Suppression of inverse magnetic energy transfer in collisionless marginally magnetized plasmas

TL;DR

This study addresses whether inverse transfer of Weibel-seeded magnetic structures can proceed in decaying, collisionless high-$β$ plasmas and how kinetic instabilities regulate it. Using fully kinetic PIC simulations and analytical CGL-MHD reasoning, the authors show that pressure-anisotropy–driven microinstabilities, especially the firehose, can quench magnetic tension and arrest reconnection-driven coalescence when the plasma is only marginally magnetized. In the absence of a strong guide field, the inverse cascade slows and the structures elongate near the Larmor scale; a finite guide field or larger scale separation between island size and the Larmor radius restores tension and sustained energy transfer, with $k_{ m max} \propto (t-t_0)^{-0.42}$ in the unblocked cases. The results imply that Weibel-generated seed fields may fail to merge coherently in hot, collisionless astrophysical plasmas, potentially limiting their role in cosmic magnetogenesis.

Abstract

We investigate the inverse cascade of magnetic energy in decaying, collisionless plasmas with moderate to high-$β$ values via first-principles numerical simulations and analytical theory. We find that pressure-anisotropy-driven instabilities, in particular the firehose instability, suppress reconnection-driven coalescence of magnetic structures (i.e., inverse transfer) by nullifying magnetic tension. This suppression leaves such structures elongated and confined to scales comparable to the Larmor radius of the particles. The presence of a magnetic guide field of sufficient strength, or a greater scale separation between the initial size of the magnetic structures and the Larmor radius, restores the system's ability to inverse transfer magnetic energy. These results reveal that inverse energy transfer in collisionless plasmas is not guaranteed, but instead sensitively depends on magnetization. In the astrophysical context, this identifies a kinetic mechanism by which Weibel-generated seed fields may fail to merge consistently, potentially limiting their role in cosmic magnetogenesis.

Figures (9)

• Figure 1: Time evolution of the energy-containing wavenumber $k_{\rm max}$ (top), magnetic energy $\mathcal{E}_M$ and plasma beta $\beta$ (middle), and the Larmor radius $\rho$ as well as the ratio $\rho/R$ between the Larmor radius and the average magnetic structure size (bottom). The vertical dashed line marks the approximate onset of significant pressure anisotropy effects.
• Figure 2: Contours of magnetic flux at $\omega_{p}t = 2500$. Blue and orange identify the locations unstable to the firehose or mirror instabilities, respectively.
• Figure 3: Top row (a)–(c): Out-of-plane current density (color scale) and magnetic flux contours (curves) at $\omega_p t = 10000$ for simulations with guide field strengths $\hat{B}_G = 0$, $1.0$, and $2.0$, respectively. Middle row (d)–(f): Magnetic energy spectra at successive times for each corresponding case. Insets show the temporal evolution of the wavenumber $k$ at which the magnetic energy spectrum peaks. Bottom row (g)–(i) : Scatter plots of pressure anisotropy $T_{\perp}/T_{\|} - 1$ versus parallel plasma beta $\beta_{\|}$ at progressively later times, indicated by color. In panels (h) and (i) , arrows denote theoretical predictions for the anisotropy evolution trajectories (see Appendix \ref{['app:sec:1']} for details).
• Figure 4: Time evolution of energy containing scale $k_{\rm max}$ (top panel), magnetic energy $\mathcal{E}_M$ and plasma beta $\beta$ (middle panel), Larmor radius $\rho$, and ratio between Larmor radius and averaged magnetic structure size $\rho/R$ (bottom panel) from the well magnetized simulations without a guide magnetic field.
• Figure 5: (a) Contour plot of $G(\hat{B}_G, \beta_0)$. The red curve denotes the locus where $G(\hat{B}_G, \beta_0) = 0$, and the shaded region marks the parameter space in which inverse transfer is suppressed by the firehose instability. (b) Inverse cascade ratio as a function of plasma beta if firehose condition is triggered, obtained by solving Eq. \ref{['app:eq:tstar']}. Only the portions of the curve lying below the horizontal lines associated with a given guide field $\hat{B}_G$ represent valid solutions (see Eq. \ref{['app:eq:valid']}).