  We report a simple theoretical derivation of the spectrum and damping of spin
waves in a cylindrical periodically structured magnetic nanowire (cylindrical
magnonic crystal) in the "effective medium" approximation. The dependence of
the "effective" magnetic parameters upon the individual layer parameters is
shown to be different from the arithmetic average over the volume of the
superlattice. The formulae that are obtained can be applied firstly in the
description of spin wave dispersion in the first allowed band of the structure;
and secondly in the design of a magnonic crystal with band-gaps in an arbitrary
part of the spin wave spectrum.
