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We present the first 3+1 dimensional simulations of non-Abelian plasmainstabilities in gauge-covariant Boltzmann-Vlasov equations for the QCD gaugegroup SU(3) as well as for SU(4) and SU(5). The real-time evolution ofinstabilities for a plasma with stationary momentum-space anisotropy is studiedusing a hard-loop effective theory that is discretized in the velocities ofhard particles. We find that the numerically less expensive calculations usingthe group SU(2) essentially reproduce the nonperturbative dynamics ofnon-Abelian plasma instabilities with higher rank gauge groups provided themass parameters of the corresponding hard-loop effective theories are the same.In particular we find very similar spectra for the turbulent cascade that formsin the strong-field regime, which is associated with an approximately lineargrowth of energy in collective fields. The magnitude of the linear growthhowever turns out to increase with the number of colors.

Non-Abelian plasma instabilities: SU(3) vs. SU(2)