ABSTRACT
In a colliding-beam storage ring, the beam-beam interaction is the collective, relativistically enhanced, transverse electromagnetic force experienced by a beam particle as it passes through a bunch of the opposing beam. Every time a particle of one beam passes through a bunch of the opposing beam, it experiences a transverse kick which changes the amplitude of its vertical and horizontal betatron oscillation. 692The beam-beam kicks are important because they can cause the amplitudes of both the vertical and horizontal betatron oscillations to increase, either via diffusion caused by a sequence of uncorrelated kicks, or via resonant pumping caused by a sequence of highly correlated kicks. This growth of betatron amplitudes can cause loss of luminosity and/or beam lifetime. To investigate analytically (and numerically) the cumulative effect of many beam-beam kicks, a mathematical model is needed. This model necessarily involves several approximations (historically, the usual approach has been to start with as many approximations as possible, removing them one-by-one, as one-by-one they prove to be unrealistic). https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/fig43_1.tif"/> https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/fig43_2.tif"/> (a) Diffusive kicks (b) Resonant kicks (c) Regular oscillation https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003069515/f3ef54a9-ca7f-48a5-bad6-5d54427f48cf/content/fig43_3.tif"/>
