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Modeling a Temperature Distribution of Thermionic Energy Converter Components Cover

Modeling a Temperature Distribution of Thermionic Energy Converter Components

Open Access
|Dec 2025

Figures & Tables

Fig. 1.

Normalized electron thermionic emission current of a dispenser cathode operating at 1373.2 K as a function of metal temperature (based on [10, 11])
Normalized electron thermionic emission current of a dispenser cathode operating at 1373.2 K as a function of metal temperature (based on [10, 11])

Fig. 2.

Normalized electron thermionic emission current of a dispenser cathode operating at 1373.2 K as a function of metal vapor pres-sure (based on [10, 11])
Normalized electron thermionic emission current of a dispenser cathode operating at 1373.2 K as a function of metal vapor pres-sure (based on [10, 11])

Fig. 3.

Schematic diagram of a thermionic energy converter
Schematic diagram of a thermionic energy converter

Fig. 4.

S. Distribution of potential energy of an electron in the cathodeanode region for an ideal converter (based on [12, 13])
S. Distribution of potential energy of an electron in the cathodeanode region for an ideal converter (based on [12, 13])

Fig. 5.

Model of current-voltage characteristics for an ideal converter and a real converter, taking into account the influence of negative space charge in the cathode-anode area. d is the mutual distance between the cathode and the anode
Model of current-voltage characteristics for an ideal converter and a real converter, taking into account the influence of negative space charge in the cathode-anode area. d is the mutual distance between the cathode and the anode

Fig. 6.

Model of a vacuum thermionic heat-to-electric energy converter test stand. 1 – manipulator, 2 – vacuum electrical feedthroughs, 3 – vacuum chamber, 4 – viewing window, 5 - vacuum gauge, 6 - test stand frame
Model of a vacuum thermionic heat-to-electric energy converter test stand. 1 – manipulator, 2 – vacuum electrical feedthroughs, 3 – vacuum chamber, 4 – viewing window, 5 - vacuum gauge, 6 - test stand frame

Fig. 7.

Virtual model of the chamber in a semi-cross-section view, adapted for numerical analysis. 1 – manipulator core, 2 – ceramic cathode pad, 3 – cathode mounting base, 4 – internal cathode insulation (half-cross-section view), 5 – cathode heater, 6 – cathode front surface, 7 – anode, 8 – anode mounting base, 9 – borosilicate glass of the viewfinder, 10 – ceramic anode pad
Virtual model of the chamber in a semi-cross-section view, adapted for numerical analysis. 1 – manipulator core, 2 – ceramic cathode pad, 3 – cathode mounting base, 4 – internal cathode insulation (half-cross-section view), 5 – cathode heater, 6 – cathode front surface, 7 – anode, 8 – anode mounting base, 9 – borosilicate glass of the viewfinder, 10 – ceramic anode pad

Fig. 8.

Discrete model of the test chamber
Discrete model of the test chamber

Fig. 9.

Temperature distribution in the test chamber model
Temperature distribution in the test chamber model

Fig. 10.

Temperature distribution in the cathode model
Temperature distribution in the cathode model

Fig. 11.

Temperature distribution in the anode model
Temperature distribution in the anode model

Fig. 12.

Temperature distribution in the cathode mounting base model
Temperature distribution in the cathode mounting base model

Fig. 13.

Temperature distribution in the anode mounting base model
Temperature distribution in the anode mounting base model

Fig. 14.

Temperature distribution in the model of the cathode ceramic pad surface
Temperature distribution in the model of the cathode ceramic pad surface

Fig. 15.

Temperature distribution in the manipulator core model
Temperature distribution in the manipulator core model

Fig. 16.

Temperature distribution in the model of the anode ceramic pad surface
Temperature distribution in the model of the anode ceramic pad surface

Fig. 17.

A comparative graph of the maximum cathode base temperature for three materials as a function of heater temperature
A comparative graph of the maximum cathode base temperature for three materials as a function of heater temperature

Fig. 18.

