Plasma Expansion into a Vacuum

The charge separation effects in the collisionless plasma expansion into a vacuum are studied in great detail. Accurate results are obtained concerning the structure of the ion front, the resultant ion energy spectrum, and more specifically the maximum ion energy. These are of crucial importance for the interpretation of recent experiments, where high-energy ion jets were produced from short pulse interaction with solid targets.

Figure 1

Charge separation at time ${\omega }_{pi}t=50$. The ion front stands at $x/c_{s}t\simeq 5.59$.

Figure 2

Electric field at time ${\omega }_{pi}t=50$. The ion front stands at $x/c_{s}t\simeq 5.59$ where the electric field peaks. The dotted line corresponds to the usual self-similar solution, Eq. (6). Note that the electric field at the ion front is approximately twice the self-similar field, as predicted by Eq. (7).

Figure 3

Electric field at the ion front as a function of time. The empty circles correspond to the numerical results and the full line to the theoretical formula, Eq. (9). The maximum relative error is of the order of $1.3\times {10}^{-2}$ for ${\omega }_{pi}t\simeq 5$ and is hardly seen in this picture.

Figure 4

Ion front velocity as a function of time. The empty circles correspond to the numerical results and the full line to the theoretical formula, Eq. (10). The maximum relative error is of the order of $7\times {10}^{-3}$ for ${\omega }_{pi}t\simeq 9$.

Figure 5

Structure of the ion front at ${\omega }_{pi}t=50$ and ${\omega }_{pi}t=100$. The dotted line corresponds to the usual self-similar solution.

Figure 6

Electron and ion densities, and their logarithmic derivatives at the ion front, as functions of time. Densities are normalized to $n_{e0}$ and length to ${\lambda }_{D0}$.

Figure 7

Energy spectrum per unit surface at ${\omega }_{pi}t=30$ and ${\omega }_{pi}t=100$. Energy is normalized to $Z{k}_B{T}_e$, and the number of ions per unit surface and unit energy is normalized to $n_{i0}{\lambda }_{D0}/Z{k}_B{T}_e$. The dotted lines correspond to the prediction of the self-similar solution, Eq. (21).