  According to a proposal by Arnold and Yaffe, the non-perturbative
g^2T-contribution to the Debye mass in the deconfined QCD plasma phase can be
determined from a single Wilson line operator in the three-dimensional pure
SU(3) gauge theory. We extend a previous SU(2) measurement of this quantity to
the physical SU(3) case. We find a numerical coefficient which is more accurate
and smaller than that obtained previously with another method, but still very
large compared with the naive expectation: the correction is larger than the
leading term up to T ~ 10^7 T_c, corresponding to g^2 ~ 0.4. At moderate
temperatures T ~ 2 T_c, a consistent picture emerges where the Debye mass is
m_D ~ 6T, the lightest gauge invariant screening mass in the system is ~ 3T,
and the purely magnetic operators couple dominantly to a scale ~ 6T. Electric
(~ gT) and magnetic (~ g^2T) scales are therefore strongly overlapping close to
the phase transition, and the colour-electric fields play an essential role in
the dynamics.
