  We consider the polarization tensor of a color charged gluon field in SU(2)
in the background of a homogeneous color magnetic field and calculate its
projection onto the lower (tachyonic) state. We obtain a quite simple
representation of the polarization tensor in terms of double parametric
integral. We provide examples for the numerical evaluation of the polarization
tensor in this case. Also, we consider the corresponding expressions at high
temperature and calculate the charged gluon magnetic mass in this limit. We
conclude that radiation corrections stabilize the ground state. Applications of
the results obtained are discussed.
