Driven Collisionless Reconnection of Force-free Flux Tubes: From Onset to Coalescence

Abstract

We investigate the onset of driven collisionless reconnection and plasmoid formation in a magnetically dominated pair plasma, using 2D Particle-in-Cell simulations. Two force-free flux tubes of radius $R$ are initially pushed together with a prescribed velocity, forming a current sheet whose width shrinks until reconnection sets in. % Even in our largest simulation with $R\approx 1600$ plasma skin depths, the sheet thickness at reconnection onset is comparable to the skin depth. Plasmoid chains develop when the sheet length-to-width aspect ratio $A\gtrsim30$. In the strongly magnetized limit, the onset of reconnection occurs in roughly 2--6 light-crossing times, depending on the imposed driving timescale, which controls the duration of the thinning phase. In the subsequent nonlinear merging phase, the evolution becomes effectively independent of the initially imposed velocity, leading to magnetic-energy dissipation consistent with a normalized reconnection rate $\sim 0.1$. Our results have important implications for explosive release of magnetic energy in magnetospheres of astrophysical compact objects and their surroundings.

Figures (11)

• Figure 1: (a)--(c): Contours of out-of-plane current density $J_z$ (color scale) and magnetic field lines (black) during the evolution of the flux tubes. The dashed black boxes mark the regions shown in the zoomed-in view below. (d): Temporal evolution of the energy components, $\varepsilon_i = (E_i(t)-E_i(0))/E_{B_\perp} (0)$. (e): Time evolution of the normalized reconnection rate. (f): $k_x$-spectra of the magnetic flux function averaged inside the current sheet (over $10 d_{e0}$ along $y$). The color-coded intensity represents the logarithmic amplitude of the wavenumbers. Key time thresholds ($t_{\rm onset}$, $t_{\rm merg}$, and $t_{\rm relax}$) are indicated by vertical dashed lines. This simulation was run with $v_{\text{push}}=0.05c$ ($t_{\rm drive}=20R/c$), $\sigma_0=50$ ($\sigma_{\text{in}}=8)$, and $R/d_{e0}=205$.
• Figure 2: Time evolution of the normalized current sheet width, $a(t)/d_{e0}$, and the aspect ratio, $A(t)=\ell(t)/a(t)$, for different system sizes at $\sigma_{\text{in}}=8$. Inset: the evolution of $\ln\left(a(t)/d_{e0}\right)$, showing the exponential thinning.
• Figure 3: (a): Reconnection onset times as a function of the driving timescale for $\sigma_{\text{in}}=8$ and $\sigma_{\text{in}}=128$ at $R/d_{e0} = 204$. (b): Onset times as a function of in-plane magnetization for $t_{\rm drive} c/R = 50$. The dashed lines show the theoretical estimate, Eq. \ref{['tons']}.
• Figure 4: (a): Evolution of the out=-of-plane current density $J_z$ for $R/d_{e0}=408$ and $v_{\text{push}}=0.02c$ (data shown have been downsampled by a factor of 8). (b): Maximum number of plasmoids and the minimum interplasmoid distance at the start of Phase II as functions of the system size $R/d_{e0}$, for $t_{\rm drive}=50 R/c$ ($v_{\text{push}}=0.02c$) and $\sigma_{\text{in}}=8$. Crosses indicate the same quantities for a shorter driving time, $t_{\rm drive}=2.5 R/c$ ($v_{\text{push}}=0.4c$).
• Figure 5: Reconnection rate $R_{\rm rec }$ as measured via Eq. \ref{['recmeassure']}. (a): values averaged over time during Phase II (i.e., from $t_{\rm onset}$ to $t_{\rm merg}$, where $t_{\rm merg}$ marks the beginning of the merger Phase III). (b): evolution of $R_{\rm rec}$ in time for various $v_{\rm push}$. Dashed vertical lines mark $t_{\rm merg}$.