Triggering physical plasmoids in forming current sheets: conditions and diagnostics

Abstract

We investigate the conditions for triggering the plasmoid instability in a dynamically forming current sheet in the resistive magnetohydrodynamic framework, using a pseudo-spectral code applied to the Orszag-Tang vortex at Lundquist number $S \sim 10^5$. Following García Morillo \& Alexakis (2025), we use the power spectrum of the current density $E_J(k)$, complemented by the vorticity spectrum $E_ω(k)$, to assess the convergence of our simulations, and show that this diagnostic remains valid even in the presence of physical plasmoids, allowing us to unambiguously distinguish them from spurious ones. We then show that physical plasmoids can be triggered in a well-resolved spectral simulation when three conditions are simultaneously met: a perturbation applied near the time of maximum current density, with amplitude above a critical threshold $\varepsilon_c \sim 10^{-5}$ for our numerical scheme, and with spectral content containing the unstable wavenumbers. These conditions are confirmed using continuous noise injection, which yields similar results at amplitudes one to two orders of magnitude lower. The resulting growth rates and plasmoid numbers are in good agreement with the theory of \citet{Comisso2017}. These results resolve the apparent paradox raised by García Morillo \& Alexakis (2025) and also clarify the role of numerical noise in the triggering of the plasmoid instability.

Figures (8)

• Figure 1: Initial configuration of the Orszag-Tang vortex. Color map shows the current density $J = \nabla^2 A$ and white streamlines indicate the velocity field $\mathbf{v}$. The black rectangle delimits the current sheet region along $y = 0$ that is the focus of this study.
• Figure 2: Zoom onto the current sheet (region indicated by the black rectangle in Figure \ref{['fig:OTini']}) at $t = 0.9$, $1.4$, $1.9$, and $2.4$ (from up to down). Color map shows the squared current density $J^2$. The sheet thins and intensifies up to the peak at $t \simeq 1.9$, then relaxes. $N = 2048$, $\eta = 10^{-4}$, and no perturbation ($\varepsilon = 0$). Times are expressed in Alfvén time units (see text for definition)
• Figure 3: Transverse profiles of the current density $J$ (left panel) and magnetic field components (right panel) at $x = 0$ and $t = 1.9$. The half-thickness $\delta$ and upstream Alfvén velocity $v_A$ can be extracted from these profiles, and used to estimate relevant parameters as the Lundquist number $S$ (see text). $N = 2048$, $\eta = 10^{-4}$, and $\varepsilon = 0$.
• Figure 4: Squared current density $J^2$ in the current sheet region at $t = 2.2$, $2.3$, and $2.4$ (top to bottom) for $N = 1024$, $\eta = 10^{-4}$, and $\varepsilon = 0$. Spurious plasmoids develop and grow during the relaxation phase, in stark contrast with the smooth, plasmoid-free sheet observed at the same times for the converged case $N = 2048$ (Figure \ref{['fig:sheet_evolution']}). Times are expressed in Alfvén time units (see text for definition)
• Figure 5: Power spectra of the current density $E_J(k)$ (blue) and vorticity $E_\omega(k)$ (red) at $t = 2.3$, for $N = 1024$ (left) and $N = 2048$ (right), at $\eta = 10^{-4}$ and $\varepsilon = 0$. At $N = 1024$, both spectra fail the convergence criterion $\max_k\{E_J(k)\} \geq 10\,E_J(k_{\max})$, indicating an incomplete dissipative cascade in both fields (spurious plasmoids are present, see figure 4). At $N = 2048$, both spectra are well-resolved, with energy decreasing to negligible values before $k_{\max}$ (plasmoids are absent, see figure 2).