Low-emittance Storage Rings

The effects of synchrotron radiation on particle motion in storage rings are discussed. In the absence of radiation, particle motion is symplectic, and the beam emittances are conserved. The inclusion of radiation effects in a classical approximation leads to emittance damping: expressions for the damping times are derived. Then, it is shown that quantum radiation effects lead to excitation of the beam emittances. General expressions for the equilibrium longitudinal and horizontal (natural) emittances are derived. The impact of lattice design on the natural emittance is discussed, with particular attention to the special cases of FODO-, achromat- and theoretical-minimum-emittance-style lattices. Finally, the effects of betatron coupling and vertical dispersion (generated by magnet alignment and lattice tuning errors) on the vertical emittance are considered.