Modeling of the thermal regulation of IPHI's RFQ - Calculation note

The surface currents generated by the Radio Frequency (RF) power supply (352 MHz) to IPHI's Radio Frequency Quadrupole (RFQ) accelerator cavity heat it up significantly (210 W/cm² locally at some ends, 16 W/cm² in the right-hand section). This heat is dissipated by water circulating in cooling channels running through the blades, but nevertheless leads to deformation of the cavity transverse profile. Thermo-mechanical modelling of the cross-sections using finite elements, enables us to estimate the displacements and stresses undergone by the cavity during operation in its central section. The new profile obtained can then be transmitted to the HF Superfish calculation code, in order to calculate the section's new tuning frequency. By taking into account the heating of the water circulating in the cooling channels, it is also possible to evaluate, for the RFQ in operation, the regulation that will induce the minimum frequency shift. The first part of this note describes the finite-element modeling of the thermo-mechanical behavior of the straight sections of the cavity (carried out on Castem2000 2D software). The second part describes how the overall behavior of the RFQ and its control system can be modeled, by successively using such modeling on several sections. Its aim is not to give results on the thermo-mechanical behavior of the cavity, but rather to describe how the regulation of the complete RFQ can be modeled