A comparative graph of the maximum anode temperature for three materials as a function of cathode temperature
A comparative graph of the maximum anode temperature for three materials as a function of cathode temperature

Temperature values of key converter components as a function of tungsten microheater temperature for design with molybdenum bases

Theater [K]873.2973.21073.21173.21273.21373.21473.2
CathodeTaverage795.5879.9964.21048.61132.81217.01300.7
Tmax873.2973.21073.21173.21273.21373.21473.2
Tmin520.9550.4579.9609.3638.7668.0697.2
Cathode baseTaverage516.4544.9573.5602.0630.5658.9687.2
Tmax649.4704.5759.6814.5869.4924.2978.6
Tmin450.6466.1481.5497.0512.4527.8543.1
AnodeTaverage397.9432.1468.8507.7548.6590.8633.6
Tmax408.0447.6491.8540.5593.7651.4713.1
Tmin404.0441.5482.7527.6575.9627.5681.6
AnodebaseTaverage397.8432.0468.6507.4548.2590.3632.9
Tmax400.1435.5473.8514.9558.5604.0650.9
Tmin396.7430.3466.1503.8543.3583.7624.3

Temperature values of key converter components as a function of tungsten microheater temperature for design with copper bases

Theater [K]873.2973.21073.21173.21273.21373.21473.2
CathodeTaverage779.4860.6941.81022.91104.01185.01266.0
Tmax873.2973.21073.21173.21273.21373.21473.2
Tmin509.1536.3563.5590.6617.7644.7671.7
Cathode baseTaverage509.1536.2563.3590.4617.5644.5671.5
Tmax570.4609.8649.2688.5727.8767.0806.2
Tmin474.9495.3515.6535.9556.2576.4596.7
AnodeTaverage402.3438.9479.0522.3568.7618.0669.7
Tmax406.3445.1488.0535.2586.6642.0701.4
Tmin397.4431.3467.7506.2546.5588.2630.5
Anode baseTaverage397.4431.3467.6506.1546.5588.1630.4
Tmax398.2432.5469.5508.8550.1593.0636.9
Tmin396.9430.6466.6504.7544.4585.3626.9

Thermal and physical properties of materials used in the model

MaterialThermal Conductivity[W/(m·K)]Specific heat[J/(kg·K)]Density[kg/m3]Emissivity[–]
Stainless Steel 316L16.2500.080000.28
Molybdenum (Mo)138.0250.0102000.05
Copper (Cu)398.0385.089600.03
Aluminum Oxide (Al2O3)30.0880.039600.25
Pyrex 7740 borosilicate glass1.14830.022300.92

Temperature values of key converter components as a function of tungsten microheater temperature in a design with bases made of 316L steel

Theater [K]873.2973.21073.21173.21273.21373.21473.2
CathodeTaverage839.7932.81025.81118.71211.41304.01396.4
Tmax873.2973.21073.21173.21273.21373.21473.2
Tmin555.7592.1628.4664.6700.7736.6780.4
Cathode baseTaverage540.1573.4606.6639.6672.6705.5738.2
Tmax817.3905.7993.81081.51169.01255.91359.1
Tmin393.4397.5401.6405.8409.9414.0417.8
AnodeTaverage420.3465.9517.9576.2640.0709.3783.6
Tmax424.8472.8528.0590.4659.4735.1817.8
Tmin403.4440.1480.1523.0567.9614.5662.2
Anode baseTaverage402.2438.2477.4519.3562.9607.9653.8
Tmax417.9462.2512.5568.5629.5695.3764.8
Tmin394.8426.9461.0496.5532.2567.9603.2
DOI: https://doi.org/10.2478/ama-2025-0072 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Language: English
Page range: 644 - 652
Submitted on: Aug 12, 2025
Accepted on: Nov 3, 2025
Published on: Dec 19, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2025 Krzysztof SKIBA, Dariusz KUŚ, Jarosław SIKORA, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.