  The screening of magnetic Z(N)-monopoles and the associated screening length
in SU(N) gauge theories are analyzed theoretically, and computed numerically in
the 3d SU(2) theory. The nature of the screening excitations as well as their
mass have so far remained inconclusive in the literature. Here we show that the
screening mass is identical to the lowest J^{PC}_R=0^{++}_+ excitation of the
Yang-Mills Hamiltonian with one compact direction with period 1/T, the
subscript R referring to parity in this direction. We extend the continuum
formulation to one on the lattice, and determine the transfer matrix governing
the decay of the spatial monopole correlator at any finite lattice spacing. Our
numerical results for SU(2) for the screening mass in the dimensionally reduced
(high temperature) theory are compatible with the 0^{++} glueball mass in 3d
SU(2).
