  In quantum electrodynamics, static electric fields are screened at non-zero
temperatures by charges in the plasma. The inverse screening length, or Debye
mass, may be analyzed in perturbation theory and is of order $eT$ at
relativistic temperatures. An analogous situation occurs when non-Abelian gauge
theories are studied perturbatively, but the perturbative analysis breaks down
when corrections of order $e^2 T$ are considered. At this order, the Debye mass
depends on the non-perturbative physics of confinement, and a perturbative
``definition'' of the Debye mass as the pole of a gluon propagator does not
even make sense. In this work, we show how the Debye mass can be defined
non-perturbatively in a manifestly gauge invariant manner (in vector-like gauge
theories with zero chemical potential). In addition, we show how the $O(e^2 T)$
correction could be determined by a fairly simple, three-dimensional, numerical
lattice calculation of the perimeter-law behavior of large, adjoint-charge
Wilson loops.
