Laser Ion-Acceleration Scaling Laws Seen in Multiparametric Particle-in-Cell Simulations

The ion acceleration driven by a laser pulse at intensity $I={10}^{20}–{10}^{22}\mathrm{W}/{\mathrm{cm}}^2\times (\mu \mathrm{m}/\lambda {)}^2$ from a double layer target is investigated with multiparametric particle-in-cell simulations. For targets with a wide range of thickness $l$ and density $n_e$, at a given intensity, the highest ion energy gain occurs at certain electron areal density of the target $\sigma =n_{e}l$, which is proportional to the square root of intensity. In the case of thin targets and optimal laser pulse duration, the ion maximum energy scales as the square root of the laser pulse power. When the radiation pressure of the laser field becomes dominant, the ion maximum energy becomes proportional to the laser pulse energy.

Figure 1

Proton maximum energy (contours) vs target thickness and density (log-log scale) for different laser intensities (a)–(e), for $L_p=10\lambda$, $D=10\lambda$. The laser pulse (${\mathrm{d}}_1$) reflection, (${\mathrm{d}}_2$) absorption, and (${\mathrm{d}}_3$) transmission coefficients related to frame (d). The dashed line in (d), (${\mathrm{d}}_{1–3}$) is for the best $n_{e}l$, corresponding to maximum energy gain. (f) Proton maximum energy vs laser intensity and target electron areal density $\sigma =n_{e}l$ (log-log scale). The dashed line is for optimal ${\sigma }_{\mathrm{opt}}\propto I^{1/2}$. Intensity unit $\mathrm{W}/{\mathrm{cm}}^2\times (\mu \mathrm{m}/\lambda {)}^2$.

Figure 2

Proton maximum energy (contours) vs laser length and target thickness (log-log scale) for different laser intensities [columns (a)–(e)] and different laser focal spots (rows 1–3), for $n_e=100n_{\mathrm{cr}}$.

Figure 3

Proton maximum energy vs laser pulse energy for $l=\lambda$, $n_e=100n_{\mathrm{cr}}$. The dashed lines exemplify possible scalings.

Figure 4

Proton maximum energy vs laser power for optimal plasma slab thickness and $n_e=100n_{\mathrm{cr}}$. The inset is for $L_p\sim D$.