I think the 'high potential' will be a negative one - a positive electrode would attract the electrons, diverging the beam and it may even act as another anode, if the beam diverges enough to hit it. With a negative potential, the ring will repel the electrons in the beam, diverting them towards the beam centre. This, on its own is a crude focusing effect which can be improved to get an actual 'spot' by using more than one ring at different potentials - the field between each ring can be made stronger on the outside and weaker on the inside (further from the gap) and so the outer parts of the beam will be bent more than the inner parts. (Hence the lens analogy) If you get it right, they should all be bent towards the same spot. There is a further problem which an optical lens doesn't suffer from and that is the fact that the electrons actually repel each other. That means you have to try harder (higher potentials) and that the beam will naturally separate after a while.
I guess this is rapidly becoming old technology as we can analyse most time dependent signals in real time (or quasi real time) and then put the result onto a non-CRT display. Shame, in a way, when you think how ingenious the best CRT designs are / were.