QCD plasma instabilities: The non-Abelian cascade

Abstract

Magnetic plasma instabilities appear to play an important role in the early stages of quark-gluon plasma equilibration in the high energy (weak coupling) limit. Numerical studies of the growth of such instabilities from small seed fluctuations have found initial exponential growth in their energy, followed by linear growth once the associated color magnetic fields become so large that their non-abelian interaction are non-perturbative. In this paper, we use simulations to determine the nature of this linear energy growth. We find that the long-wavelength modes associated with the instability have ceased to grow, but that they cascade energy towards the ultraviolet in the form of plasmon excitations of ever increasing energy. We find a quasi-steady-state power-law distribution $f_k \propto k^{-\nu}$ for this cascade, with spectral index $\nu \simeq 2$.