Analytical considerations for linear and nonlinear optimization of the TME cells. Application to the CLIC pre-damping rings

The theoretical minimum emittance cells are the optimal configurations for achieving the absolute minimum emittance, if specific optics constraints are satisfied at the middle of the cell's dipole. Linear lattice design options based on an analytical approach for the theoretical minimum emittance cells are presented in this paper. In particular the parametrization of the quadrupole strengths and optics functions with respect to the emittance and drift lengths is derived. A multi-parametric space can be then created with all the cell parameters, from which one can chose any of them to be optimized. An application of this approach are finally presented for the linear and non-linear optimization of the CLIC Pre-damping rings.