Transition of Magnetic Reconnection Regimes in Partially Ionized Plasmas

Abstract

Magnetic reconnection in partially ionized plasmas plays a crucial role in a wide range of solar, astrophysical, and laboratory environments. While reconnection in such plasmas is commonly characterized by the ion-neutral coupling strength and the ionization fraction $χ=n_{i}/(n_{i}+n_{n})$, most previous studies have focused primarily on the former. A systematic exploration of the ionization fraction, particularly in combination with ion-neutral coupling, is still lacking. This study presents the first systematic scan of the two-dimensional parameter space defined by ion-neutral collisionality and ionization fraction, enabling investigation of the transition from strongly coupled reconnection to faster, decoupled reconnection. To achieve this, we employ a new three-fluid, five-moment numerical model that treats electrons, ions, and neutrals as separate species on an equal footing. We find that in the strongly coupled regime, the reconnection rate is consistent with a $χ^{1/4}$ scaling. As collisionality decreases, the system transitions to a fast, ionization-independent regime. On the other hand, in all simulations, the current sheet thins down to the ion inertial length di, rather than the expanded hybrid scale $d_{i}χ^{-1/2}$ predicted by analytic fluid theories. The identified critical thickness and the resulting onset of fast reconnection agree reasonably well with recent fully kinetic simulations and laboratory experiments. In addition, we show that, over a wide range of coupling strengths, the ion outflow velocities remain Alfvénic, scaling with the appropriate ion or hybrid Alfvén speed, while the hybrid outflow velocity scales as $χ^{1/2}$ when normalized by ion Alfvén speed.

Figures (5)

• Figure 1: Overview of the temporal evolution of reconnection rates and the spatial structure of electron outflows across the parameter space. (Top Row): Time-dependent reconnection rates normalized by the product of the asymptotic reconnecting magnetic field, $B_{0}$, and the ion Alfvén speed, $v_{A0}=B_{0}/\sqrt{\mu_{0}m_{i}n_{b}}$. The rates are computed as the time derivative of the globally reconnected flux, i.e., $\max(\psi)-\min(\psi))$ along the midplane, $\psi$ is the magnetic flux function. The columns correspond to runs with increasing ion-neutral collisionality, parameterized by the ratio of the mean free path to the ion inertial length, $\lambda_{{\rm mfp,in}}/d_{i0}$. Within each panel, curves represent different initial ionization fractions, $\chi_{0}$. (Rows 2--4): 2D snapshots of electron outflow velocities (normalized by the speed of light) taken at the time of the first primary peak in the reconnection rate. Each row corresponds to a specific ionization fraction. Note that such primary peak times may precede the global maximum rate in cases where secondary plasmoid formation occurs later.
• Figure 2: Scaling dependencies of the reconnection rate and current sheet geometry at onset. (a) Peak reconnection rate as a function of ionization fraction, $\chi_{0}$. Data points on the same curves represent the same ion-neutral collisionality, $\lambda_{{\rm mfp,in}}/d_{i0}$. The dashed line indicates the theoretical $\chi^{1/4}$ scaling for the resistive Sweet-Parker regime. (b) Peak reconnection rate as a function of the collisionality parameter, $\lambda_{{\rm mfp,in}}/d_{i0}$, for fixed $\chi_{0}$. A $\lambda_{{\rm mfp,in}}^{1/4}$ reference scaling is provided. (c) Scaling of the critical current sheet half-thickness, $\delta_{\rm CS}$, measured at the onset time (defined as 10% of the peak reconnection rate). The dashed slanted line represents the theoretical prediction for fully coupled fluids, while the horizontal dashed line marks the ion inertial length, $d_{i0}$.
• Figure 3: Dependence of current sheet morphology on ionization fraction and collisionality at the time of peak reconnection rate. (a) Current sheet half-thickness, $\delta_{\rm CS}$, and (b) half-length, $L_{\rm CS}$, plotted against the initial ionization fraction $\chi_{0}$. Dimensions are measured at the first primary peak of the reconnection rate to minimize effects from secondary island formation. The dashed line in panel (b) represents a $\chi_{0}^{1/4}$ scaling.
• Figure 4: Spatial profiles of ion (blue solid) and neutral (orange dashed) inflow (first and third rows) and outflow (second and bottom rows) velocities in the vicinity of the X-point. (Top Two Rows) Velocity profiles taken at the pre-onset phase (5% of peak reconnection rate). (Bottom Two Rows) Velocity profiles taken during the fast reconnection phase (90% of peak rate). All panels display results for the low ionization case ($\chi_{0}=0.02$), with ion-neutral collisionality decreasing from left to right ($\lambda_{{\rm mfp,in}}/d_{i0}$ increasing).
• Figure 5: Scaling of maximum ion-only and hybrid-ion-neutral inflow/outflow velocities versus ionization fractions. Different lines correspond to run sets with different ion-neutral collisionality. The velocities are evaluated at the time of the first primary peak in each run, measured along inflow and outflow cuts through the primary X-point. All velocities are normalized to the initial asymptotic ion-only Alfvén speeds, $v_{A,{\rm ion,up}}$. Dashed lines indicate the reference $\chi^{1/2}$ scaling.