Theory and Observations of Slow-Mode Solitons in Space Plasmas

A generalized model for one-dimensional magnetosonic structures of large amplitude in space plasmas is presented. The model is verified with multipoint measurements on Cluster satellites in the magnetosheath and the boundary layer under conditions of plasma beta (plasma/magnetic pressure) between 0.1–10. We demonstrate good agreement between the model and observations of large amplitude structures and wave trains, which represent increases of magnetic field and plasma density 2–5 times the ambient values, or local decreases (holes) by $\sim (50–80)\%$. Theoretically derived polarization and propagation properties of slow-mode nonlinear structures are also in agreement with in situ measurements in space.

Figure 1

Normalized field $b$ versus density $n$ described by (6) for a number of plasma regimes. Quadrant Q1: fast shocklets ($\beta =10,M_A=9$). Q2: bright solitons ($\beta =10,M_A=0.2$), and Q4: dark solitons ($\beta =0.3,M_A=0.2$). In all cases $\gamma =1.6$, $\kappa =0$, and $a_p=0$.

Figure 2

Spatial growth rate $\log {\lambda }^{-1}$ of nonlinear waves for $\beta =5$, $\gamma =1.6$, $\kappa =0$, and $a_p=-0.2$. The vertical border starting at $M_A\approx 2$ corresponds to a singularity at $M_{As}$ which separates slow modes (left) from fast modes (right).

Figure 3

Same as in Fig. 2 for $\beta =0.5$ and $a_p=0$. The oblique line corresponds to $A=0$ in Eq. (11).

Figure 4

Cluster measurements of large amplitude magnetosonic structures in the magnetosheath, shown with total magnetic field and plasma density.

Figure 5

Three-component magnetic field measured on Cluster-3 and displayed in minimum variance coordinates.

Figure 6

A train of solitons obtained as an exact solution of Eqs. (6, 7, 8) for $\beta =10$, $M_A=0.1$, $\alpha =81.6°$, $\gamma =1.6$, $\kappa =0$, and $a_p=-0.1$ (normalized units). The distance of $300{\lambda }_i$ corresponds to 100 s of Cluster data in Fig. 4.

Figure 7

Transverse components of the magnetic field taken from solutions shown in Fig. 6. The solutions resemble Cluster measurements. The distance of $30{\lambda }_i$ corresponds to 10 s in Fig. 5.