Final answer:
Magnetic field strength and synchrotron radiation are the two primary limitations in constructing smaller, high-energy accelerators, with synchrotron radiation being more problematic for lighter particles like electrons.
Step-by-step explanation:
The two major limitations that prevent us from building high-energy accelerators that are physically small are magnetic field strength and energy dissipation in the form of synchrotron radiation. When particles accelerate, they emit synchrotron radiation, which increases with the particle's energy and inversely with its mass.
Energy dissipation refers to the loss of energy as the particles in the accelerator collide with other particles or interact with the accelerator's components. This limits the maximum energy that can be achieved in a small accelerator.
Synchrotron radiation occurs when charged particles are accelerated in a circular path. This radiation causes a loss of energy from the particles, which also limits the maximum energy that can be achieved in a small accelerator.
Therefore, dealing with synchrotron radiation is more challenging in accelerators for lighter particles like electrons compared to heavier particles like protons. Moreover, imposing stronger magnetic fields to maintain a fixed-radius path for the particles requires large facilities, as there is a limit to the strength of the magnetic fields we can currently produce.