Crossing Angle Collision and Lifetime: Simulations, Analysis, Measurements and More Simulations

The introduction of a crossing angle in e+ecolliders causes nonlinear coupling between horizontal motion and longitudinal motion. This is illustrated in Figure 1. The beam-beam kick occurs when the particle passes the center of the opposing bunch. The strength of the kick, ∆r' = F(r), is a nonlinear function of the distance, r, between the particle and the center of the opposite bunch. In head-on collisions, r is the transverse displacement, and the kick is in the transverse plane, so that the process is nonlinear but not influenced by the longitudinal motion. In collisions with a crossing angle, however, r is a function of longitudinal displacement, s, and the crossing angle, Φ, as well as transverse displacement. The distance r between the test particle and the bunch center can be written as: