Inverse transfer of energy in kinetic plasma turbulence*

The physical picture of a turbulent sea of interacting magnetic islands (or flux tubes in 3D) provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath, the Earth’s magnetosphere, or the Weibel-instability-generated magnetic fields in collisionless shocks or in the early intracluster medium.

Previous investigations conducted within the MHD framework, specifically the studies by Zhou et al. (2020, 2021), have examined the process of successive merging of magnetic islands via magnetic reconnection. However, due to the inherent collisionless nature of the systems under scrutiny, a kinetic study focused on the dynamics of magnetic islands becomes imperative. Therefore, we perform first-principles particle-in-cell simulations of this problem. Our investigations identify collisionless magnetic reconnection as the fundamental mechanism facilitating the merging of magnetic islands and the subsequent inverse transfer of energy. Qualitatively, we observe that the decay of energy and the increase of the coherence length of magnetic fields exhibit similarities to their counterparts in MHD.  Nevertheless, when the system reaches sub-ion scales, quantitative disparities emerge in properties such as the magnetic energy spectrum and the topology of merged island, which are likely attributable to kinetic effects, including the finite ion Larmor radius, electron inertial effects, and the Landau damping of kinetic Alfvén waves.