Turbulence generation during the head-on collision of Alfvénic wave packets

The description of the Moffatt and Parker problem recently revisited by O. Pezzi et al. [Astrophys. J. 834, 166 (2017)] is here extended by analyzing the features of the turbulence produced by the interaction of two colliding Alfvénic wave packets in a kinetic plasma. Although the approach based on the presence of linear modes features is still helpful in characterizing some low-energy fluctuations, other signatures, which go beyond the pure linear modes analysis, are recovered, such as the significant weakening of clear dispersion relations and the production of zero frequency fluctuations.

Figure 1

Space-time representation of Alfvénic packets collision by means of the iso-surfaces of the current density $j_z(x,y,t)$.

Figure 2

(a) Shape of $\left|\mathbf{B}\right|$ (solid black) and $n$ (dot-solid red) as a function of $x$ in the region $x=[180,220]$, for $y=y_0=12$ and $t=t^{*}=1020$. (b) Hodogram of $\delta B_z(x,y_0,t^{*})$ as a function of $\delta B_y(x,y_0,t^{*})$ for $x=[180,220], y=y_0=12$ and $t=t^{*}=1020$. The red square indicates the initial $x$ point $x=180$.

Figure 3

Contour plots of $E_{b,y}(k_x,\omega )={\langle E_b(\mathbf{k},\omega )\rangle }_{k_y}$ (left) and $E_{b,x}(k_y,\omega )={\langle E_b(\mathbf{k},\omega )\rangle }_{k_x}$ (right) in region I (before collision, top) and in region II (after collision, bottom). The green dashed lines indicate the wave number $k^{*}=1.5$, at which the cuts reported in Fig. 4 have been performed.

Figure 4

Plot of $E_{b,y}(k_x=1.5,\omega )$ as a function of $\omega$ in the region I (solid black) and II (dot-solid red). The small inset plots $E_{b,x}(k_y=1.5,\omega )$ as a function of $\omega$ in the region II.