The Large Hadron Collider (LHC) is scheduled to come on line in 2007.
 Its performance will ultimately be limited by a number of accelerator-physics constraints,
 such as intra-beam scattering, long-range beam-beam collisions,
 collimation, machine protection,
 and electron cloud. Several of these aspects are presently under
 experimental study at the CERN
 SPS. Beyond the baseline design, 10 times higher luminosities can be
 achieved by an upgraded LHC operating with long super-bunches, confined by rf barrier buckets.
 Super-bunch operation would alleviate most of the limitations impeding the baseline LHC. A
 future linear collider, e.g., a Higgs-factory, could operate in parallel to the LHC or its upgrade.
 Many of the challenges for such a collider, e.g., collimation, machine protection, or electron
 cloud, will be similar to those encountered by the LHC.