Kinetic Turbulence in Astrophysical Plasmas: Waves and/or Structures?

The question of the relative importance of coherent structures and waves has for a long time attracted a great deal of interest in astrophysical plasma turbulence research, with a more recent focus on kinetic scale dynamics. Here we utilize high-resolution observational and simulation data to investigate the nature of waves and structures emerging in a weakly collisional, turbulent kinetic plasma. Observational results are based on in situ solar wind measurements from the Cluster and Magnetospheric Multiscale (MMS) spacecraft, and the simulation results are obtained from an externally driven, three-dimensional fully kinetic simulation. Using a set of novel diagnostic measures, we show that both the large-amplitude structures and the lower-amplitude background fluctuations preserve linear features of kinetic Alfvén waves to order unity. This quantitative evidence suggests that the kinetic turbulence cannot be described as a mixture of mutually exclusive waves and structures but may instead be pictured as an ensemble of localized, anisotropic wave packets or “eddies” of varying amplitudes, which preserve certain linear wave properties during their nonlinear evolution.

Popular Summary

A wide variety of turbulent systems in nature (e.g., rotating fluid flows, turbulent surface waves, and magnetized plasmas) support linear waves. The polarization properties of these waves are often imprinted even in strongly nonlinear regimes where intense structures, such as electric current sheets in magnetized plasmas or columnar vortices in rotating flows, are observed. It is not well understood whether waves and structures simply coexist in turbulence and possibly dominate one another or whether there is a deeper connection between the two. In this study, we use high-resolution observational and simulation data to shed new light on the relationship between waves and structures emerging in the turbulent solar wind.

We analyze in situ measurements from the Earth-orbiting Cluster and Magnetospheric Multiscale spacecraft (7 h and 159 s of data, respectively) of the solar-wind plasma (magnetic field and electron density data). We also use numerical results from a three-dimensional kinetic simulation of space plasma turbulence. In order to probe the statistical field polarizations within the large-amplitude structures, we design a set of new diagnostic measures and show that the structures themselves preserve a linear, wavelike signature. Our analysis implies that the kinetic plasma turbulence can be best described as an ensemble of localized turbulent “eddies” that preserve certain linear wave features during their nonlinear evolution. Moreover, this finding challenges a presently common view of the coexistence of waves and structures.

Our results motivate a joint and self-consistent description of waves and structures in kinetic-range astrophysical plasma turbulence, with the goal of understanding how kinetic-scale structures form from a set of nonlinearly interacting waves and how their presence affects the heating of ions and electrons in weakly collisional plasmas. We expect that some of our findings will also be applicable to other turbulent wave systems, such as rotating flows.

Figure 1

Time trace of the root-mean-square fluctuating magnetic field (a) and the 1D $k_{\perp }$ magnetic spectra (b) at times $t/t_A=\{0.66,0.92,1.18,1.45,1.71,1.97,2.24\}$ in the simulation (light green to dark blue). A $-2.8$ slope is shown for reference (dotted line). The inset shows the $k_z$ spectrum. Particle noise dominated modes with $k_z{d}_i>12$ (vertical dashed line) are filtered out in the subsequent analysis. The $k_z$ filtered $k_{\perp }$ spectrum at $t/t_A=2.24$ is shown with a red dashed line in (b). All components of the magnetic field are normalized here to $B_0$.

Figure 2

Local anisotropy of the externally driven turbulence (a) and the ratio of linear to nonlinear timescales (b). A $1/3$ slope in (a) is shown for reference. All components of the magnetic field were normalized to $B_0$ in the calculation.

Figure 3

Scale-dependent flatness results obtained from the simulation (a), MMS interval (b), and the Cluster interval (c). Vertical dotted lines mark the plasma kinetic scales and the horizontal dashed lines mark the Gaussian value of 3.

Figure 4

Scale-filtered fluctuations in a given $x\text{−}y$ plane in the range $k_{\perp }{d}_i=[5,10]$ (a)–(c), and the (normalized) local wavelet spectra at scale $k_{\perp }{d}_i=5$ (d)–(f) and at scale $k_{\perp }{d}_i=10$ (g)–(i). A logarithmic scale is used to better show also the fluctuations of moderate intensity. Very weak fluctuations with amplitudes below 0.5 in the normalized units are clipped to the lower boundary of the color map.

Figure 5

Turbulent structures in a perpendicular simulation plane as seen from the perpendicular magnetic (a) and density fluctuations (b), and from their corresponding perpendicular gradients (c), (d). Large-scale modes with $k_{\perp }\le 1/{\rho }_i$, dominated by external forcing, have been filtered out in (a) and (b) to highlight the subion-scale structure.

Figure 6

Magnitude squared cross-coherence and phase between $n_e$ and $b_{\parallel }$ in the simulation (a) and in the MMS interval (b). The orientation of the arrows (relative to the positive horizontal axis) denotes the phase. Dashed lines show the cone of influence [111].

Figure 7

Generalized spectral field ratios obtained from Cluster and MMS measurements and from the 3D fully kinetic simulation (see text for further details). Panels (a)–(f) show the moment ratios [Eq. (12)] and panels (g)–(l) show the conditional ratios [Eq. (13)].

Figure 8

Sine of the scale-dependent alignment angle between the perpendicular electron fluid velocity and magnetic field, conditionally averaged on a given LIM threshold $\xi$ (see text for details). Dashed horizontal lines indicate the expected value for a randomly distributed angle.