Factors Governing Performance of Electron Guns in Television Cathode-Ray Tubes

On the basis of Langmuir's limiting-current-density relationship, it is shown that the useful beam current in a conventional television cathode-ray tube has an upper limit defined by e A2 I.= 1.13 ioE2-- tan2o where Is = the beam current; i0 = the cathode-current density; E2 = the second-anode voltage relative to the cathode; e = the electron charge; k = Boltzmann's constant; T = the absolute temperature of the cathode; A = the aperture of the final focusing system; N = the number of scanning lines; and, ϕ = the equivalent deflection angle. This result is derived for the case of an ideal electron gun with no defining apertures. In practice this upper limit of beam current is not attained because of aberrations and space-charge mutual repulsion effects.