Thin-shell instability in collisionless plasma

Thin-shell instability is one process which can generate entangled structures in astrophysical plasma on collisional (fluid) scales. It is driven by a spatially varying imbalance between the ram pressure of the inflowing upstream plasma and the downstream's thermal pressure at a nonplanar shock. Here we show by means of a particle-in-cell simulation that an analog process can destabilize a thin shell formed by two interpenetrating, unmagnetized, and collisionless plasma clouds. The amplitude of the shell's spatial modulation grows and saturates after about ten inverse proton plasma frequencies, when the shell consists of connected piecewise linear patches.

Figure 1

(a) The collision of the equally dense plasma 1 (at rest) and plasma 2 (speed $v_0$) yields two plasma shocks (blue sinusoidally varying curves), which enclose a plasma shell. Each shock is displaced along $x$ with respect to its average plane (horizontal dashed black lines). The electric field $\mathbf{E}$, which mediates the plasma shock, points along the shock normal. (b) focuses on the center of (a), where the horizontal electric field component $E_y$ is strongest. Ions ($p$) and electrons ($e$) are deflected into opposite directions as they cross a shock, and the resulting net current $\mathbf{J}$ yields a magnetic $\mathbf{B}$ field.

Figure 2

The thin shell at the time $t=4.5$: (a) shows $n_p(x,y)$. (b)–(d) show the $E_x, E_y$, and $B_z$ components, respectively. The value of $B_z$ has been multiplied by the factor ${10}^5$.

Figure 3

The thin shell at the time $t=24$: (a) shows $n_p(x,y)$. (b)–(d) show the $E_x, E_y$, and $B_z$ components, respectively. The value of $B_z$ has been multiplied by ${10}^5$.

Figure 4

The density distribution of the protons of plasma 2 at the time $t=24$. Overplotted is the contour $0.23$ of the electric field modulus ${\left(E_x^2+E_y^2\right)}^{1/2}$.

Figure 5

The thin shell at the time $t=68$: (a) shows $n_p(x,y)$. (b) shows ${\left(E_x^2+E_y^2\right)}^{1/2}$.

Figure 6

The proton phase space density distribution $f_i(x,y,p_x)$ at the time $t=68$: The color range is linear. The $x$ position is given in units of $100{\lambda }_D$ and $v_x$ is given in units of $v_0$. The full width of the $y$ axis is displayed.