Can Hall Magnetohydrodynamics Explain Plasma Turbulence at Sub-ion Scales?

Abstract

We investigate the properties of plasma turbulence by means of two-dimensional Hallmagnetohydrodynamic (HMHD) and hybrid particle-in-cell (HPIC) numerical simulations. We find that HMHD simulations exhibit spectral properties that are in most cases in agreement with the results of the HPIC simulations and with solar wind observations. The energy spectra of magnetic fluctuations exhibit a double power-law with spectral index −5/3 at MHD scales and −3 at kinetic scales, while for velocity fluctuations the spectral index is −3/2 at MHD scales. The break between the MHD and the kinetic scales occurs at the same scale in both simulations. In the MHD range the slopes of the total energy and residual energy spectra satisfy a fast Alfvén-dynamo balance. The development of a turbulent cascade is concurrently characterized by magnetic reconnection events taking place in thin current sheets that form between large eddies. A statistical analysis reveals that reconnection is qualitatively the same and fast in both the HMHD and HPIC models, characterized by inverse reconnection rates much smaller than the characteristic large-eddy nonlinear time. The agreement extends to other statistical properties, such us the kurtosis of the magnetic field. Moreover, the observation of a direct energy transfer from the large vortices to the small sub-ion scales triggered by magnetic reconnection, further supports the existence of a reconnection-mediated turbulent regime at kinetic scales. We conclude that the Hall-MHD fluid description captures to a large extent the transition of the turbulent cascade between the large MHD scales and the sub-ion scales.

The Interplay of Magnetically Dominated Turbulence and Magnetic Reconnection in Producing Nonthermal Particles

“…An animation showing the current density Jz in different xy slices can be found at https://doi.org/10.7916/d8-prt9-kn88. vidio et al 2009;Wan et al 2013;Franci et al 2017;Haggerty et al 2017;Dong et al 2018;Comisso & Sironi 2018;Papini et al 2019), play an important role for particle injection into the acceleration process (Comisso & Sironi 2018). Finally, we also point out that in the strongly magnetized regime of plasma turbulence investigated here, the plasma bulk speed can reach very high values.…”

Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

“…Moreover, the interplay between fast reconnection and turbulence can be crucial, as predicted by reconnection-mediated turbulence models (Boldyrev & Perez 2012;Loureiro & Boldyrev 2017;Mallet et al 2017) and by recent numerical simulations of the solar wind plasma retaining kinetic effects (Franci et al 2017), where the role of reconnection in driving the turbulent cascade at sub-ion scales through the destabilization of current sheets of thickness a ≃ d i is estabilished. However, a recent study by Papini et al (2019) has demonstrated that the role of reconnection in shaping the spectrum of solar wind turbulence, including the change of slope at the ion inertial length d i , may be captured even without resorting to (hybrid) particle-in-cell simulations, by just retaining the Hall effect within a macroscopic MHD description, as in the present study.…”

“…obtained by taking, at each time, the logarithmic time derivative of the reconnected flux Φ i between the i-th pair of X-and O-points and then averaging over the number of pairs, N, in the main current sheet. Here, Φ i is the difference between the scalar potential φ at the O-and the X-point in the i-th pair (for more details and applications to simulations of plasma turbulence see the Appendix of Papini et al 2019 panel of Figure 4 shows γ rec for our MHD reference run. As we can see, after the initial perturbations have rearranged to select the fastest tearing eigenmodes, γ rec reaches a plateau with a value γ rec τ A ≃ 0.4.…”

Reconnection from a turbulence perspective

“…In some observations, the reconnection does not couple to the ions 35,50 because the length scales associated with the turbulence are too small 38,48 , a fact born out by simulations of turbulence 8,17 . Finally, reconnection has been shown in some cases to modify the cascade of turbulent of energy from large to small scales 6,9,11,14,27,33 .…”