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Extra info for CAS-CERN Accelerator School - Meas. and Alignment of Accel and Detector Magnets
Similarly, it can be shown that magnetic flux density produced by the current shell of Fig. 5(b) is given by Eq. (12), where ⑥ 2 0J ✈ B2 = Ro ln R i ①②③ ✇ ④ ⑤ sin2 0 (23a) ⑦ and B4k+2 = ✇ 0J ⑥ 1 1 – 4k 4k k(4k+2) Ri Ro ✈ ①②③ ④ sin[ (4k+2) 0] ⑦ ⑤ for k, k ³ 1 (23b) Note that B2 corresponds to the quadrupole field gradient, g, and that B6 (first allowed multipole field coefficient after B2 in a current distribution with a quadrupole symmetry) is nil for 0 = /6. 1 Symmetry considerations The field computations carried out in the previous section have shown that current distributions with the symmetries of Fig.
In a dipole coil, the Lorentz force has three main components which are represented Fig. 6 (38, 60): (1) an azimuthal component which tends to squeeze the coil towards the coil assembly midplane (which, in the coordinate system defined previously, corresponds to the horizontal ( x , z ) plane), (2) a radial component which tends to bend the coil outwardly, with a maximum displacement at the coil assembly midplane (along the horizontal x-axis), and (3) an axial component, arising from the solenoidal field produced by the conductor turnaround at the coil ends and which tends to stretch the coil outwardly (along the z-axis).
CAS-CERN Accelerator School - Meas. and Alignment of Accel and Detector Magnets