Ion Temperature Anisotropy Limits from Magnetic Curvature Scattering in Magnetotail Reconnection Jets

TL;DR

This work addresses how ion temperature anisotropy in collisionless magnetotail current sheets is limited to preserve stability during reconnection jets. It develops a quasi-1D current-sheet model with three ion populations and derives two curvature-driven thresholds: a Firehose-like limit for parallel anisotropy and a drift-type limit for perpendicular anisotropy associated with Speiser ions, with the adiabaticity parameter $\kappa$ governing the regime. The authors validate these limits against MMS near-Earth observations, ARTEMIS lunar-distance data, and two fully kinetic PIC simulations (Lembège–Pellat and Harris equilibria), finding substantial agreement between theory and measurements. The results emphasize that curvature scattering and the presence of Speiser ions jointly constrain current-sheet dynamics, providing a unified framework linking anisotropy, current-sheet stretching, and stability in magnetotail plasmas.

Abstract

In collisionless plasmas, relaxation of the deviations of ion velocity distribution functions (VDFs) from local thermodynamic equilibrium (LTE) occurs through particle interactions with electromagnetic fields. In particular, in the Earth's magnetotail, the deviations of the ion VDFs, typically consisting of multiple components, from the equilibrium must be limited to maintain stability of the current sheet. Curvature scattering is a leading candidate mechanism to limit such deviations, but its role remains insufficiently understood. We investigate the limits of ion temperature anisotropy in a magnetotail-like configuration by modeling a quasi-1D current sheet with a finite magnetic field curvature and three ion populations. We derive analytical thresholds for anisotropy based on current sheet stability and validate against spacecraft observations and numerical results. Our findings demonstrate that curvature scattering imposes limits on ion anisotropies, thereby maintaining the stability of the current sheet.

Figures (5)

• Figure 1: (a) Current density and (b) adiabaticity parameter in the model 1D current sheet with three ion populations with $\eta_e=$, $\eta_s=$, and $\eta_c=$. The parallel anisotropy limit [Eqs. \ref{['eq:j-tot-cold']} and \ref{['eq:kappa-cold']}] is shown in the lower half of each panel $T_{i\bot}/T_{i\parallel} < 1$, and the perpendicular anisotropy limit [Eqs. \ref{['eq:j-tot-speiser']} and \ref{['eq:kappa-speiser']}] is shown in the upper half $T_{i\bot}/T_{i\parallel} > 1$. The black thick line indicate $\kappa=1$ and the black thin lines indicate $\kappa=10^{-2},\,10^{-1},\,10^{1},\,10^{2}$. The dashed cyan lines indicate the anisotropy thresholds [Eqs. \ref{['eq:threshold-cold']} and \ref{['eq:threshold-speiser']}].
• Figure 2: Overview of the example event from MMS. (a) Magnetic field in the minimum variance. (b) Ion bulk velocity in GSM coordinates. (c) Ion number density. (d) Ion temperature anisotropy with respect to the local magnetic field. (e) Curvature parameter $\kappa$.
• Figure 3: Comparison between MMS observations and PIC simulation results for ion temperature anisotropy. Panels (a)–(d) and (e)–(h) show 1D profiles of: (a, e) ion temperature parallel to the local magnetic field, (b, f) ion temperature perpendicular to the magnetic field, (c, g) ion temperature anisotropy, and (d, h) the magnetic field curvature parameter. Black crosses represent MMS measurements during the event shown in Fig. \ref{['fig:event']}. Solid blue and red lines correspond to profiles extracted along magnetic field lines in the PIC simulation, intersecting the $z=0$ plane at $\delta x = 5d_i$ and $\delta x = 11d_i$, respectively. Panels (i) and (j) present 2D maps of ion temperature anisotropy and curvature parameter from the PIC simulation.
• Figure 4: Distribution $\textrm{PDF}(T_{i\bot}/T_{i\parallel}, \beta_{i\parallel})$ in: (a) the near-Earth magnetotail BBFs from MMS richard_fast_2023, (b) the midtail current sheet kamaletdinov_thin_2024, (c) PIC-LP simulation of forced magnetic reconnection in a Lembege and Pellat equilibrium magnetotail current sheet an_configuration_2022, and (d) PIC-HC simulation of forced reconnection in a Harris-like equilibrium current sheet with cold ions norgren_presence_2021.
• Figure 5: Anisotropy $T_{i\bot}/T_{i\parallel}$ (a) and adiabaticity parameter $\kappa$ (b) of initially cold ions in the PIC-HC simulation. The black contour indicates $\kappa=1$. The green contour indicates the region of interest for Fig. \ref{['fig:brazil-plots']}(d).