With respect to the field of physics, discuss the historical developments that were required first, before the invention of the particle accelerator could occur.

The science behind a particle accelerator is relatively new, and therefore the technology required to create one had to be invented concurrently with the understanding of the science. Because of the high energies and complexity of technology required, there were several major developments that had to be created prior to the development of an effective particle accelerator.
Two of the main advancements that were required to properly create the particle accelerator were advanced magnetic systems and better containment systems. The magnetic systems are used to direct and accelerate the particles. Unfortunately, magnets and electric coils will degrade with significantly high voltages. More advanced and pure materials needed to be created to be able to handle the levels of energy running through them, or else they would quickly wear out and the accelerate would become ineffective.
The issue with containment is that the particle beams would disperse even in the presence of a high magnetic field if there wasn't a level of containment (meaning physical tubing that is sturdy enough to withstand the strong particle beams and magnetic fields, as well as strong gas extraction techniques to create as near a vacuum as possible, otherwise the particle beam would react with the gas and get slowed down or dispersed). These advancements didn't come around until materials science caught up with the physics technology.