Kinetic cascade in solar-wind turbulence: 3D3V hybrid-kinetic simulations with electron inertia

Understanding the nature of the turbulent fluctuations below the ion gyroradius in solar-wind turbulence is a great challenge. Recent studies have been mostly in favor of kinetic Alfv\'en wave (KAW) type of fluctuations, but other kinds of fluctuations with characteristics typical of magnetosonic, whistler and ion Bernstein modes, could also play a role depending on the plasma parameters. Here we investigate the properties of the sub-proton-scale cascade with high-resolution hybrid-kinetic simulations of freely-decaying turbulence in 3D3V phase space, including electron inertia effects. Two proton plasma beta are explored: the "intermediate" $\beta_p=1$ and "low" $\beta_p=0.2$ regimes, both typically observed in solar wind and corona. The magnetic energy spectum exhibits $k_\perp^{-8/3}$ and $k_\|^{-7/2}$ power laws at $\beta_p=1$, while they are slightly steeper at $\beta_p=0.2$. Nevertheless, both regimes develop a spectral anisotropy consistent with $k_\|\sim k_\perp^{2/3}$ at $k_\perp\rho_p>1$, and pronounced small-scale intermittency. In this context, we find that the kinetic-scale cascade is dominated by KAW-like fluctuations at $\beta_p=1$, whereas the low-$\beta$ case presents a more complex scenario suggesting the simultaneous presence of different types of fluctuations. In both regimes, however, a non-negligible role of ion Bernstein type of fluctuations at the smallest scales seems to emerge.Comment: 6 pages, 5 figures, final version published in The Astrophysical Journal Letters: Cerri, Servidio & Califano, ApJL 846, L18 (2017

The third-order law for magnetohydrodynamic turbulence with constant shear

The scaling laws of mixed third‐order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence have been recently applied in solar wind studies, even though there is recognition that isotropy is not well satisfied. Other studies have taken account of the anisotropy induced by a constant mean magnetic field. However, large‐scale shear can also cause departures from isotropy. Here we examine shear effects in the simplest case, and derive the third‐order laws for MHD turbulence with constant shear, where homogeneity is still assumed. This generalized scaling law has been checked by data from direct numerical simulations (DNS) of two‐dimensional (2D) MHD and is found to hold across the inertial range. These results suggest that third‐order structure function analysis and interpretation in the solar wind should be undertaken with some caution, since, when present, shear can change the meaning of the third‐order relations

Generation of X-points and secondary islands in 2D magnetohydrodynamic turbulence

We study the time development of the population of X-type critical points in a two-dimensional magnetohydrodynamic model during the early stages of freely decaying turbulence. At sufficiently high magnetic Reynolds number Rem, we find that the number of neutral points increases as Rem3/2, while the rates of reconnection at the most active sites decrease. The distribution of rates remains approximately exponential. We focus in particular on delicate issues of accuracy, which arise in these numerical experiments, in that the proliferation of X-points is also a feature of under-resolved simulations. The “splitting” of neutral points at high Reynolds number appears to be a fundamental feature of the cascade that has important implications for understanding the relationship between reconnection and turbulence, an issue of considerable importance for the Magnetospheric Multiscale and Solar Probe missions as well as observation of reconnection in the solar wind

The third-order law for increments in magnetohydrodynamic turbulence with constant shear

We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic (MHD) turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano and Pouquet, Phys. Rev. E, 57 21 (1998)] between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is not simply proportional to the relative separation. Possible implications for laboratory and space plasmas are discussed

Solar wind fluctuations and the von Kármán–Howarth equations: The role of fourth-order correlations

The von Kármán-Howarth (vKH) hierarchy of equations relate the second-order correlations of the turbulent fluctuations to the third-order ones, the third-order to the fourth-order, and so on. We recently demonstrated [1] that for MHD, self-similar solutions to the vKH equations seem to require at least two independent similarity lengthscales (one for each Elsässer energy), so that compared to hydrodynamics a richer set of behaviors seems likely to ensue. Moreover, despite the well-known anisotropy of MHD turbulence with a mean magnetic field (B₀), the equation for the second-order correlation does not contain explicit dependence on B₀. We show that there is, however, implicit dependence on B₀ via the third-order correlations, which themselves have both explicit B₀-dependence and also their own implicit dependence through fourth-order correlations. Some subtleties and consequences of this implicit-explicit balance are summarized here. In addition, we present an analysis of simulation results showing that the evolution of turbulence can depend strongly on the initial fourth-order correlations of the system. This leads to considerable variation in the energy dissipation rates. Some associated consequences for MHD turbulence are discussed

Fourier-Hermite decomposition of the collisional Vlasov-Maxwell system: implications for the velocity space cascade

Turbulence at kinetic scales is an unresolved and ubiquitous phenomenon that characterizes both space and laboratory plasmas. Recently, new theories, {\it in-situ} spacecraft observations and numerical simulations suggest a novel scenario for turbulence, characterized by a so-called phase space cascade -- the formation of fine structures, both in physical and velocity space. This new concept is here extended by directly taking into account the role of inter-particle collisions, modeled through the nonlinear Landau operator or the simplified Dougherty operator. The characteristic times, associated with inter-particle correlations, are derived in the above cases. The implications of introducing collisions on the phase space cascade are finally discussed.Comment: Special issue featuring the invited talks from the International Congress on Plasma Physics (ICPP) in Vancouver, Canada 4-8 June 201

The Complex Structure of Magnetic Field Discontinuities in the Turbulent Solar Wind

Using high resolution Cluster satellite observations, we show that the turbulent solar wind is populated by magnetic discontinuities at different scales, going from proton down to electron scales. The structure of these layers resembles the Harris equilibrium profile in plasmas. Using a multi-dimensional intermittency technique, we show that these structures are connected through the scales. Supported by numerical simulations of magnetic reconnection, we show that observations are consistent with a scenario where many current layers develop in turbulence, and where the outflow of these reconnection events are characterized by complex sub-proton networks of secondary islands, in a self-similar way. The present work establishes that the picture of "reconnection in turbulence" and "turbulent reconnection", separately invoked as ubiquitous, coexist in space plasmas

The third-order law for magnetohydrodynamic turbulence with shear: Numerical investigation

The scaling laws of third-order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence relate the observable structure function with the energy dissipation rate. Recently [ Wan et al. Phys. Plasmas 16, 090703 (2009) ], the theory was extended to the case in which a constant velocity shear is present, motivated by the application of the third-order law to the solar wind. We use direct numerical simulations of two-dimensional MHD with shear to confirm this new generalization of the theory. The presence of the shear effect broadens the circumstances in which the law can be applied. Important implications for laboratory and space plasmas are discussed