The space-charge controlled focus of an electron beam

A table is given of solutions of the space-charge equations governing the defocusing of electron beams having circular symmetry. It is shown that.the approximation (rs/ri) = 5.9×l04{(zs/ri)(I/V1.5)0.5}2.5, where rs and ri are the spot and initial beam radii respectively, zs the screen distance, V the beam potential in volts and I the beam current in amperes, may be used for most beam design problems.