  In this work an extension of the Gaussian model of the stochastic vacuum is
presented. It consists of including higher cumulants than just the second one
in the cluster expansion in QCD. The influence of nonabelian fourth cumulants
on the potential of a static quark-antiquarkpair is examined and the formation
of flux tubes between a static $q\bar{q}$-pair is investigated. It is found
that the fourth cumulants can contribute to chromomagnetic flux tubes.
Furthermore the contribution of fourth cumulants to the total cross section of
soft high energy hadron-hadron scattering is examined and it is found that the
fourth cumulants do not change the general picture obtained in the Gaussian
model.
