  Recent analyses of the field enhancement factor (FEF) from multiple emitters
have revealed that the depolarization effect is more persistent with respect to
the separation between the emitters than originally assumed. It has been shown
that, at sufficiently large separations, the fractional reduction of the FEF
decays with the inverse cube power of separation, rather than exponentially.
The behavior of the fractional reduction of the FEF encompassing both the range
of technological interest $0<c/h\lesssim5$ ($c$ being the separation and $h$ is
the height of the emitters) and $c\rightarrow\infty$, has not been predicted by
the existing formulas in field emission literature, for post-like emitters of
any shape. In this letter, we use first principles to derive a simple
two-parameter formula for fractional reduction that can be of interest for
experimentalists to modeling and interpret the FEF from small clusters of
emitters or arrays in small and large separations. For the structures tested,
the agreement between numerical and analytical data is $\sim1\%$.
