Aspects of self-similar current distributions resulting from the plasma filamentation instability

Colliding plasmas can form current filaments that are magnetically confined and interact through electromagnetic fields during the nonlinear evolution of this filamentation instability. A nonrelativistic and a relativistic electron flow are examined. Two-dimensional (2D) particle-in-cell (PIC) simulations evolve the instability in a plane orthogonal to the flow vector and confirm that the current filaments move, merge through magnetic reconnection and evolve into current sheets and large flux tubes. The current filaments overlap over limited spatial intervals. Electrons accelerate in the overlap region and their final energy distribution decreases faster than exponential. The spatial power spectrum of the filaments in the flow-aligned current component can be approximated by a power-law during the linear growth phase. This may reflect a phase transition. The power spectrum of the current component perpendicular to the flow direction shows a power-law also during the nonlinear phase, possibly due to preferential attachment. The power-law distributed power spectra evidence self-similarity over a limited scale size and the wavenumber of the maximum of the spatial power spectrum of the filament distribution decreases linearly in time. Power-law correlations of velocity fields, which could be connected to the current filaments, may imply super-diffusion.