Influence of space charge on field emission of electrons from sharp edges

A sharp-edged cathode and its adjacent anode are represented as a section of a pair of coaxial cylinders with an inner radius r₀ and an outer radius r₁. The field emission current density J is determined as a function of the anode voltage V₁ and the cathode work function potential phi for degrees of space-charge that lead to a cathode field E in the range 0.9 E₀0, where E₀ is the cathode field when there is no current flow. In the case where eV₁<2 there is a particular value of J which is dependent on r₀, r₁, phi but independent of V₁, for which space-charge effects have caused the current to be reduced to half of the emission current appropriate to the field E₀. It is shown that this current is of particular significance to the experimenter when designing a field emission diode which uses a razor blade cathode.