The notional emission area for cylindrical posts and its variation with local electric field

The dependence of the notional emission area on the apex electric field for a single field-emitter tip is investigated for cylindrical posts. It is found that a power-law dependence on the local field exists only when the end-cap on the cylinder is modelled as a hemi-ellipsoid with height h
e
≥ 3R
a
. Specifically, for a hemispherical end-cap, the notional area does not increase with local field as a power law. The power law behaviour is expected to hold for generic end-caps where the end-cap shape closely follows a parabola for ρ ≤ R
a
.