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Abstract Collisionless systems often exhibit nonthermal power-law tails in their distribution functions. Interestingly, collisionless plasmas in various physical scenarios (e.g., the ion population of the solar wind) feature av⁻⁵tail in their velocity (v) distribution, whose origin has been a long-standing puzzle. We show this power-law tail to be a natural outcome of the collisionless relaxation of driven electrostatic plasmas. Using a quasi-linear analysis of the perturbed Vlasov–Poisson equations, we show that the coarse-grained mean distribution function (DF),f₀, follows a quasi-linear diffusion equation with a diffusion coefficientD(v) that depends onvthrough the plasma dielectric constant. If the plasma is isotropically forced on scales larger than the Debye length with a white-noise-like electric field,D(v) ∼v⁴forσ<v<ω_P/k, withσthe thermal velocity,ω_Pthe plasma frequency, andkthe characteristic wavenumber of the perturbation; the corresponding quasi-steady-statef₀develops av^{−(d+ 2)}tail inddimensions (v⁻⁵tail in 3D), while the energy (E) distribution develops anE⁻²tail independent of dimensionality. Any redness of the noise only alters the scaling in the highvend. Nonresonant particles moving slower than the phase velocity of the plasma waves (ω_P/k) experience a Debye-screened electric field, and significantly less (power-law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power-law tail, while its core (v<σ) eventually also heats up but over a much longer timescale. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the emergence of the universalv⁻⁵tail. 

Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall magnetohydrodynamics (MHD) models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy. 

Abstract Magnetic reconnection is an important source of energetic particles in systems ranging from astrophysics to the laboratory. The large separation of spatiotemporal scales involved makes it critical to determine the minimum physical model containing the necessary physics for modeling particle acceleration. By resolving the energy gain from ideal and nonideal magnetohydrodynamic electric fields self-consistently in kinetic particle-in-cell simulations of reconnection, we conclusively show the dominant role of the nonideal field for the early stage of energization known as injection. The importance of the nonideal field increases with magnetization, guide field, and in three dimensions, indicating its general importance for reconnection in natural astrophysical systems. We obtain the statistical properties of the injection process from the simulations, paving the way for the development of extended MHD models capable of accurately modeling particle acceleration in large-scale systems. The novel analysis method developed in this study can be applied broadly to give new insight into a wide range of processes in plasma physics.