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.

Figure 1

Monochromatization scheme for head-on collisions.

Figure 2

Collision geometry.

Figure 3

Crossing angle collision with opposite dispersion.

Figure 4

Crossing angle collision with opposite dispersion.

Figure 5

Hour-glass reduction factor.

Figure 6

Monochromatization for crossing angle collision with correlation between particle’s energy and longitudinal position.

Figure 7

Colliding beam ellipses in longitudinal plain, showing correlation between collision energy deviation $\delta$ and longitudinal position $z$.

Figure 8

Sketch of rf cavities of the toy ring.