The main aim of this work is to present a simple method, based on analytical expressions, for obtaining the temperature increase due to the Joule effect inside the metallic walls of an RF accelerating component. This technique relies on solving the 1-D heat-transfer equation for a thick wall, considering that the heat sources inside the wall are the ohmic losses produced by the RF electromagnetic fields penetrating the metal with finite electrical conductivity. Furthermore, it is discussed how the theoretical expressions of this method can be applied to obtain an approximation to the temperature increase in realistic 3-D RF accelerating structures, taking as an example the cavity of an RF electron photoinjector and a traveling wave linac cavity. These theoretical results have been benchmarked with numerical simulations carried out with commercial finite-element method (FEM) software, finding good agreement among them. Besides, the advantage of the analytical method with respect to the numerical simulations is evidenced. In particular, the model could be very useful during the design and optimization phase of RF accelerating structures, where many different combinations of parameters must be analyzed in order to obtain the proper working point of the device, allowing to save time and speed up the process. However, it must be mentioned that the method described in this article is intended to provide a quick approximation to the temperature increase in the device, which of course is not as accurate as the proper 3-D numerical simulations of the component.

The main aim of this work is to present a simple method, based on analytical expressions, for obtaining the temperature increase due to the Joule effect inside the metallic walls of an RF accelerating component. This technique relies on solving the 1-D heat-transfer equation for a thick wall, considering that the heat sources inside the wall are the ohmic losses produced by the RF electromagnetic fields penetrating the metal with finite electrical conductivity. Furthermore, it is discussed how the theoretical expressions of this method can be applied to obtain an approximation to the temperature increase in realistic 3-D RF accelerating structures, taking as an example the cavity of an RF electron photoinjector and a traveling wave linac cavity. These theoretical results have been benchmarked with numerical simulations carried out with commercial finite-element method (FEM) software, finding good agreement among them. Besides, the advantage of the analytical method with respect to the numerical simulations is evidenced. In particular, the model could be very useful during the design and optimization phase of RF accelerating structures, where many different combinations of parameters must be analyzed in order to obtain the proper working point of the device, allowing to save time and speed up the process. However, it must be mentioned that the method described in this article is intended to provide a quick approximation to the temperature increase in the device, which of course is not as accurate as the proper 3-D numerical simulations of the component.