Spontaneous Generation of Self-Organized Solitary Wave Structures at Earth’s Magnetopause

Spontaneous formation of solitary wave structures has been observed in Earth’s magnetopause, and is shown to be caused by the breakup of a zonal flow by the action of drift wave turbulence. Here we show matched observations and modeling of coherent, large-scale solitary electrostatic structures, generated during the interaction of short-scale drift wave turbulence and zonal flows at the Earth’s magnetopause. The observations were made by the Cluster spacecraft and the numerical modeling was performed using the wave-kinetic approach to drift wave-zonal flow interactions. Good agreement between observations and simulations has been found, thus explaining the emergence of the observed solitary structures as well as confirming earlier theoretical predictions of their existence.

Figure 1

Configuration of the four cluster spacecraft on an outbound pass through the magnetopause, at the time the observations were made. The figure shows the projection on a plane containing the Earth’s axis of rotation. The heavy blue lines denote the magnetic field lines close to the polar cusp. The color coding is black for C1, red for C2, green for C3, and blue for C4, while the black curve with blue dots denotes the orbit of C1, which is taken as a reference for the orbit of the entire Cluster system. Distances are measured in Earth radii. The pictured size of the tetrahedron is 100 times the actual size.

Figure 2

Cluster observations of a thin magnetopause, taken on 30 March, 2002, between 13:11:40 and 13:11:46 UT. Clockwise, the top four figures display the $L$ component (component of maximum variance) of the magnetic field in an LMN coordinate system (the $N$ component is normal to the boundary), the equilibrium plasma density as derived from the spacecraft potential, the ac electric field ($N$ component, 20–180 Hz), and the dc electric field ($N$ component, 0–20 Hz), all versus time (bottom scale) or distance (upper scale). Color coding is the same as in Fig. 1. In the graphs showing the ac electric field, the fields for C3 and C4 have been shifted by 50 and $100\mathrm{mV}/\mathrm{m}$, respectively, for clarity. The $B_L$ graph shows that the peak current within the current layer occurs just upstream of the main density gradient (top panel right), while the electric field graphs exhibit, respectively, that the dc electric field perturbation and the main burst of ac power lie on the inner edge of the current layer and in the density gradient. The highlighted regions in the overall electric field graphs have been enlarged in the bottom two frames. In both the enlarged field graphs, a solitary wave packet, indicated by arrows, can be seen to separate itself from the bulk of the turbulence and move down the plasma density gradient into a previously turbulence-free region. Its direction follows from the order of the spacecraft boundary crossings (C4, C1, C2, C3).

Figure 3

Simulation results for a thin magnetopause, where the background plasma density profile has been chosen to match the sudden rise in the plasma density at the magnetopause boundary. Snapshots of the slow electrostatic field (representing the zonal flow) and the drift mode phase space (representing the fast drift wave turbulence) were taken at ${\Omega }_{ci}t=500$ (top), 666 (middle), and 833 (bottom). The left column shows the slow electrostatic field (red) and the background plasma density (black), while on the right the drift mode phase space can be seen. The excitation of a zonal flow through the modulational instability only occurs for larger $x$, where the relative density gradient is shallow. A solitary wave structure breaking off the main zonal flow and drifting down the density gradient is indicated by arrows.