Hello I'm still trying to get to the bottom of this conundrum about the change in electric potential that happens when a charged particle beam transmits through a beam splitter. In the rest frame the particles experience an electric potential due to the nearest neighbours in the beam, calculated from the axial field. This type of analysis is in a link here by Humphries, (page 687 section 14.2) http://www.fieldp.com/freeware/cp_beams_text.pdf If it goes through a beam splitter, then the density of the beam is smaller for each output so the axial field is reduced and also the potential is reduced. Therefore the splitting must cause a blueshift. Is this analysed anywhere in the literature?
