Possible resonance free lattices for the VLHC

A systematic search for resonance-free lattices has been performed. Numerous solutions exist for sets of about fifty cells. A VLHC-like machine could be made of blocks of 61 cells which are free from resonances up to tenth order. A tracking test shows a 20% improvement of the dynamic aperture with respect to standard cells, for several multi-pole components. It opens the possibility of relaxing the constraints on systematic multipole components for the cells. The tolerances on field quality will then be by chromatic and an-harmonic effects of the mul-tipole components.