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.
@article{arxiv.0804.1195,
title = {Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle},
author = {Evgeny G. Pogorelov and Alexander I. Zhbanov and Yia-Chung Chang},
journal= {arXiv preprint arXiv:0804.1195},
year = {2008}
}