Comment Re:Not exactly (Score 4, Informative) 161
There's no problem in daisy chaining them, but I don't think you can guarantee the same energy boost each time. One of the big physics problems here is that accelerating charged particles radiate when they are accelerated, which acts as a sort of friction. The amount that is radiated increases quite dramatically as the particle gets closer to the speed of light (the energy loss scales as (E/(mc^2))^4). In practice, this means that if you dump a bunch of energy into an electron to accelerate it, you'll only add a fraction of that amount to its kinetic energy (the rest will be lost in radiation).
Given this, the naive expectation is that each subsequent box will add less and less to the energy of the particles. The disclaimer here is that I haven't studied the specific physics of plasma shock acceleration, so I don't know how such acceleration scales with energy. I do know, however, that this is the exact same mechanism that is suspected to be behind the "oh my god" particles (single particles with more than ten million times the energy that the LHC can produce): plasma shock fronts in the galaxy accelerate some small fraction of the interstellar protons to unbelievable speeds.