Plasmoid growth in 2D Full-F Gyrofluid Magnetic Reconnection

Abstract

Plasmoid growth is considered to enhance the rate of magnetic reconnection and is frequently used to explain fast mag netic reconnection in highly conductive (collisionless) plasmas. In strongly magnetized plasmas, the long wavelength dimension parallel to the magnetic field can be separated from the small wavelength perpendicular plane, justifying an isolated 2D approach. While 2D systems have been simulated using delta F gyrofluids, a novel Full-F gyrofluid model with arbitrary wavelength polarization is used to simulate 2D Harris-sheet magnetic reconnection with domain aspect ratios Ly/Lx < 16 and investigate the corresponding plasmoid growth and tearing instability growth rates. In addition to linear tearing analysis, a non-modal stability analysis of the linearised system is performed. The evolution operator is shown to be strongly non-normal, exhibiting large condition numbers and extended pseudospectra, which indicate the possibility of significant transient amplification even in marginally stable regimes. This non-normal behavior pro vides a mechanism for explosive reconnection and helps explain the transition from linear tearing growth to rapid nonlinear acceleration. We focus on low plasma beta magnetic reconnection on the scale of the hybrid drift scale and incorporate ion finite Larmor radius (FLR) effects, putting the simulations in the perspective of magnetically confined nuclear fusion devices such as tokamaks. After discussing requirements on numerical resolution and convergence we present a parameter scan, varying the electron skin depth and the ion-to-electron temperature ratio. Finally, we present a discussion on the influence of aspect ratio, different models and possible contributions due to FLR effects.

Figures (13)

• Figure 1: The linear growth rate $\hat{\gamma}_{\mathrm{lin}}$ at marginal stability as a function of $\beta$. The growth rate declines approximately as $\beta^{-1/2}$, predicted for large pressure dominated regimes.
• Figure 2: Mode-resolved evolution matrix $\mathcal{A}_m$ obtained from the Fourier-sum representation of the initial parallel vector potential $\hat{A}_{\parallel,0} = a_0 \cos(mx)$. Using the sifting property of the Dirac delta distribution, the convolution reduces to an algebraic eigensystem for each mode number $m$. The spectrum of $\mathcal{A}_m$ is analyzed as a function of $\beta$, $k_x$, and $\hat{k}_{\hat{y}}$, allowing investigation of the condition number and pseudospectral behavior near marginal stability.
• Figure 3: Contour plots of the $\epsilon$-pseudospectrum of $\mathcal{A}_m$, overlaid with the numerical abscissa (blue dotted line), for $m=1$ and $\hat{k}_{\hat{y}} = 0.1,\,1,\,10$ (left, right, bottom). When $\hat{k}_{\hat{y}} \geq 1$, the spectrum becomes purely real and shifts progressively toward the unstable half-plane.
• Figure 4: Explosive magnetic reconnection for a warm $\tau_i=1$ Harris-sheet at $\beta=5\cdot 10^{-3}$ and $m=1$. The initial phase is followed by a hyper-linear (I), linear (II), and again hyper-linear (III) (explosive) phase until the reconnection is complete (IV). The linear phase grows around $\gamma=0.1 v_A B_0$ while the explosive reconnection peaks at $\gamma \approx 0.2 v_A B_0$.
• Figure 5: Logarithmic plot of the time evolution of $\Delta \Psi$ for different values of $\beta$. As expected from the dispersion relation, the change in $\Delta \Psi$ decreases with $\beta$ and the reconnection shows a clear linear phase (straight line).

Theorems & Definitions (1)

• Definition 3.1: $\epsilon$- pseudospectrum