The Estimation of Thermal Velocity Effects in Thick Steady Beams†

†Communicated by the Author

Abstract

Previous analyses for estimating thermal velocity effects in paraxial, axially symmetric, beams are extended to cover thick beams. By using a perturbation of the zero-temperature behaviour, a 6 × 6 matrix is set up relating the exit parameters of the beam with the entrance ones. By suitable assumptions at the cathode, e.g. assuming a half-Maxwellian current distribution, expressions are derived for the current density emerging from the system. It is shown that in the limiting case of a paraxial, solid beam, the expressions simplify to ones developed earlier.

Notes

†Communicated by the Author