Beam-Beam Simulations for Lepton Machines

We survey the range of techniques for numerical simulation of the beam-beam interaction in circular colliders in which synchrotron radiation is present. These include techniques used in weak-strong, quasi-strong-strong, and strong-strong simulations. Self-consistent strong-strong simulations usually use macroparticle-in-cell methods with a variety of refinements to increase the computational speed. Other approaches include macroparticle sampling methods and numerical solution of the Vlasov equation. We also describe and compare the existing beam-beam simulation codes for circular lepton colliders