Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle

TL;DR

This paper provides an exact analytical solution for electrostatic fields, field enhancement, and emission current from a hemi-ellipsoidal metallic needle, advancing understanding of field emission phenomena.

Contribution

It introduces an exact analytical method to calculate electrostatic fields, enhancement factors, and emission currents for a hemi-ellipsoidal metallic needle setup.

Findings

Calculated the field enhancement factor on the needle surface.

Derived an exact formula for the total emission current.

Analyzed the ponderomotive force acting on the needle.

Abstract

We present an exact solution for the electrostatic field between a metallic hemi-ellipsoidal needle on a plate (as a cathode) and a flat anode. The basic idea is to replace the cathode by a linearly charged thread in a uniform electric field and to use a set of "image" charges to reproduce the anode. We calculate the field enhancement factor on the needle surface and ponderomotive force acting on the needle. Using the Fowler-Nordheim theory we obtain an exact analytical formula for the total current.