The turbulent spectrum created by non-Abelian plasma instabilities

Recent numerical work on the fate of plasma instabilities in weakly-coupled non-Abelian gauge theory has shown the development of a cascade of energy from long to short wavelengths. This cascade has a steady-state spectrum, analogous to the Kolmogorov spectrum for turbulence in hydrodynamics or for energy cascades in other systems. In this paper, we theoretically analyze processes responsible for this cascade and find a steady-state spectrum f_k ~ k^-2, where f_k is the phase-space density of particles with momentum k. The exponent -2 is consistent with results from numerical simulations. We also discuss implications of the emerging picture of instability development on the "bottom-up" thermalization scenario for (extremely high energy) heavy ion collisions, emphasizing fundamental questions that remain to be answered.