As I understand, the kinetic energy of the proton beam in a hadron collider is quite large. Can you build a space propulsion system that is based on accelerating a proton bean to relativistic speeds and then using the resulting kinetic energy to propel a space vehicle?
Edit: In the large hadron collider, the kinetic energy of a proton reaches 7 Tev, which translate to about 6.71E+20 joules of kinetic energy per kg of accelerated protons.
If the Collider can accelerate 1 kg of proton every hour and point it downwards, then the resulting thrust could launch into orbit the entire collider structure.
Of course, the LHC cant accelerate 1 kg of protons in an hour, but maybe a derivative of it could and would be the basis of space propulsion system.
This is basically the idea. I know that it is enormously hard to build, but can it be done, in theory?