Long-living Equilibria in Kinetic Astrophysical Plasma Turbulence

TL;DR

This work addresses the formation and sustenance of coherent structures in fully kinetic plasma turbulence by simulating 2.5D PIC turbulence and observing long-lived magnetic vortices with force-free-like cores, where $\bm{J} \approx \lambda(r)\bm{B}$. The authors develop a self-consistent kinetic vortex reconstruction (KVR) in cylindrical coordinates, based on a Harris-like drifting-Maxwellian ansatz and stationary Vlasov–Maxwell equations, resulting in a reduced ODE system for the vector potentials, which they fit to data via a data-driven Monte Carlo approach for each vortex. The KVR solutions reproduce inner-vortex fields and currents and connect to a Gold-Hoyle vortex in the appropriate limit; magnetic helicity is shown to be conserved through mergers, enabling self-similar creation of new metastable equilibria. The study provides a framework for interpreting plasmoid and coherent-structure formation across astrophysical plasmas, with implications for accretion-flow plasmoids and heliospheric flux ropes, while acknowledging the limitations of a 2.5D model and pointing to future 3D extensions.

Abstract

Turbulence in classical fluids is characterized by persistent structures that emerge from the chaotic landscape. We investigate the analogous process in fully kinetic plasma turbulence by using high-resolution, direct numerical simulations in two spatial dimensions. We observe the formation of long-living vortices with a profile typical of macroscopic, magnetically dominated force-free states. Inspired by the Harris pinch model for inhomogeneous equilibria, we describe these metastable solutions with a self-consistent kinetic model in a cylindrical coordinate system centered on a representative vortex, starting from an explicit form of the particle velocity distribution function. Such new equilibria can be simplified to a Gold-Hoyle solution of the modified force-free state. Turbulence is mediated by the long-living structures, accompanied by transients in which such vortices merge and form self-similarly new metastable equilibria. This process can be relevant to the comprehension of various astrophysical phenomena, going from the formation of plasmoids in the vicinity of massive compact objects to the emergence of coherent structures in the heliosphere.

Figures (8)

• Figure 1: (a) Magnetic power spectrum at a time beyond the peak of nonlinear activity vs $k d_e$. The vertical (orange) line represents the persistent structures wavenumber $k_0 d_e$, which identifies the typical scale of the vortices. (b) 2D contour of the magnetic vector potential component $a_z$ (right side) and the cosine angle between the current density and the total magnetic field (left side). The y-axis is normalized to both the electron (left side) and the proton skin depth $d_p$ (right side).
• Figure 2: (a) Radial behavior of the angle between the current density and the total magnetic field (azimuthal averages) for each structure depicted in Fig. \ref{['fig:speccontours']}-(b). (b) Force-free parameter $\lambda(r)$. We define $r_0$ as the vortex eye radius, namely the position of the first spiraling arm.
• Figure 3: (a) Total magnetic field and current density components for the central vortex in Fig. \ref{['fig:speccontours']} (open symbols) and the KVR model (solid lines). Data have been averaged over time in the vortex frame.
• Figure 4: Merging history of two long-lived structures as a function of Alfvénic crossing time (from top to bottom). The plot shows the plasma density (left column), the (force-free) cosine angle (middle column), and the magnetic helicity density (right column). Circumferences (in black) represent the eye of each vortex.
• Figure 5: Radial behavior of the magnetic field components of all the long-lived vortices appearing during the simulation (points). Components have been rescaled to the field at the center $B_0$ and using their typical gradient $\xi$. The GH solution (shaded) describes qualitatively well the profiles, near the eye.