Ukraine, Kyiv, National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute".

A thermophysical model was built and the temperature field of a cylindrical thermionic cathode with induction heating was calculated, taking into account the initial and boundary conditions, based on the adoption of assumptions to simplify the mathematical model. During the induction heating of the cathode, a non-stationary heat conduction process is established, which is described by the differential equation of heat conduction with internal sources of Joule heat. The distribution of internal heat sources in the volume of the cathode is determined by the distribution of the ring induced current. The cylindrical design of the inductive thermionic cathode, due to spatial symmetry, allows to reduce the number of spatial variables, significantly simplify functional dependencies, and limit the algorithm for solving the problem. The problem was solved in the cylindrical coordinate system.
The obtained approximate solutions were assessed for the correctness of the accepted simplifications when finding the distribution of the temperature field with a sufficient degree of accuracy. Despite the high thermal conductivity of the cathode material, when the cathode is inductively heated, there can be a significant temperature difference between its outer and inner surfaces. The article shows the permissible temperature difference on the surface of the cathode, which limits the choice of geometric dimensions of the cathode. The temperature difference on the surfaces of the induction thermionic cathode is most affected on the end (annular) surfaces of the cathode, so it is better to apply emitting coatings to the side surfaces of the cylindrical cathode, thus complicating the design of the cathode.
The application of induction heating of the thermionic cathode allows to simplify the heating unit, increase the reliability and service life of powerful electronic devices. The obtained results are planned to be used in further research as test data for the analysis of more complex problems of numerical calculation of the thermal regimes of the cathode unit with heat shields and focusing elements of thermoelectron flows.

Keywords: thermionic cathode, induction heating, mathematical model, approximate solution, electronic devices.

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