  We study the structure of the hybrid static potential flux tube in the
$\Pi_u$ sector in SU(2) lattice Yang-Mills theory. To this end, we compute the
squares of the chromoelectric and chromomagnetic field strengths in the
presence of a static quark-antiquark pair. We show clear evidence that the
gluon distribution is significantly different compared to that of the ordinary
static potential with quantum numbers $\Sigma_g^+$.
