  Schottky Conjecture is analytically proved for multi-stage field emitters
consisting on the superposition of rectangular or trapezoidal protrusions on a
line under some specific limit. The case in which a triangular protrusion is
present on the top of each emitter is also considered as an extension of the
model. The results presented here are obtained via Schwarz-Christoffel
conformal mapping and reinforce the validity of Schottky Conjecture when each
protrusion is much larger than the ones above it, even when an arbitrary number
of stages is considered. Moreover, it is showed that it is not necessary to
require self-similarity between each of the stages in order to ensure the
validity of the conjecture under the appropriate limits.
