Proposal for hollow cathode electron gun for electron cooling

A magnetic shunt, an iron plate with a hole in it, sandwiched between two solenoids which are polarized in opposite direction, can shape the resulting magnetic field. Putting a voltage between the magnetic shunt and two conducting plates perpendicular to the z axis in a symmetric fashion, produces the same shape of the electric field, because both E and B may be derived as gradient of a potential. This simple physical system, in which E and B are everywhere parallel is explored in an effort to obtain low temperature, magnetically confined electron beams.