THE GEOMETRY OF THE MAIN DIPOLE

The main lines of discussion and analysis for the LHC dipole geometry are related to the shape of the cold mass at different stages of production and tests. The limitations in the stability of the cold mass shape induces constraints for the positioning of the spool pieces (feed down effects), for the flanges (interconnectivity) and the overall shape (aperture considerations). The geometry after acceptance in industry may change by the time of measurements at CERN. Tolerances that are needed by hardware and by beam physics will be reviewed. GEOMETRY OF THE DIPOLE The theoretical geometry of the dipole is shown in figure 1, and a table of some of the important parameters are given in table 1. The (x,y) plane is the plane of the accelerator. The two theoretical beam-trajectories (the two bent curves in figure 1) consist of an arc of a circle with the angle Θ and the radius ρ and of straight lines between magnets. The 3 dimensional measurements of the centre of the two cold bore tubes are fitted to the two theoretical curves. The plane obtained in this way is called the mean plane and the axes the geometrical axes. Table 1: Dipole geometry parameters at room and operational temperature Parameter Symbol Value warm Value cold Unit Bending angle per dipole Θ 5.0999988 5.099988 mrad Magnetic length of each aperture lm 14.343 14.300 m Radius of curvature r 2812.360 2803.9281 m Separation of tube centers d 194.52 194 mm Sagitta s 9.143 9.116 mm We are interested in the excursions of the cold bore tube relative to the theoretical shape, in the sagitta s, the positions of the spool pieces (MCS and MCDO), as well Θ ρc lc Θ/2