| In the future, multi-TeV high-luminosity linear collider systems will require ultra-low-emittance damping rings. By greatly increasing the density of particles within a bunch, the damping rings drastically improve the luminosity of the collision point. Also, the damping process must be done very quickly in order to supply a new bunch to the linear accelerator within about a millisecond.;The model damping ring proposed in this thesis pushes the practical lower limit of equilibrium emittance by including many strong wigglers in dispersion-free straight sections to help in the damping. This damping, in turn, reduces the equilibrium emittance. Quantum excitation is kept low by choosing a large circumference (2 km) and strongly focusing quadrupoles (FODO-unit-cell length of 7 m). The emittance achieved at 4 GeV is 2.5 ;Both the use of strong quadrupoles and large circumference lead to particularly strong sextupoles for chromatic correction to counter the head-tail instability. Unfortunately, sextupoles induce another type of instability, that of transvere-oscillation amplitude growth, which limits the lifetime of the stored beam. The resonant motion originates from the nonlinearity of the sextupole field and exists in all low-emittance lattices. The effects of sextupole geometric aberrations are reduced by applying the achromat concept in transport beamlines (FODO-cell modules with self-compensating sextupoles). The calculated dynamic aperture (maximum stable amplitude for transverse nonlinear oscillations) for horizontal and vertical oscillations is surprisingly big for the magnetic lattice proposed. In contrast, conventional sextupole arrangements produce a dynamic aperture at least three times smaller.;The self-compensating sextupole configuration would be perfect except for the effects of the sextupole magnet thickness. An analytical formula for the sextupole-thickness aberrations is derived, and immediately reveals that octupolar fields can selectively cancel out some of the strongest aberration terms. An increase in dynamic aperture of at least 30% is calculated. Thus this octupole correction scheme offers the convenience of "shaping" the dynamic aperture in the horizontal and vertical planes according to one's needs. |
