CLIC Main Beam Quadrupole Eigen Mode computation

In this report, we summarise the work done on the CLIC Main Beam Quadrupole. There are about 4000 MB quadrupoles of 4 types with lengths ranging from 420mm to 1900mm. In order to obtain the desired CLIC luminosity, the MB quadrupoles have to be stable to 1nm above 1Hz. The region of interest for the study is between 0.5Hz and about 100Hz. In order to achieve the specifications, the magnet should not have any resonance peaks in this region of Interest. In addition, the magnet on its support shouldn’t have any resonance peak in the same frequency range. The first step is to determine if the designed magnet has its first resonance peak above 100Hz. We are studying the longest quadrupole more susceptible to internal resonances. In a second step, the magnet on ideal supporting points has been evaluated. The current magnet design can be seen on following figure. One can see that it is composed of 4 quadrants assembled so as to have a quadrupole magnetic field. As a last step, the mechanical model has been used to study the influence of the quadrant assembly. Note that in this report, the quadrant design varies slightly from one calculation to another since these studies have been performed in parallel with the magnet design process. It can be noticed that the results of the calculations are not significantly influenced by these design variations. In the last paragraph, the latest design has been considered to build finite element model.