Peculiar behavior of Si cluster ions in a high-energy-density solid Al plasma

Peculiar behavior is found in a Si cluster ion, moving with a speed of $\sim 0.22c$ ($c$: speed of light) in a solid Al plasma in the context of cluster-ion beam driven inertial confinement fusion: The Si ion, moving closely behind the forward-moving Si ion for a distance of several Å in the cluster, feels the wake field generated by the forward Si. The acceleration interaction force on the rear Si ion by the forward-moving ion may balance with the deceleration backward force in the longitudinal-moving direction. The forward-moving Si ion would be decelerated, as an isolated ion is decelerated without correlation. However, the deceleration of the rear Si ion, moving behind closely, would be reduced significantly. The rear Si ion may catch up and overtake the forward-moving Si ion in the cluster during the Si cluster-ion interaction with the high-density Al plasma. This peculiar behavior appears when the ions are aligned well longitudinally. The wake field is confined around the Si ion in the forward and transverse directions for a distance smaller than the Si cluster interionic distance $l_c$. However, the tail of the wake field extends beyond $l_c$ due to the Si ion high speed of $\sim 0.22c$. Therefore, the peculiar behavior shown above appears only for the ions in one cluster aligned well longitudinally.

Figure 1

Schematic diagram of the electric net potential (the wake potential and the potential of the bare Si ion) generated by a swift ion. In high-density solid Al the wake field is localized in the transverse direction and elongated longitudinally behind the Si ion, so that only the Si ion just behind the Si ion in the linearly aligned direction is influenced, ${\lambda }_{\text{De}}<l_c$. Here, $l_c$ is the Si cluster interionic distance. The wake field in the high-energy-density Al covers ions just behind the fast-moving ion.

Figure 2

(a) $E_x$ and (b) $E_y$ generated by a single Si ion moving in a solid Al with a speed ($v_x$) of $0.221c$.

Figure 3

A Si cluster, composed of six Si ions, interacts with the solid Al. The Si cluster speed is $v_x=0.221c$. The six Si ions consists of a regular octahedron, and the distance between the adjacent two Si ions is 5 Å. The six Si ion positions at (a) $t=0$, (b) 0.5 fs, (c) 1.0 fs, and (d) 1.5 fs.

Figure 4

(a) The history of the position in $x$, and (b) the kinetic energy history for Si(1) and Si(2) in one Si cluster, which is composed of six Si ions moving in the solid Al in the $x$ direction. The forward-moving Si(1) dissipates its energy in the Al target, and the following Si(2) feels the acceleration wake field, generated by the forward-moving Si(1).

Figure 5

Three Si clusters, traveling in $x$ with $0.221c$, interact with the solid Al at a temperature of 10 eV. Each cluster consists of two Si ions. Cluster 2 is located in the middle of each figure, and has two Si ions in parallel. Cluster 1 is rotated by ${45}^{\circ }$, and cluster 3 by ${90}^{\circ }$. (a) The initial state of the three clusters. (b) Only the Si(2b) catches up to the Si(2a) at $t=0.7$ fs, and (c) at $t=1.4$ fs, Si(2b) exchanges positions with Si(2a). The wake field generated by each ion is localized transversely in the high-energy-density Al, and Si(1b), Si(3a), and Si(3b) do not feel the wake field. The Si ions, except for Si(2b), lose their energy, as an isolated ion loses its energy.