Dense Attosecond Electron Sheets from Laser Wakefields Using an Up-Ramp Density Transition

Controlled electron injection into a laser-driven wakefield at a well defined space and time is reported based on particle-in-cell simulations. Key novel ingredients are an underdense plasma target with an up-ramp density profile followed by a plateau and a fairly large laser focus diameter that leads to an essentially one-dimensional (1D) regime of laser wakefield, which is different from the bubble (complete blowout) regime occurring for tightly focused drive beams. The up-ramp profile causes 1D wave breaking to occur sharply at the up-ramp-plateau transition. As a result, it generates an ultrathin (few nanometer, corresponding to attosecond duration), strongly overdense relativistic electron sheet that is injected and accelerated in the wakefield. A peaked electron energy spectrum and high charge ($\sim \mathrm{nC}$) distinguish the final sheet.

Figure 1

(a) Schematic of AES generation. Localized electron injection occurs as ${\beta }_{\mathrm{ph}}$, at which the apex of the first wakefield bucket is moving, undergoes a fast switch from above to well below unity near the UPT. (b) Evolution of ${\beta }_{\mathrm{ph}}$ and ${\beta }_m$ from 1D PIC simulations, where the initial plasma density rises linearly from zero at $x=20{\lambda }_L$ to $0.04n_c$ at $65{\lambda }_L$ and then keeps constant.

Figure 2

Results of 1D PIC simulation. (a) Spatial-temporal plot of the electron density. The dashed line marks the UPT at $x=65{\lambda }_L$, and the white arrow is parallel to $x=t$. (b) The first density wave crest before (black curve) and after (red curve) the transition. The dashed line shows the initial target profile. (c) Temporal evolution of the experienced electric field $E_x$ (black curve) and the $\gamma$ factor (red curve) for AES electrons. The solid curves are for $n_0=0.04n_c$ and the dashed curve for $n_0=0.02n_c$. (d) Energy spectra of the trapped electrons at $t=83T_L$ and $t=101T_L$. The black curves are 1D results, the red curve is a 2D result, and the green curve is obtained according to Eq. (2) at $t=101T_L$.

Figure 3

(a) Charge carried by the AES versus laser amplitude $a_0$. In the case of $n_0=0.04n_c$, the laser-target parameters are $L_1=45{\lambda }_L$ and ${\tau }_L=10T_L$, while for $n_0=0.01n_c$ they are $L_1=80{\lambda }_L$ and ${\tau }_L=14T_L$. (b) Threshold laser amplitude $a_{\mathrm{th}}$ versus the plateau density $n_0$.

Figure 4

Results of 2D PIC simulation. Snapshots (a) and (b) show the electron density at $t=71T_L$ and $t=83T_L$, respectively. (c) Snapshots of the trapped electrons (colored according to $\gamma -1$) during acceleration. (d) Particle-tracking plot. It is obtained by first tracking back AES electrons to find their initial $x$ range and then tracking a random sample of 24 electrons within this $x$ range. ($y=50{\lambda }_L$ corresponds to the center axis.) (e) Energy spectra of the trapped electrons for different spot radii at $t=83T_L$ while keeping the other parameters fixed. The inset shows a spectrum at $t=98T_L$ for $\sigma =20{\lambda }_L$.