High Energy Physics and Mechanical Engineering are worlds apart. Can there be an area that belongs to HEP but has implications in Mechanical Engineering?
I do not know your background but naively speaking if I look from HEP side, the answer to this question is "many". As a start experimental HEP uses particle detector where huge amount of radiation and hence heat exposure is highly possible. Not to mention "beam dumps" where we use to stop high energy beams when we are done with them or in case of an emergency to abort.
Moreover, to be able to do particles physics experiments you need to get the relativistic particles from somewhere. And they are particle accelerators where have an entire spectrum from radio-frequency engineering to beam diagnostics where we highly rely on mechanical engineering.
From the other point of view, you might have a look at concepts as RF breakdown, multipacting, phenomena observed in the presence of high energy particles or high fields. They might be interesting to look at from an mechanical engineer's eyes.
In addition design of 'magnets' of various shapes for high energy accelerators.Very very long arms of Michelson-Morley type experimental set up to study and dtect gravitational waves as in the L shaped detector used by LIGO expt. LIGO L1 ans LIGO H1.