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In order to achieve luminosities significantly higher than in existingmachines, future storage-ring based colliders will need to operate in novelparameter regimes combining ultra-low emittance, large Piwinski angle and highbunch charge; implementation of techniques such as a "crab waist" will addfurther challenges. Understanding the beam-beam interaction in these situationswill be essential for the design of future very high luminosity colliders.Recent developments in modeling tools for studying beam-beam effects, capableof investigating the relevant regimes, will be discussed and examples,including tests with crab waist collisions in DAFNE, will be presented.

Beam-Beam Interaction in Novel, Very High Luminosity Parameter Regimes