Particle accelerator research has resulted in theories and equipment as a byproduct of what they found - either proving or disproving specific theories, or by producing new or unexpected results. The last of which results in new theories to explain those results. Those new theories producing “useful results”.

MRIs and PET scans were the result of theories that only came about as a result of data that came out of particle accelerators. The goal of the accelerators was never specifically “develop new medical imaging devices”, it was simply the “basic research” that makes thing like that possible in the future.