Power-Law Injection Spectrum from an Ensemble of Reconnecting Current Sheets

A collisionless, low- β plasma undergoing strong sub-Alfvénic turbulence is expected to form a broad hierarchy of reconnecting current sheets immersed in a strong guide magnetic field. If the reconnecting field strength of a sheet scales with its length as a power law of index κ, and the number of sheets per unit interval of sheet length decreases as a power law of index x, the current-sheet ensemble injects nonthermal particles with a power-law energy spectrum proportional to γ-s, where s = 1 + (x-2)/(1 + κ). The spectrum is hard (s < 2) when the longest sheets deliver most of the injected energy, which requires x < 3 + κ. Past numerical studies have measured 2 x 3.3, and the scalings of intense current sheets support κ 0, resulting in 1 s 2.3. This injection may yield flat or mildly steep radio spectra in optically thin sources and hard ion spectra in the coronae of active galactic nuclei.