I.K. Belova1, E.O. Deryugina2, I.V. Chukhraev3

1-3 Kaluga branch of Bauman Moscow State Technical University (Kaluga, Russia)

Currently, high-current plasma systems (SPS) are widely used in various fields of science and technology. These include low-temperature plasma generators, which are used in physico-chemical research, high-temperature technologies, plasma metallurgy and welding production; plasma accelerators and ion injectors - in plasmodynamics and plasma optics, rocket and space and vacuum technology; sources of high-intensity radiation - solving problems of quantum electronics, radiation heating of aircraft when simulating the entrance to dense layers of the atmosphere, etc.

The solution of the problem of improving and creating new SPS is closely related to the problem of increasing the life of the ATP electrodes and, in particular, the cathodes of the elements in direct contact with the discharge plasma under extreme conditions in terms of heat fluxes, radiation emissions, temperatures and current densities.

Today, analytical and experimental studies of thermophysical processes in thermal cathodes have been carried out, the connection of the readiness time of devices with the heating time of thermal cathodes has been established, the analysis of the thermal balance of cathodes has been carried out, the equation of thermal conductivity has been derived. The equation of thermal conductivity is used to analyze thermal processes in real cathodes of direct and indirect incandescence. As a result of computational and theoretical studies, the main physical factors affecting the heating duration and emission parameters of low-inertia cathodes have been determined. The electrophysical and emission parameters of model thermocathodes have been studied. A physicomathematical model describing the processes and evolution of the system «activated thermionic cathode - gas-discharge plasma» has been constructed, with the help of which the thermophysical state of high-current cathode nodes of plasma devices, physical laws of the processes of electro- and heat-mass transfer of emissively activated thermocathodes have been studied.

One of the main parameters of the thermal diode is its output to the stationary mode. The article presents formulas for calculating this parameter for ideal and real cathodes operating in various conditions: in vacuum and gas environment. The general equation of thermal conductivity is shown, which allows a qualitative analysis of the cathode heating process and is the mathematical basis for obtaining the equations of the heating process of real cathodes. The presented mathematical apparatus is ready for use in software tools that allow complex mathematical calculations and can become part of the mathematical support of information systems for calculating thermophysical parameters of thermocathodes for high-current plasma systems.

Belova I.K., Deryugina E.O., Chukhraev I.V. Mathematical support of the information system for calculating the thermophysical parameters of thermocathodes of high-current plasma systems. Science Intensive Technologies. 2022. V. 23. № 6. P. 12−20. DOI: https://doi.org/10.18127/j19998465-202206-02 (in Russian)

1. Cydypov B.D. Teplomassoperenos i dinamika katodnyh i prikatodnyh processov sil'notochnyh plazmennyh sistem: Dis. … dokt. tekhn. nauk. Ulan-Ude, 2011. 258 s. URL: https://www.dissercat.com/content/teplomassoperenos-i-dinamika-katodnykh-i-prikatodnykh-protsessov-silnotochnykh-plazmennykh-s. Rezhim dostupa: DisserCat. Elektronnaya biblioteka dissertacij (in Russian).
2. Galanin M.P., Rodin A. S. Issledovanie i primenenie metoda dekompozicii oblasti dlya modelirovaniya teplovydelyayushchego elementa. Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 2022. T. 62. № 4. S. 659–676. URL: http://mi.mathnet.ru/rus/zvmmf/ v62/i4/p659. Rezhim dostupa: Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki (in Russian).
3. Zlotnik A.A., Zlotnik I.A. Bystrye Fur'e-solvery dlya MKE vysokogo poryadka s tenzornymi proizvedeniyami dlya uravneniya tipa Puassona. Zhurnal vychislitel'noj matematiki i matematicheskoj fiziki, 2020. T. 60, № 2. C. 234–252. URL: http://mi.mathnet.ru/zvmmf11033. Rezhim dostupa: ZHurnal vychislitel'noj matematiki i matematicheskoj fiziki (in Russian).
4. Bogovskij M.E. Uravneniya matematicheskoj fiziki: uchebnoe posobie. Moskovskij fiziko-tekhnicheskij institut (gosudarstvennyj universitet). M.: MFTI, 2019. 106 s. (in Russian).
5. Belova I.K., Deryugina E.O. Emissionnye parametry termokatodov v razryade nizkogo davleniya. Elektromagnitnye volny i elektronnye sistemy. 2013. № 10. C. 59–57 (in Russian).
6. Petrov I.B. Vychislitel'naya matematika dlya fizikov: Uchebnik dlya vuzov. M.: Fizmatlit, 2021. 376 s. (in Russian)
7. Belova I.K. Modelirovanie teplovyh processov ideal'nogo termokatoda s ispol'zovaniem paketa prikladnyh programm MathCad. Inzhenernyj zhurnal: nauka i innovacii. 2014. Vyp. 8. URL: http://engjournal.ru/catalog/machin/energy/1276.html Rezhim dostupa: Inzhenernyj zhurnal: nauka i innovacii (in Russian).
8. Gagarina S.N., Gagarin Yu. E. Interval'noe prognozirovanie ob"emov sprosa na uslugi sub"ektov estestvennyh monopolij s uchetom neopredelennosti informacii. Vestnik universiteta. 2013. № 22. S. 101–110 (in Russian).