Observation and simulation of nonlinear behavior of betatron oscillations during the beam-beam collision

It has been found that, when electron and positron beams collide in a storage ring, the space charge force of one of the beams gives the other beam a transverse kick. This beam-beam force is nonlinear. When an additional kick is applied to the beam, coherent oscillations will occur. It is pointed out that it is difficult to solve such a nonlinear forced oscillation analytically and exactly. Therefore, the nonlinear oscillation was investigated experimentally by using a tune measurement system. In addition, a simple program was used to simulate the nonlinear beam-beam force.<>