Subion-Scale Turbulence Driven by Magnetic Reconnection

The interplay between plasma turbulence and magnetic reconnection remains an unsettled question in astrophysical and laboratory plasmas. Here, we report the first observational evidence that magnetic reconnection drives subion-scale turbulence in magnetospheric plasmas by transferring energy to small scales. We employ a spatial “coarse-grained” model of Hall magnetohydrodynamics, enabling us to measure the nonlinear energy transfer rate across scale $\ell$ at position $\mathit{x}$. Its application to Magnetospheric Multiscale mission data shows that magnetic reconnection drives intense energy transfer to subion-scales. This observational evidence is remarkably supported by the results from Hybrid Vlasov-Maxwell simulations of turbulence to which the coarse-grained model is also applied. These results can potentially answer some open questions on plasma turbulence in planetary environments.

Figure 1

MMS1 data: (a) the three components of the magnetic field in GSE (geocentric solar ecliptic); (b) $\mathit{J}·{\mathit{E}}^{\prime }$, where ${\mathit{E}}^{\prime }$ is the electric field in the electron rest frame; (c) the estimated transfer rate ${\pi }_{\tau }(t)$ using the CG Hall-MHD model. The curves in panel (c) indicate the local Taylor shifted ion Larmor radius ${\rho }_i$ and inertial length $d_i$. The dashed line at $1/f_b\sim 10\mathrm{s}$ marks the transition into the inertial range (cfr. Fig 2). Arrows 1-6 show reconnecting CS. Panels (d)–(i) are an enlargement of a reconnecting CS (the vector components are given in LMN coordinates). In panels (e) and (f) the background mean flow $⟨v_i⟩$ was removed to highlight the super-Alfvénic ($V_A=B_0/\sqrt{{\mu }_0{\rho }_0}=120\mathrm{km}/\mathrm{s}$) outflows in the $L$ direction. In panel (h) ${\mathit{J}}_c=\nabla \times \mathit{B}/{\mu }_0$ (red) is the electric current computed using the curlometer technique plotted for comparison.

Figure 2

Magnetic field power spectrum for the interval displayed in Fig. 1; dotted lines denote power-law fits within the different spectral ranges. The spectrum at low frequency (red curve) is computed over the full burst mode interval, $12:52:43–13:03:03$. Panel (b) shows the histogram of $\delta B(\tau )=|\mathit{B}|(t+\tau )-|\mathit{B}|(t)$ for two values of $\tau$ marked in (a) with a green cross. Superimposed is a Gaussian with matching first and second order moments (green curves).

Figure 3

Panel (a) shows the out-of-plane current $j_z$ at $t{\mathrm{\Omega }}_i=272$ and the trajectory $S_1$ crossing a reconnecting region highlighted with a black frame and in the inset (b). Panels (c)–(e) show quantities interpolated along $S_1$ in the reconnecting region: (c) the three components of the magnetic field (the background field $B_0\widehat{z}$ was removed), (d) the out-of-plane electric field in the ion (electron) rest frame as a marker of the ion (electron) diffusion region, (e) the nonlinear transfer rate ${\pi }_{\ell }(\mathit{x})$ as a function of scale $\ell$ and position along the curve. Numbers 1–4 denote the reconnection sites.

Figure 4

Panels (a)–(d) show the cross-scale transfer rate ${\pi }_{\ell }(\mathit{x})$ computed at $\ell =0.3d_i$ within the current sheet undergoing MR. Superimposed are the magnetic field lines. Panel (e) shows the prominence of the $E_z^{\prime ,e}$ peak at each $X$ point (denoted 1–4) and referenced in panels (a)–(d) as a function of time while in panels (f),(g) we display ${\pi }_{\ell }$ averaged along the trajectory $S_1$ and the max value of $|j|$ along the same trajectory. Lastly, panel (h) shows the evolution of the magnetic field spectrum computed along $S_1$.