The Electron Sheath Around an Emissive Wire in Vacuum

An orbit-motion-limited (OML) theory is developed for the electron sheath and the virtual cathode that forms around an emissive wire in vacuum. The electron cloud above the wire surface is assumed to be described by a 2-D Maxwellian distribution function. A comparison is made with a 1-D theory having only radial velocities for the electrons. The OML theory gives a greater electron density and a more negative virtual cathode because of differences between the 1-D and 2-D distribution functions. Expressions are derived for the current from the cathode to the anode.