Stability assessment of an optimized cooling configuration of a fusion gyrotron resonant cavity through an analytical model

One of the main issues for the gyrotrons remains an efficient cooling of the resonant cavity, as the high amount of energy released on its inner wall leads to high temperatures, cavity expansion, and subsequent frequency down-shifts in the electromagnetic power, reducing the efficiency of the tube, resulting in a multi-physics problem. Moreover, the heat load released is not uniform, causing thermal gradients in the cavity structure and, consequently, thermal stresses. In a previous optimization study, a Biogeography-Based optimization algorithm was used to determine an optimized axial profile for the heat transfer coefficient (HTC) of the cavity coolant. A straightforward engineering solution, based on an annular region for the coolant passage, was designed to achieve the identified HTC profile. However, even with the optimized HTC the cavity wall will still experience displacements, potentially changing the cooling system configuration and, consequently, the expansion. In the present study a stability analysis of the mentioned optimized cooling configuration is performed by means of a 0D model. A linearization of the model is performed, including the linear thermal expansion of the metal, and the stability of the system is verified. Then, the response in time of the linear model is validated through a comparison with the non-linear one.