  This review of quantitative field emitter electrostatics, covering
analytical, numerical and fitted-formula approaches, is thought the first of
its kind. The review relates chiefly to situations where emitters operate in an
electronically ideal manner, and zero-current electrostatics is applicable.
Terminology is carefully described and is polarity independent; thus the review
applies to both field electron and field ion emitters. It also applies more
generally to charged, pointed electron-conductors that exhibit the
"electrostatic lightning-rod effect", but are poorly discussed in general
electricity and magnetism literature. Modern electron-conductor electrostatics
is an application of the chemical thermodynamics and statistical mechanics of
electrons. The review focuses chiefly on the electrostatics of two common basic
emitter forms: the needle-shaped emitters used in traditional projection
technologies; and the post-shaped emitters often used in modelling large-area
multi-emitter electron sources. In the post-on-plane context, we consider in
detail both the electrostatics of the single post and the interaction between
two identical posts that occurs as a result of electrostatic depolarization
(often called "screening" or "shielding"). Core to the review are discussions
of the "minimum domain dimensions" method for implementing effective
finite-element-method electrostatic simulations, and of the variant that leads
to very precise estimates of dimensionless field enhancement factors (error
typically less than 0.001 % in situations where analytical comparisons exist).
Brief outline discussions, and core references, are given for each of many
"related considerations" that are relevant to the electrostatic situations,
methods and results described. Many areas of field emitter electrostatics are
suggested where further research and/or separate mini-reviews would probably be
useful.
