Stability analysis of a periodic system of relativistic current filaments

The nonlinear evolution of current filaments generated by the Weibel-type filamentation instability is a topic of prime interest in space and laboratory plasma physics. In this paper, we investigate the stability of a stationary periodic chain of nonlinear current filaments in counterstreaming pair plasmas. We make use of a relativistic four-fluid model and apply the Floquet theory to compute the two-dimensional unstable eigenmodes of the spatially periodic system. We examine three different cases, characterized by various levels of nonlinearity and asymmetry between the plasma streams: a weakly nonlinear symmetric system, prone to purely transverse merging modes; a strongly nonlinear symmetric system, dominated by coherent drift-kink modes whose transverse periodicity is equal to, or an integer fraction of the unperturbed filaments; a moderately nonlinear asymmetric system, subject to a mix of kink and bunching-type perturbations. The growth rates and profiles of the numerically computed eigenmodes agree with particle-in-cell simulation results. In addition, we derive an analytic criterion for the transition between dominant filament-merging and drift-kink instabilites in symmetric two-beam systems.