Diffraction limit.

You cannot achive electron beam transverse dimension less than half de Broglie wave length corresponding to the specific electron energy. This is valid for an electron linac. As to circular accelerators, it also depends on the accelerator lattice that forms beam equilibrium orbit and must be in certain extent larger

~ 50 nm

http://newsline.linearcollider.org/2014/06/19/how-small-can-you-go/