Collision monochromatization in $e^+e^-$ colliders

The manuscript describes several monochromatization schemes starting from A. Renieri’s [Report No. LNF-75/6(R)] proposal for head-on collisions based on correlation between particles transverse position and energy deviation. We briefly explain the initial proposal and expand it for crossing angle collisions. Then we discuss new monochromatization scheme for crossing angle collisions based on correlation between particles longitudinal position and energy deviation.