The LHC doesn't generate anything like the kind of energy that you get when interstellar particles hit the Earth's upper atmosphere, nevermind what's happening inside the sun - and any of these are many, many orders of magnitude below the energies you get in a supernova, for example.

The LHC is extremely impressive from a human engineering perspective, but it's nowhere close to pushing the boundaries of what's going on every second in the universe at large.