Impact of Thermal Radiation by Electron Beam on Inner Thermal State of Traveling Wave Tube

In this article, the impact of thermal radiation by the electron beam on the inner thermal state of a traveling wave tube (TWT) under operation is explored. A theoretical model for analyzing heat transfer by thermal radiation from the cylindrical electron beam is derived, in which the electron beam is treated as an equivalent dynamic circular disk with gray-body radiation from its side surface. By using the cathode temperature and the compression ratio of the electron beam in a TWT, the temperature of the equivalent disk is calculated. By considering the Bremsstrahlung radiation and the cyclotron radiation, the power radiated from the electron beam is derived, and the emissivities of the gray-body radiation from the equivalent disk are calculated. Using the parameters of a wideband TWT, we obtain the heat transfer via thermal radiation from the electron beam and conduct thermal analysis by simulation with and without considering thermal radiation from the electron beam, respectively. The result at 11 GHz shows that the temperature rise on the inner surface of the helix tape due to thermal radiation from the electron beam is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.67~^{\circ }$</tex-math> </inline-formula>C and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.49~^{\circ }$</tex-math> </inline-formula>C at the beginning/ending point of the helix, respectively. In the working frequency band, the temperature rise at the beginning point of the helix ranges from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.65~^{\circ }$</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.72~^{\circ }$</tex-math> </inline-formula>C, while that at the ending point ranges from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.46~^{\circ }$</tex-math> </inline-formula>C to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$0.52~^{\circ }$</tex-math> </inline-formula>C.