Emittance reduction with variable bending magnet strengths: Analytical optics considerations and application to the Compact Linear Collider damping ring design

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 on 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 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.