Abstract
The paraxial electron trajectory equation applicable at relativiatic speeds, including the effects of self-magnetic field and space-charge of the beam is derived. Employing the above, problems concerning beam spreading, electrostatic lenses (unipotential Pierce gun being an example), magnetic lenses, Brillouin flow and beam stability are treated. Most of tho results are presented graphically and also discussed in detail. Applications of tho above results to practical situations is indicated.