  Non-Abelian plasma instabilities play a crucial role in the nonequilibrium
dynamics of a weakly coupled quark-gluon plasma and they importantly modify the
standard perturbative bottom-up thermalization scenario in heavy-ion
collisions. Using the auxiliary-field formulation of the hard-loop effective
theory, we study numerically the real time evolution of instabilities in an
anisotropic collisionless Yang-Mills plasma expanding longitudinally in free
streaming. In this first real-time lattice simulation we consider the most
unstable modes, long-wavelength coherent color fields that are constant in
transverse directions and which therefore are effectively 1+1-dimensional in
spacetime, except for the auxiliary fields which also depend on discretized
momentum rapidity and transverse velocity components. We reproduce the
semi-analytical results obtained previously for the Abelian regime and we
determine the nonlinear effects which occur when the instabilities have grown
such that non-Abelian interactions become important.
