Dynamics of electron injection and acceleration driven by laser wakefield in tailored density profiles

The dynamics of electron acceleration driven by laser wakefield is studied in detail using the particle-in-cell code WARP with the objective to generate high-quality electron bunches with narrow energy spread and small emittance, relevant for the electron injector of a multistage accelerator. Simulation results, using experimentally achievable parameters, show that electron bunches with an energy spread of $\sim 11\%$ can be obtained by using an ionization-induced injection mechanism in a mm-scale length plasma. By controlling the focusing of a moderate laser power and tailoring the longitudinal plasma density profile, the electron injection beginning and end positions can be adjusted, while the electron energy can be finely tuned in the last acceleration section.

Figure 1

Evolution of $a_0$ with respect to the propagation axis $z$. The grey dashed line shows the longitudinal density profile of the gas cell, or ELISA profile. The shaded area represents the injection range of length $\sim 630\mu \mathrm{m}$. We define four markers in the injection zone: $z_0$, the position where injection begins; $z_1$, a position between $z_0$ and $z_2$; $z_2$ the position where $a_0$ is maximum; $z_3$, the position where injection stops.

Figure 2

The blue dashed line shows the energy spectrum of electrons from ${\mathrm{N}}^{5+}\to {\mathrm{N}}^{6+}$, whereas the red, dash-dotted line shows the energy spectrum of electrons from the ionization of ${\mathrm{N}}^{6+}\to {\mathrm{N}}^{7+}$. The black solid line represents the sum of the two spectra. Only $K$-shell electrons contribute to the electron beam energy spectrum at $z_{\mathrm{exit}}$. Other electrons are not trapped but contribute to building the plasma wake. An energy cutoff at 10 MeV is applied.

Figure 3

Trapped $K$-shell electrons energy at $z_{\mathrm{exit}}$ as a function of their ionization position; (a) blue crosses: electrons from ${\mathrm{N}}^{5+}\to {\mathrm{N}}^{6+}$, (b) red asterisks: electrons from ${\mathrm{N}}^{6+}\to {\mathrm{N}}^{7+}$. Two regions are marked in the distributions: Distribution I has energy larger than 55 MeV and a position of ionization smaller than $z=1480\mu \mathrm{m}$; Distribution II exhibits a decrease of energy for increased position of ionization.

Figure 4

Evolution of the normalized laser field, $e{E}_y/2mc{\omega }_0$ (in light blue/light gray), the normalized wakefield, $e{E}_z/mc\mathbf{max}({\omega }_p)$ (in red/gray) and the energy, $\mathcal{E}$ of electrons (represented by a set of points) for the three positions of interest $z_{1-3}$ as marked in Fig. 1. The color bar represents charge density. The black rectangle at $z_3$ represents electrons in the high charge density region, with energy above 50 MeV.

Figure 5

Electron density in the ($x-z$) plane at $z_2$, with superimposed laser amplitude and injected electron bunch. The horizontal color bar represents the normalized electron density in arbitrary unit and the vertical color bar depicts the energy of trapped electrons. A black dashed circle of $4.7\mu \mathrm{m}$ radius is superimposed on the map to show the shape of the blown-out region.

Figure 6

Evolution of the charge density with respect to the energy with an energy cutoff at 10 MeV at three different positions: $z_{1–3}$ corresponding to the cases of Fig. 4.

Figure 7

Emittance of the electron bunch at the exit of the plasma, $z_{\mathrm{exit}}$, as a function of electron energy in (a) $x$ and in (b) $y$ directions. The energy bin interval is 6.4 MeV. Insets of (a) and (b) represent the distribution of electrons with $\mathcal{E}\ge 10\mathrm{MeV}$ in $(x,p_x)$ and in $(y,p_y)$ phase space. The color bars represent the electron density normalized to its maximum.

Figure 8

(a) Tailored longitudinal density profile with a constant density extended from the end of the injection process. Three positions are marked, $z_3$, the end of the injection process; $z_4$, intermediate position between the end of the injection and the exit of the gas cell, $z_{\mathrm{exit}}$. Two distinct instants $z_4$ and $z_{\mathrm{exit}}$ of the normalized laser fields, $e{E}_y/2mc{\omega }_0$ (in light blue/light gray), the normalized wakefield, $e{E}_z/mc\mathbf{max}({\omega }_p)$ (in red/gray) and the energy, $\mathcal{E}$, of traced electrons ($\mathcal{E}\ge 50\mathrm{MeV}$ at $z_3$) represented by a set of points, are shown in (b) and (c).

Figure 9

Charge density of accelerated electrons having $\mathcal{E}\ge 30\mathrm{MeV}$ with respect to electron energy obtained from the simulation using the longitudinal density profile featured in Fig. 8 at different positions $z_3$, $z_4$ and $z_{\mathrm{exit}}$.

Figure 10

Normalized beam emittances, ${ϵ}_{x_{\text{rms}}}$ (blue solid line) and ${ϵ}_{y_{\text{rms}}}$ (red dashed line) simulated with the longitudinal density profile in Fig. 8 with respect to energy. The energy bin interval is 6.8 MeV.

Figure 11

(a) Tailored longitudinal density profile with a linear density down-ramp extended from the end of the injection process to the plasma exit. Three positions are marked, $z_3$, the end of the injection process; $z_4$, intermediate position between the end of the injection and the exit of the gas cell, $z_{\mathrm{exit}}$. Two distinct instants $z_4$ and $z_{\mathrm{exit}}$ of the normalized laser fields, $e{E}_y/2mc{\omega }_0$ (in light blue/light gray), the normalized wakefield, $e{E}_z/mc\mathbf{max}({\omega }_p)$ (in red/gray) and the energy, $\mathcal{E}$ of traced electrons ($\mathcal{E}\ge 50\mathrm{MeV}$ at $z_3$) represented by a set of points, are shown in (b) and (c).

Figure 12

Charge density of the accelerated electrons with respect to the electron energy simulated using the longitudinal density profile featured in Fig. 11 at different positions $z_3$, $z_4$ and $z_{\mathrm{exit}}$.

Figure 13

Normalized beam emittances, ${ϵ}_{x,\text{rms}}$ (blue solid line) and ${ϵ}_{y,\text{rms}}$ (red dashed line) simulated with the longitudinal density profile in Fig. 11 with respect to energy. Only electrons of $\mathcal{E}\ge 25\mathrm{MeV}$ are depicted. The energy bin interval is 6.7 MeV.

Figure 14

Energy distribution of the traced electron bunch ($\mathcal{E}\ge 50\mathrm{MeV}$ at $z_3$) at the exit of the gas cell, $z_{\mathrm{exit}}$, the onsets above each spectrum show the corresponding tailored longitudinal density profile: (a) with ELISA profile, (b) with a descending gradient, (c) with a plateau.