  We present an alternative way to calculate the screening of the static
potential between two charges in (non)abelian gauge theories at high
temperatures. Instead of a loop expansion of a gauge boson self-energy, we
evaluate the energy shift of the vacuum to order e^2 after applying an external
static magnetic field and extract a temperature- and momentum-dependent
dielectric permittivity. The Hard Thermal Loop (HTL) gluon and photon Debye
masses are recovered from the lowest lying Landau levels of the perturbed
vacuum. In QED, the complete calculation exhibits an interesting cancellation
of terms, resulting in a logarithmic running alpha(T). In QCD, a Landau pole in
alpha_s arises in the infrared from the sign of the gluon contribution, as in
more sophisticated thermal renormalization group calculations.
