Laser Acceleration of Ion Bunches at the Front Surface of Overdense Plasmas

The acceleration of ions in the interaction of high intensity laser pulses with overdense plasmas is investigated with particle-in-cell simulations. For circular polarization of the laser pulses, high-density ion bunches moving into the plasma are generated at the laser-plasma interaction surface. A simple analytical model accounts for the numerical observations and provides scaling laws for the ion bunch energy and generation time as a function of pulse intensity and plasma density.

Figure 1

Ion density $n_i$ (top row, solid lines) electrostatic field $E_x$ (top row, dotted lines), and ($x,p_x$) phase space projection (bottom row) at different times (labels) from 1D PIC simulations. Run parameters are $a_L=2$, $n_0/n_c=5$, and $\ell =2{\lambda }_L$. The field is normalized to $E_n=m_e\omega c/e$.

Figure 2

(a) Schematic of the model profiles of the ion density (green thick line), the electron density (blue thin line), and the electric field (red dashed line) at the initial stage when the electrons are in equilibrium and the ions have not moved yet. Label $A$ indicates the electron front where the laser evanescence starts; $B$ indicates the point where the ponderomotive force vanishes so that $\overline{AB}=l_s$. (b) A comparison between the ion bunch velocity observed in simulations (data points) and the model prediction (lines), as a function of the laser pulse amplitude $a_L$ and the normalized density $N=n_0/n_c$. The cases studied are as follows: $N=100$, $Z/A=1/2$ (red stars); $N=20$, $Z/A=1$ (blue crosses); $N=5$, $Z/A=1/2$ (green diamonds).

Figure 3

(a) Ion bunch acceleration from a thin ($\ell =0.1{\lambda }_L$), solid-density ($n_0/n_c=100$) target irradiated by a short laser pulse with amplitude $a=5$ and duration of $6T_L$ (FWHM). The ion density profile (solid line) and the ($x,p_x$) phase space distribution (dotted line) are shown at $t=13T_L$. (b) Ion density (top) and phase space ($x,p_x$) projection (bottom) at $t=86T_L$, for the same simulation parameters of Fig. 1, but linear polarization of the laser pulse.

Figure 4

Contours of ion density $n_i/n_c$ from 2D simulations at three different times. The laser pulse impinges from the left and has a transverse FWHM of $4{\lambda }_L$. Notice the different scales on the $x$ and $y$ axis.

Figure 5

The $(y,p_x)$ and $(p_x,p_y)$ phase space projections [panels (a),(b)] and the energy spectrum [panel (c)] of ions from the 2D simulation of Fig. 4, at $t=47T_L$.