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This review of quantitative field emitter electrostatics, coveringanalytical, numerical and fitted-formula approaches, is thought the first ofits kind. The review relates chiefly to situations where emitters operate in anelectronically ideal manner, and zero-current electrostatics is applicable.Terminology is carefully described and is polarity independent; thus the reviewapplies to both field electron and field ion emitters. It also applies moregenerally to charged, pointed electron-conductors that exhibit the"electrostatic lightning-rod effect", but are poorly discussed in generalelectricity and magnetism literature. Modern electron-conductor electrostaticsis an application of the chemical thermodynamics and statistical mechanics ofelectrons. The review focuses chiefly on the electrostatics of two common basicemitter forms: the needle-shaped emitters used in traditional projectiontechnologies; and the post-shaped emitters often used in modelling large-areamulti-emitter electron sources. In the post-on-plane context, we consider indetail both the electrostatics of the single post and the interaction betweentwo identical posts that occurs as a result of electrostatic depolarization(often called "screening" or "shielding"). Core to the review are discussionsof the "minimum domain dimensions" method for implementing effectivefinite-element-method electrostatic simulations, and of the variant that leadsto very precise estimates of dimensionless field enhancement factors (errortypically 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 aresuggested where further research and/or separate mini-reviews would probably beuseful.

Field emitter electrostatics: a review with special emphasis on modern high-precision finite-element modelling