Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Physical electrostatics of small field emitter arrays/clusters   This paper improves understanding of electrostatic influences on apex field
enhancement factors (AFEFs) for small field emitter arrays. Using the "floating
sphere at emitter-plate potential" (FSEPP) model, it re-examines the
electrostatics and mathematics of three simple systems of identical post-like
emitters. For the isolated emitter, various approaches are noted. On need
consider only the effects of sphere charges and (for separated emitters) image
charges. For the 2-emitter system, formulas are found for "charge-blunting" and
"neighbour-field" effects, for widely spaced and "sufficiently closely spaced"
emitters. Mutual charge-blunting is always dominant, with a related (negative)
fractional AFEF-change {\delta}_two. For sufficiently small emitter spacing c,
|{\delta}_two| varies as 1/c; for large spacing, |{\delta}_two| decreases as
1/c^3. In a 3-emitter linear array, differential charge-blunting and
differential neighbor-field effects occur, but the former are dominant, and
cause the "exposed" outer emitters to have higher AFEF ({\gamma}_0) than the
central emitter ({\gamma}_1). Formulas are found for the exposure ratio
{\Xi}={\gamma}_0/{\gamma}_1, for large and for sufficiently small separations.
The FSEPP model for an isolated emitter has accuracy around 30%. Line-charge
models (LCMs) are an alternative, but an apparent difficulty with recent LCM
models is identified. Better descriptions of array electrostatics may involve
developing good fitting equations for AFEFs derived from accurate numerical
solution of Laplace's equation, perhaps with equation form(s) guided
qualitatively by FSEPP-model results. In existing fitting formulas, the
AFEF-reduction decreases exponentially as c increases, which differs from
FSEPP-model formulas. FSEPP models might provide a useful guide to the
qualitative behaviour of small field emitter clusters larger than those
investigated.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
2
The categories of this paper are: math
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics