ABSTRACT
This chapter first discusses the sources of imperfections, such as additional dipole, quadrupole, or skew-quadrupole fields, followed by methods to describe them in the framework of transfer matrices. Then, the effect of the imperfections on the particles in a beam line, where they affect the orbit and the beam sizes, is described. In the following section on rings, the corresponding effects, but also the inuence on the tune and the generation of stop bands, are covered. The two following sections are devoted to the correction methods, first in beam lines and then in rings. Here, knobs to combine several magnets to affect a particular imperfections are discussed and complemented by several methods to correct the orbit, including dispersion-free steering. Advanced methods from linear algebra, such as singular-value decomposition to determine the excitations of the correction elements, are discussed in some detail. After methods to correct the tunes, chromaticities, and coupling, the analysis of the orbit-response matrix is covered in some detail.
