Collective modes and instabilities in anisotropically expanding ultarelativistic plasmas

Understand

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.