  One of the main challenges of the lattice design of synchrotrons, used as
light sources or damping rings (DRs), is the minimization of the emittance. The
optimal lattice configurations for achieving the absolute minimum emittance are
the theoretical minimum emittance (TME) cells. This paper elaborates the
optimization strategy in order to further reduce the betatron emittance of a
TME cell by using dipoles whose magnetic field varies longitudinally. Based on
analytical results, the magnet design for the fabrication of variable bends
with the optimal characteristics is discussed. In order to have a global
understanding of all cell properties, an analytical approach for the
theoretical minimum emittance (TME) cells with variable bends is elaborated.
This approach is employed for the design optimization of the Compact Linear
Collider (CLIC) DRs. The margin gained in the emittance including IBS based on
this new design strategy enables the removal of a number of TME cells from the
existing arcs while still keeping the requirements of the collider. The
reduction of the circumference is further enhanced by the use of optimized
high-field wigglers. The optimization strategy followed for the CLIC DRs is
explained in detail and the output parameters of the new design are presented.
