Inverse Transfer in Non-helical 2D Collisionless Magnetic Turbulence: Island-Merger Picture with Kinetic Effects

Abstract

Magnetic inverse transfer is often invoked to connect small-scale magnetic-field generation to larger coherence scales in high-energy and cosmological plasmas. The underlying magnetohydrodynamic (MHD) arguments combine two logically distinct ingredients: a bulk quantity that is asymptotically conserved in the limit of small resistivity, and a time scale determined by the decay dynamics. In this work, we explore whether this scenario still holds in decaying nonhelical turbulence formed by collisionless plasmas using particle-in-cell simulations. The simulations approximately satisfy $B^2\xi_B^2\simeq{\rm const}$ as in the MHD case, and the fitted exponents in $B^2\propto t^{-p}$ and $\xi_B\propto t^q$ obey $p\simeq2q$. Here $B^2\equiv\langle B_x^2+B_y^2\rangle$ is the average in-plane magnetic energy density, and $\xi_b$ is the magnetic integral scale. However, the decay time scale differs from the MHD case as inferred from the decay exponents. We found $p<1$ and $q<1/2$ in all cases with different initial magnetization $\sigma_0$, with both exponents lower than the MHD values and varying systematically with $\sigma_0$. The spectral peak also migrates toward lower wavenumber at a rate faster than the growth of $\xi_B$, indicating a broken self-similarity. The broken self-similarity is attributed to the appearance of kinetic scales in the magnetic energy spectrum due to pressure anisotropy and Larmor-scale magnetic structures. These results indicate that in astrophysical collisionless plasmas, including but not restrict to solar wind, pulsar-wind nebulae, interstellar medium, and cosmological plasmas, magnetic coherence can continue to grow by inverse transfer, but extrapolations based on MHD decay-time scaling can overestimate the rate of large-scale field growth.