 12 (in Russian).
  6. Kozlov V. I. Emission properties and durability of metalporous cathodes for microwave devices. Obzory po elektronnoi tekhnike. Ser. 1. Elektronika SVCh [Reviews on electronic technology. Ser. 1. Microwave Electronics]. Moscow, Elektronika Central Scientific Research Institute, 1983, iss. 8 (541). 54 p (in Russian).
  7. Shroff A. M. Review of dispenser cathodes. Revue Technique Thomson-CSF, 1991, vol. 23, pp. 948–1026. https://doi.org/10.5555/151680.151696
  8. Kudintseva G. A., Melnikov A. I., Morozov A. V., Nikonov B. P. Termoelektronnye katody [Thermoelectronic cathodes]. Moscow, Leningrad, Energiya, 1966. 366 p. (in Russian).
  9. Zyablikova A. N., Nekrasov V. I. Some parameters of impregnated cathodes coated with osmium. Elektronnaya tekhnika. Ser. 1. Elektronika SVCh [Electronic Engineering. Ser. 1. Microwave Engineering], 1970, no. 7, p. 157 (in Russian).
  10. Emelyanov A. S., Bogachev R. Yu., Zhuravlev S. D., Krachkovskaya T. M., Shesterkin V. I., Shumikhin K. V. Investigation of the evaporation rate of the active substance of a metal-porous cathode by the method of piezoelectric resonance. Vakuumnaya tekhnika i tekhnologii – 2022: trudy 29-j Vserossijskoj nauchno-tekhnicheskoj konferentsii s mezhdunarodnym uchastiem (Sankt-Peterburg, 21–23 iyunya 2022 g.). Pod red. D. K. Kostrina, S. A. Martsynyukova [Kostrin D. K., Martsynyukov S. A., eds. Vacuum technique and technologies – 2022: Proc. 29th All-Russian Sci.-Tech. Conf. with Int. Participation (St. Petersburg, June 21– 23, 2022)]. St. Petersburg, SPbGETU “LETI” Publ., 2022, pp. 24–26 (in Russian).
  11. Emelyanov A. S., Krachkovskaya T. M., Shesterkin V. I., Zhuravlev S. D., Biktimirova G. R., Shumikhin K. V. Influence of technological parameters and impregnation compositions on the evaporation rate of the active substance from the surface of metal-porous cathodes. 65 let deyatel’nosti na rynke SVCh-elektroniki: itogi i sovremennye tendentsii: materialy yubileinoi nauch.-tekhn. konf. AO “NPP ’Almaz’” [65 Years of Activity in the Microwave Electronics Market: Results and current trends: Materials of the anniversary sci.-tech. conf. JSC “NPP ‘Almaz’”]. Saratov, Saratov Technical University Press, 2022, pp. 33–37 (in Russian).
  12. Krachkovskaya T. M., Melnikov L. A., Glukhova O. E., Shunaev V. V., Shalaev P. D. Nanocarbon-Modified Metal Porous Cathodes with High Durability for Application in Microwave Devices. Technical Physics Letters, 2020, vol. 46, no. 7, pp. 673–676. https://doi.org/10.1134/S106378502007010X
  13. Heaney D. F. Vacuum sintering. In: Zhigang Zak Fang, ed. Sintering of Advanced Materials. [Amsterdam], Woodhead Publ., 2010, pp. 189–221. https://doi.org/10.1533/9781845699949.2.189
  14. Storn R., Price K. Differential evolution – A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 1997, vol. 11, no. 4, pp. 341–359. https://doi.org/10.1023/A:1008202821328
  15. Roquais J. M., Poret F., Doze R. le, Ricaud J. L., Monterrin A., Steinbrunn A. Barium depletion study on impregnated cathodes and lifetime prediction. Applied Surface Science, 2003, vol. 215, iss. 1–4, pp. 5–17. https://doi.org/10.1016/S0169-4332(03)00318-0
  16. Lai C., Wang J., Zhou F., Liu W., Engelsen D., Miao N. Emission and Evaporation Properties of 75 at% Re – 25 at% W Mixed Matrix Impregnated Cathode. Applied Surface Science, 2018, vol. 427, pp. 874–882. https://doi.org/10.1016/j.apsusc.2017.08.038
Received: 
02.02.2026
Accepted: 
07.04.2026
Published: 
30.06.2026
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