Fully Kinetic Simulation of 3D Kinetic Alfvén Turbulence

We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfvén waves. Furthermore, we calculate the local anisotropy, defined by the relation $k_{\parallel }(k_{\perp })$, where $k_{\parallel }$ is a characteristic wave number along the local mean magnetic field at perpendicular scale $l_{\perp }\sim 1/k_{\perp }$. The subion range anisotropy is scale dependent with $k_{\parallel }<k_{\perp }$ and the ratio of linear to nonlinear time scales is of order unity, suggesting that the kinetic cascade is close to a state of critical balance. Our results compare favorably against a number of in situ solar wind observations and demonstrate—from first principles—the feasibility of plasma turbulence models based on a critically balanced cascade of kinetic Alfvén waves.

Figure 1

Time evolution of the mean magnetic energy (a) and of the mean-square electric current (b). The curves are normalized to the values at $t=0$. The markers in panel (b) denote the times at which we analyze the spectral properties ($t_1/t_A=0.71$, $t_2/t_A=0.88$, $t_3/t_A=1.06$).

Figure 2

One-dimensional $k_{\perp }$ spectra of magnetic, perpendicular electric, and density fluctuations at time $t_1=0.71t_A$. The $-2.8$ slope is shown for reference. Gray shading is used to indicate the range of scales dominated by particle noise.

Figure 3

Ratios of the $k_{\perp }$ spectra obtained from the simulation (solid lines; see text for further details). Dashed lines show the analytical predictions for KAWs [11, 35].

Figure 4

Scale-dependent anisotropy with respect to the direction of the local mean magnetic field (a) and the scale-dependent ratio of the linear (KAW) and nonlinear time scales (b). The $1/3$ slope in panel (a) is shown for reference.