Time dilation with atomic clocks near accelerators or colliders

Question

Consider an atomic clock positioned close to a high energy particle accelerator or collider.

1. Would the atomic clock read different values when the accelerator is operating at different "energy scales" or when we compare clock reading before the accelerator is started and after it has been started?
2. Would there even be time dilation effect at all?

Let me explain better: so we know that when a clock (can be any clock but I'm using atomic clock as case study due to its level of precision) is closer to a source of gravitation compared to when far from it, the gravitational time dilation occurs. Now, if the high energy acceleration or collision can be considered a source of stress energy acting on spacetime then the accelerator/collider may lead to small gravitational effects, leading to a small time dilation effect that the atomic clock can notice. But I wasn't sure if we can truly think of the acceleration or collision as a source of stress energy, hence not sure if time dilation would happen or if the readings may be different at different energy scales.

Answer 1

The clock would be fine and read normally, except for the stray magnetic fields, EMI/EMC, and high radiation environment....but that has nothing to do with time dilation.

From the clock (i.e., the lab) frame, an LHC proton would look Lorentz contracted from 1.6 fm sphere to a 1.6 x 1.6 x 0.0002 fm disk, with a very slow clock, though I don't know what a proton's clock looks like.

From the proton's frame, the atomic clock would be dilated, and tick one second every two hours, or so. That's on the straight section, I do not know what happens in the bending part.