Collective modes and instabilities in anisotropically expanding ultarelativistic plasmas

TL;DR

This paper analyzes the evolution of collective modes in an expanding ultrarelativistic plasma, generalizing previous models to 3+1 dimensions and including initial fluctuations in gauge fields and currents, highlighting potential early-stage instabilities in heavy-ion collisions.

Contribution

It extends the hard-loop approximation to arbitrary wave vector orientations and initial conditions, enhancing understanding of plasma instabilities in realistic scenarios.

Findings

Unstable Weibel modes can grow more rapidly with initial fluctuations.

Generalization to 3+1 dimensions reveals more realistic instability behavior.

Initial fluctuations significantly reduce delay in instability onset.

Abstract

The time evolution of collective modes in an expanding ultarelativistic and (effectively) Abelian plasma is studied in the hard-loop approximation semi-analytically by means of integro-differential equations. A previous treatment is generalized to arbitrary orientation of wave vectors with respect to the direction of anisotropy and thus to a fully 3+1 dimensional situation. Moreover, initial fluctuations are allowed in both gauge fields and currents, which is necessary in the case of (stable) longitudinal modes. For unstable (Weibel) modes, this generalization of initial conditions reduces drastically the lower bound on the delay in the onset of growth that was found previously by considering only collective gauge fields as seeds. This makes it appear much more likely that non-Abelian plasma instabilities seeded by small initial rapidity fluctuations could play an important role in the early stage of heavy-ion collisions at LHC energies.