With the upcoming restart of the Large Hadron Collider, the short attention span of our nation has already turned to the next big thing. At the end of October was a Symposium on Accelerators for America's Future, and the overall consensus seems to be that scientists, if they want a new particle accelerator, they need to be better about communicating the worth of accelerators to the general populace, in areas such as nuclear energy, prevention of nuclear terrorism, clean water, food packaging, and medical treatments. (When conducting my own work during a 1998 undergraduate research internship at the Indiana University Cyclotron Facility, the facility was just beginning to use their accelerated proton beam to treat optical tumors. Many of the undergraduate research projects over that summer were focused on preparations for that new application, which has since become the Midwest Proton Radiotherapy Institute.)
One of the major proposals as a successor to the Large Hadron Collider is a muon collider being proposed by Fermilab. The collider would accelerate muon particles, which are about 200 times heavier than electrons, into beams that would collide with each other, creating interactions more energetic than electron collisions. They followed up the report with a possible schematic of what a muon collider could look like.
A benefit of muons over electrons is that, since they are heavier, they won't emit as much electromagnetic radiation (and lose as much energy) when going around a circular accelerator ring. Such an accelerator could be built in the existing Fermilab facility.
The muon collider isn't the only possibility out there. Both the International Linear Collider and the Compact Linear Collider (CLIC) are proposed as well, and while all could in theory be built, there's a question of how any of them will actually get funded, especially in the United States, where budget deficits make any major national project of this type highly unlikely.
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