Techniques are described for a charged particle optical apparatus that includes a loop of solid material that encloses a bore and a wire winding poloidally wrapped around the loop surrounding the bore. A current is applied to the toroidal winding generating a magnetic field inside the loop along a toroidal direction of the loop and generating magnetic vector potential within the bore. When charged particle(s) pass through the bore of the loop, the magnetic vector potential focuses the charged particles based on the focal point of the charged particle optical apparatus.