Peter Woit suggests at Not Even Wrong,
For many years now discussion in the HEP community of what might be the appropriate next machine to try and finance and build after the LHC has centered around the idea of a linear electron-positron collider. The logic has been that an electron-positron machine would provide a much better environment that the LHC for detailed studies of physics at the TeV scale. At these energies, synchrotron radiation losses when accelerating electrons are so high in a circular geometry that such a machine would have to be a linear collider to keep the power needed something plausible. The two main proposals under study have been the ILC (250 GeV + 250 GeV, later upgradeable to 500 GeV + 500 GeV) and, a less mature technology, CLIC (1.5 TeV + 1.5 TeV). These would be very expensive machines to build and operate ($10 billion and up?), requiring completely new technology, tunnels and detectors. More.