  Confinement may be more easily demonstrated at finite temperature using the
Polyakov loop than at zero temperature using the Wilson loop. A natural
mechanism for confinement can arise via the coupling of the adjoint Polyakov
loop to F_{mu nu}^2. We demonstrate this mechanism with a one-loop calculation
of the effective potential for SU(2) gluons in a background field consisting of
a non-zero color magnetic field and a non-trivial Polyakov loop. The color
magnetic field drives the Polyakov loop to non-trivial behavior, and the
Polyakov loop can remove the well-known tachyonic mode associated with the
Saviddy vacuum. Minimizing the real part of the effective potential leads to
confinement, as determined by the Polyakov loop. Unfortunately, we cannot
arrange for simultaneous stability and confinement for this simple class of
field configurations. We show for a large class of abelian background fields
that at one loop tachyonic modes are necessary for confinement.
