Bidirectional Energy Cascades and the Origin of Kinetic Alfvénic and Whistler Turbulence in the Solar Wind

The observed steep kinetic scale turbulence spectrum in the solar wind raises the question of how that turbulence originates. Observations of keV energetic electrons during solar quiet time suggest them as a possible source of free energy to drive kinetic turbulence. Using particle-in-cell simulations, we explore how the free energy released by an electron two-stream instability drives Weibel-like electromagnetic waves that excite wave-wave interactions. Consequently, both kinetic Alfvénic and whistler turbulence are excited that evolve through inverse and forward magnetic energy cascades.

Figure 1

(a) Time evolution of energy of $⟨\delta E_x^2⟩$ (black line), $⟨\delta B_x^2⟩$ (red line), $⟨\delta B_y^2⟩$ (green line), and $⟨\delta B_z^2⟩$ (blue line). The embedded plot is an expanded view of the time evolution from ${\omega }_{pe}t=0–230$. The orange line indicates ${\omega }_{pe}t=230$. (b) Power spectrum of $|\delta E_x(k_x,k_y){|}^2$ at ${\omega }_{pe}t=24$ on a logarithmic scale.

Figure 2

Images of $B_z/B_0$ at ${\omega }_{pe}t=24$ (a), 480 (b), 2424 (c), and 10 560 (d). Refer to the movie in the Supplemental Material [24].

Figure 3

The transition of $j_{ex}$ wave patten when Weibel-like instability occurs. (a) $j_{ex}$ at ${\omega }_{pe}t=96$, the late stage of two-stream instability. (b) $j_{ex}$ at ${\omega }_{pe}t=168$, the transition stage from the two-stream instability to the Weibel-like instability. (c) $j_{ex}$ at ${\omega }_{pe}t=240$, the beginning of the Weibel-like instability.

Figure 4

Power spectra $|B_z(k_x,k_y){|}^2$ on logarithmic scale at ${\omega }_{pe}t=24$ (a), 480 (b), 2424 (c), and 10 560 (d).

Figure 5

The 1D spectra of $\delta B^2(k)$ vs $k_x{d}_i$ and $k_y{d}_i$. The blue short-dashed line is the $k_y$ space range for magnetic energy injection. In the simulation, we have $d_i=2{\rho }_i$ and $d_e=2{\rho }_e$, and ${\rho }_i$ and ${\rho }_e$ correspond to $k_{x,y}{d}_i=2$ and 20 respectively.