Abstract
A theoretical analysis has been made of the negative electrostatic potential well formed by electron injection in spherical geometry. Poisson's equation has been modified to include spreads in the total energy of the injected electrons as well as spreads in their angular energies. Solutions have been obtained for both rectangular and Boltzmann distributions in total and angular energy. The resulting solutions agree very well with the experimental data, showing a potential well of approximately parabolic radial dependence whose depth depends essentially linearly on the injected current and whose well depth is relatively independent of the anode voltage for a constant anode current.
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