Abstract
A technique to take into account the initial transverse electron thermal velocities in converged sheet electron beams has been developed. This determines the main integral characteristics of a thermal beam in a gun and transportation region of the paraxial approximation via chosen characteristic electron trajectories. We have equations of characteristic electrons motion, initial conditions to solve equations, and formulas for the current density distribution in the thermal beam cross-section and current fraction in conventional boundary. The derived equations and formulas may be used in modeling electron-optical systems and choosing parameters in which the effect of heat electron motion on beam characteristics will lie within tolerable limits.
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