  In this paper the structure of the next-to-leading (NLO) static gluon self
energy for an anisotropic plasma is investigated in the limit of a small
momentum space anisotropy. Using the Ward identities for the static hard-loop
(HL) gluon polarization tensor and the (nontrivial) static HL vertices, we
derive a comparatively compact form for the complete NLO correction to the
structure function containing the space-like pole associated with magnetic
instabilities. On the basis of a calculation without HL vertices, it has been
conjectured that the imaginary part of this structure function is nonzero,
rendering the space-like poles integrable. We show that there are both positive
and negative contributions when HL vertices are included, highlighting the
necessity of a complete numerical evaluation, for which the present work
provides the basis.
