  We analyze the free energy of a static quark anti-quark pair in quenched QCD
at short and large distances. From this we deduce running couplings, g^2(r,T),
and determine the length scale that separates at high temperature the short
distance perturbative regime from the large distance non-perturbative regime in
the QCD plasma phase. Ambiguities in the definition of a coupling beyond the
perturbative regime are discussed in their relation to phenomenological
considerations on heavy quark bound states in the quark gluon plasma. Our
analysis suggests that it is more appropriate to characterize the
non-perturbative properties of the QCD plasma phase close to T_c in terms
remnants of the confinement part of the QCD force rather than a strong
Coulombic force.
