Due to its ubiquitous presence, turbulence is often invoked to explain the origin of nonthermal particles in astrophysical sources of high-energy emission. With particle-in-cell simulations, we study decaying turbulence in magnetically-dominated (or equivalently, "relativistic") pair plasmas. We find that the generation of a power-law particle energy spectrum is a generic by-product of relativistic turbulence. The power-law slope is harder for higher magnetizations and stronger turbulence levels. In large systems, the slope attains an asymptotic, system-size-independent value, while the highenergy spectral cutoff increases linearly with system size; both the slope and the cutoff do not depend on the dimensionality of our domain. By following a large sample of particles, we show that particle injection happens at reconnecting current sheets; the injected particles are then further accelerated by stochastic interactions with turbulent fluctuations. Our results have important implications for the origin of non-thermal particles in high-energy astrophysical sources.

Magnetized turbulence and magnetic reconnection are often invoked to explain the nonthermal emission observed from a wide variety of astrophysical sources. By means of fully-kinetic 2D and 3D particle-in-cell simulations, we investigate the interplay between turbulence and reconnection in generating nonthermal particles in magnetically-dominated (or, equivalently, "relativistic") pair plasmas. A generic by-product of the turbulence evolution is the generation of a nonthermal particle spectrum with a power-law energy range. The power-law slope p is harder for larger magnetizations and stronger turbulence fluctuations, and it can be as hard as p 2. The Larmor radius of particles at the high-energy cutoff is comparable to the size l of the largest turbulent eddies. Plasmoid-mediated reconnection, which self-consistently occurs in the turbulent plasma, controls the physics of particle injection. Then, particles are further accelerated by stochastic scattering off turbulent fluctuations. The work done by parallel electric fields -naturally expected in reconnection layers -is responsible for most of the initial energy increase, and is proportional to the magnetization σ of the system, while the subsequent energy gain, which dominates the overall energization of high-energy particles, is powered by the perpendicular electric fields of turbulent fluctuations. The two-stage acceleration process leaves an imprint in the particle pitch-angle distribution: low-energy particles are aligned with the field, while the highest energy particles move preferentially orthogonal to it. The energy diffusion coefficient of stochastic acceleration scales as D γ ∼ 0.1σ(c/l)γ 2 , where γ is the particle Lorentz factor. This results in fast acceleration timescales t acc ∼ (3/σ) l/c. Our findings have important implications for understanding the generation of nonthermal particles in high-energy astrophysical sources.

A general theory of the onset and development of the plasmoid instability is formulated by means of a principle of least time. The scaling relations for the final aspect ratio, transition time to rapid onset, growth rate, and number of plasmoids are derived and shown to depend on the initial perturbation amplitude (ŵ0), the characteristic rate of current sheet evolution (1/τ ), and the Lundquist number (S). They are not simple power laws, and are proportional to S α τ β [ln f (S, τ,ŵ0)] σ . The detailed dynamics of the instability is also elucidated, and shown to comprise of a period of quiescence followed by sudden growth over a short time scale.The rapid conversion of magnetic energy into plasma particle energy through the process of magnetic reconnection is of great importance in the realm of plasma physics and astrophysics [1][2][3][4]. Sawtooth crashes, magnetospheric substorms, stellar and gamma-ray flares are just a few examples of pheneomena in which magnetic reconnection plays an essential role.In large systems, such as those found in space and astrophysical environments, the potential formation of highly elongated current sheets would result in extremely low reconnection rates, which fail to account for the observed fast energy release rates [5][6][7]. However, such current sheets are subject to a violent linear instability that leads to their breakup, giving rise to a tremendous increase in the reconnection rate that appears to be very weakly dependent on the Lundquist number of the system in the nonlinear regime [8][9][10][11][12][13][14][15][16][17]. This crucial instability, which serves as a trigger of fast reconnection, is the plasmoid instability [2], thus dubbed as it leads to the formation of plasmoids.In the widely studied Sweet-Parker current sheets, which are characterized by an inverse aspect ratio a/L ∼ S −1/2 , Tajima and Shibata [1], as well as Loureiro et al.[18], have found that the growth rate γ and the wavenumber k of the plasmoid instability obey γτ A ∼ S 1/4 and kL ∼ S 3/8 , where τ A is the Alfvénic timescale based on the length of the current sheet. Since the Lundquist number S is extremely large in most space and astrophysical plasmas [19], the linear growth of the instability turns out to be surprisingly fast, and the number of plasmoids produced is also very high. Other notable works have since followed, which have verified and extended the work on the plasmoid instability in different contexts [20][21][22][23][24].Despite the success of the theory, its limitations soon became evident. For sufficiently high growth rates, Sweet-Parker current sheets cannot be attained as current layers are linearly unstable and disrupt before this state is achieved. In order to bypass this limitation, Pucci and Velli [25] conjectured that current sheets break up when γτ A ∼ 1. Later, Uzdensky and Loureiro [26] considered a similar criterion (γτ = 1) as the end-point of the linear stage of the instability, presenting an appealing but heuristic discussion for the case of a current sheet evolving...