As I understand, the kinetic energy of the proton beam in a hadron collider is quite large. Can you build a energy storage system that is based on accelerating a proton beam to relativistic speeds to retrieve the energy later?
Here is my related question: Can the technology behind particle accelerators be used for space propulsion?
There is actually a technology called "energy recovery linac" that is designed to take the power stored in a beam and deposit it back into the fields of the accelerating cavity (always superconducting in this case, it seems) so that the next beam can take it. Sort of a relay race -- when one beam gets exhausted after too many collisions, another, higher quality beam takes over.
However, as a storage device, an accelerator would be terrible. The Relativistic Heavy Ion Collider at Brookhaven National Lab uses 5 megawatts of power just to keep its refrigeration system working so that the superconducting magnets stay at a nice, chill handful of Kelvin temperature. This excludes the power required to actually run the magnets, to drive the accelerating cavity, and to operate the machine proper (lots of computers).
Smaller accelerators would use substantially less power, but they would also be able to store much less because you need a bigger ring to store higher energy particles. So an accelerator would not be a very good power storage unit in the modern synchrotron sense.
Even if you were to use a more DC accelerator like the old betatrons that used permanent magnets, you would still have energy loss to the walls of the accelerator due to wake fields generated by the beam. Those fields interact with the beam pipe, which has a finite resistance, and then sucks energy out of the beam and into the walls as heat.
So there really isn't a place where an accelerator would work as a battery.
