Line-Tied Flux Rope Relaxation and Reconnection: A 3D Kinetic Case Study

Abstract

Magnetic flux ropes are ubiquitous magnetic structures found in plasmas ranging from astrophysical to laboratory. We employ a newly-developed parallel-kinetic-perpendicular-moment (PKPM) model to simulate the 3D interaction and evolution of two line-tied flux ropes at realistic laboratory plasma parameters, while retaining essential parallel kinetic physics in the system. We find that ropes undergo a current-dependent transition from a diamagnetic to paramagnetic regime, which we quantify with a simple analytic model. Although the macroscopic structural evolution qualitatively differs significantly between these regimes, analyzing the reconnection in proper field-aligned coordinates reveals that the underlying kinetic dynamics remain similar. Using the squashing factor and quasi-potential as diagnostics of 3D magnetic reconnection, we identify the formation of a quasi-separatrix layer and show that these quantities provide consistent metrics for reconnection rate and structure.

Figures (7)

• Figure 1: 3D structure of the interacting flux ropes in the low-current case (case I, top) and high-current case (case II, bottom). Representative field lines are drawn originating at $z=\qty{0}{\meter}$ near the flux rope centers, with the blue or red color indicating which center the line started near. The volume-filling orange color indicates current magnitude in $\unit{\ampere\per\square\centi\meter}$, and the cyan surface indicates the QSL structure by a surface of constant squashing factor, $Q=1000$. Contours of the 2D flux function $\psi$ are also indicated on 2D cuts at $z=0$, $5$, and $\qty{10}{\meter}$.
• Figure 2: 2D cuts in the $x$-$y$ plane of the low-current (case I) and high-current (case II) 3D simulations at the $z=\qty{5}{\meter}$ plane at early time (a, c, e) and late time (b, d, f) showing plasma density (a, b), current density (c, d), and magnetic field deviation from the background, $\Delta{\bm{B}} = {\bm{B}} - B_0\hat{z}$ (e, f). For vector quantities ${\bm{J}}$ and ${\bm{B}}$, the out-of-plane ($\hat{z}$) component is indicated by the color, while the in-plane component direction and magnitudes are indicated by the arrow direction and lengths. The cyan contour indicates a contour of constant squashing factor $Q=500$ to show the QSL structure. Note that at late time, the squashing factor has dropped below this value everywhere in case I.
• Figure 3: Azimuthal current-induced magnetic perturbation in the $\hat{z}$ direction for a single flux rope after initial electron-scale relaxation of the system as a function of the total current, from 2D simulations (blue) and Eq. \ref{['eq:paradia']} (orange). The transition from diamagnetism at low current to paramagnetism at high current occurs when $\delta B$ switches signs at $I\approx\qty{600}{\ampere}$ in simulations compared to $I\approx\qty{550}{\ampere}$ from Eq. \ref{['eq:paradia']}.
• Figure 4: Comparison of electric field support in case I and case II. The top row shows out-of-plane current $J_z$ in an $x$-$y$ plane slice at $z=\qty{3.6}{\meter}$ at a normalized time of $t/\tau_{Am}=0.6$. The overlayed contours indicate surfaces of the flux function $\psi$. Term-by-term components of line-outs taken along the indicated magenta dashed line are shown for $x'$, $y'$, and $z'$ directions in the next three rows, respectively, as they vary along the $x'$ coordinate direction. We indicate the axes of this rotated coordinate system with arrows on the top row plots.
• Figure 5: The $\hat{z}'$ component of the pressure gradient term of the electric field (green) shown in the cuts in Fig. \ref{['fig:ohm_cartesian']}, separated further into its individual pressure tensor component terms.