Fate of non-Abelian plasma instabilities in 3+1 dimensions

Plasma instabilities can play a fundamental role in plasma equilibration. There are similarities and differences between plasma instabilities in Abelian and non-Abelian gauge theories. In particular, it has been an open question whether non-Abelian self-interactions are the limiting factor in the growth of non-Abelian plasma instabilities. We study this problem with 3+1 dimensional numerical simulations. We find that non-Abelian plasma instabilities behave very differently from Abelian ones once they grow to be nonperturbatively large, in contrast with earlier results of 1+1 dimensional simulations. In particular, they grow more slowly at late times, with linear rather than exponential dependence of magnetic energy on time.