Beam Dynamics Challenges for Future Circular Colliders

The luminosity of hadron colliders rises with the beam intensity, until some limit is encountered, mostly due to head-on and long-range beam-beam interaction, due to electron cloud, or due to conventional impedance sources. Also beam losses caused by various mechanisms may affect the performance. The limitations can be alleviated, if not overcome, by a proper choice of beam parameters and by dedicated compensation schemes. Examples include alternating crossing at several interaction points, electromagnetic wires, super-bunches, electron lenses, clearing electrodes, and nonlinear collimation. I discuss such mitigating measures and related research efforts, with special emphasis on the LHC and its upgrade.