Disruption of sheet-like structures in Alfvénic turbulence by magnetic reconnection

Abstract

We propose a mechanism whereby the intense, sheet-like structures naturally formed by dynamically aligning Alfv\'enic turbulence are destroyed by magnetic reconnection at a scale $\hat{\lambda}_{\rm D}$, larger than the dissipation scale predicted by models of intermittent, dynamically aligning turbulence. The reconnection process proceeds in several stages: first, a linear tearing mode with $N$ magnetic islands grows and saturates, and then the $X$-points between these islands collapse into secondary current sheets, which then reconnect until the original structure is destroyed. This effectively imposes an upper limit on the anisotropy of the structures within the perpendicular plane, which means that at scale $\hat{\lambda}_{\rm D}$ the turbulent dynamics change: at scales larger than $\hat{\lambda}_{\rm D}$, the turbulence exhibits scale-dependent dynamic alignment and a spectral index approximately equal to $-3/2$, while at scales smaller than $\hat{\lambda}_{\rm D}$, the turbulent structures undergo a succession of disruptions due to reconnection, limiting dynamic alignment, steepening the effective spectral index and changing the final dissipation scale. The scaling of $\hat{\lambda}_{\rm D}$ with the Lundquist (magnetic Reynolds) number $S_{L_\perp}$ depends on the order of the statistics being considered, and on the specific model of intermittency; the transition between the two regimes in the energy spectrum is predicted at approximately $\hat{\lambda}_{\rm D} \sim S_{L_\perp}^{-0.6}$. The spectral index below $\hat{\lambda}_{\rm D}$ is bounded between $-5/3$ and $-2.3$. The final dissipation scale is at $\hat{\lambda}_{\eta,\infty}\sim S_{L_\perp}^{-3/4}$, the same as the Kolmogorov scale arising in theories of turbulence that do not involve scale-dependent dynamic alignment.