|MadSci Network: Physics|
There is one very realistic plan on the table for a post-LHC collider. It is usually called the ILC (International Linear Collider). You will also hear references to the NLC ("Next Linear Collider"), or TESLA ("Tera-Electron volt Superconducting Linear Accelerator") or JLC ("Japan Linear Colider"), but you can think of these as different options for how to build the ILC.
Unlike LHC, which collides protons from a pair of 7 TeV circular accelerators, the ILC will collide electrons and positrons from a pair of 1-TeV (or thereabouts) straight-line electron-positron colliders.
You will notice that the ILC energy is lower than the LHC energy. The luminosity will probably also be lower. Therefore, the ILC probably cannot create any new particles which were not already created at LHC. If the LHC does not make SUSY particles, black holes, the Higgs, etc., then it is very likely that the ILC will not make them either. What's the point, then? Well, the LHC's proton-proton collisions are very messy. There are thousands of different ways for the protons' multiple quarks and gluons to interact, and all of these interactions have to be disentangled in order to search for a new rare type of event. By contrast, the ILC's electron-positron collisions are very simple. The events are much easier to analyze; the analysis can be very precise; the backgrounds are easy to predict, and can be made fairly low by choosing the right energy for the beams. Thus, we hope to discover new physics at the LHC (SUSY, the Higgs, extra dimensions, gravity?) by picking out a few events among the huge backgrounds. Then, we hope to study these new particles at the ILC, by producing thousands of them in a low-background environment.
So, you should take everything you know about LHC physics---black hole production, SUSY, Higgs, large extra dimensions---and think of the ILC as doing the same thing with lower backgrounds. Yevgeniy, since I know you are interested in black holes and strangelets, I should point out that a) ILC will be less likely than LHC to produce black holes, since the energies will be lower, and b) ILC will have essentially no chance of producing strangelets, since e+ e- collisions do not involve large numbers of quarks. You can read more about the ILC at linearcollider.org.
There are a few other ideas for future colliders: a muon collider, which would do ILC-like physics at higher energies as well as provide intense neutrino beams. There is some thought about a VLHC (Very Large Hadron Collider), resembling LHC but reaching 60+ TeV. (Again, when thinking about black holes or whatever at the VLHC, you can apply everything you know about black holes at the LHC. The underlying physics is the same; it would search for the same phenomena, just in a higher energy region.) There are also several ideas for accelerators (not colliders!) to create especially-intense neutrino beams; these include the fascinating "beta beam" proposals (an oval accelerator carrying beta-decaying radioactive nuclei) and various ideas for high-intensity, medium-energy proton accelerators (sometimes called "proton drivers" or "neutrino factories").
These machines may never be built at all, though. The obstacles are: 1) What are they looking for? If LHC sees nothing new, what makes us think that a VLHC will have more luck? 2) Are they possible at all? Accelerator engineers can do amazing things, but they can't change the basic laws of particle motion; maybe these laws will make some accelerators (especially the muon collider) physically impossible. 3) Who is willing to spend $10 billion dollars on it? Accelerators are very expensive.
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