Proposal for Hollow Cathode Electron Gun for Electron Cooling*

If we put a voltage between the magnetic shunt and two conducting plates perpendicular to the z-axis in a symmetric fashion, we would obtain the same shape of the electric field, because both E and B may be derived as gradient of a potential. We propose to explore this simple physical system, in which E and B are everywhere parallel, to obtain low temperature, magnetically confined electron beams.