Effect of the Sextupole Finite Length on Dynamic Aperture in the Collider Final Focus

In a collider final focus (FF) system chromaticity generated by FF quadrupoles is compensated by sextupole pairs with -I map in between to cancel geometrical aberrations. However, it works perfectly only for zero-length sextupole kicks; for realistic thick magnets only quadratic aberrations are cancelled exactly while higher order terms appear and may deteriorate the transverse dynamic aperture. The latter is particularly important for prospective projects of the future circular colliders based on the Crab-Waist collision approach where extremely low beta at IP generates very large chromatic effects. In the present paper, we study these high aberrations by the power series technique and propose the method of the dynamic aperture recover. Results of analytic study are compared with those obtained by tracking.