Pulsed vrs continuous
So the LHC can push protons to 14 Tev, the total energy in a beam is significant.
Using data from CERN:
2808 bunches of protons * 1.2 x 10^11 protons * 6.5 Tev / proton ~= 3.78 10^9 joules
I know we say 14 Tev, that would up the energy to ~7.5 10^9 joules
Pardon my crude calculations....
I bet the quasar is outputting more than that per day...
I would say the total energy, were it directed directly at Earth might cause some problems