Generation of a Purely Electrostatic Collisionless Shock during the Expansion of a Dense Plasma through a Rarefied Medium

A two-dimensional numerical study of the expansion of a dense plasma through a more rarefied one is reported. The electrostatic ion-acoustic shock, which is generated during the expansion, accelerates the electrons of the rarefied plasma inducing a superthermal population which reduces electron thermal anisotropy. The Weibel instability is therefore not triggered and no self-generated magnetic fields are observed, in contrast with published theoretical results dealing with plasma expansion into vacuum. The shock front develops a filamentary structure which is interpreted as the consequence of the electrostatic ion-ion instability, consistently with published analytical models and experimental results.

Figure 1

Proton phase space distributions at $t_1=15\mathrm{ps}$ (a) and $t_2=0.35\mathrm{ns}$ (b). The color scale is 10-logarithmic and in units of the average density of the tenuous plasma. (c) Spatial distribution of the electric field amplitude at $t_1=15\mathrm{ps}$. (d) Electric field distribution $E_x$, averaged over $y$ for $t_2=0.35\mathrm{ns}$. Electric fields are in unit of ${10}^6\mathrm{V}/\mathrm{m}$.

Figure 2

Mean values of $B_y$ (a) and $B_z$ (b), averaged along the $y$ direction, and the standard deviation of $B_z$ along the $y$ direction (c). All graphs refer to $t_2=0.35\mathrm{ns}$ and are in units of Tesla.

Figure 3

(a) Electron phase space at $t_2=0.35\mathrm{ns}$. The color scale is 10-logarithmic and in units of the average density of the dense plasma. (b) Difference between the electron distribution function at $t_2=0.35\mathrm{ns}$ and the initial Maxwellian distribution. The color scale is normalized to the peak of the distribution.

Figure 4

(a) Proton density map, integrated over $v_x$, in units of the initial density of the dense plasma. The related electric field components $E_x$ and $E_y$ are displayed in (b) and (c), respectively. The color scale is in units of MV. The standard deviation of $E_x$ (black) and $E_y$ [gray (red)], in units of ${10}^6\mathrm{V}/\mathrm{m}$, is shown in (d).