Nanoscale Electron Bunching in Laser-Triggered Ionization Injection in Plasma Accelerators

Ionization injection is attractive as a controllable injection scheme for generating high quality electron beams using plasma-based wakefield acceleration. Because of the phase-dependent tunneling ionization rate and the trapping dynamics within a nonlinear wake, the discrete injection of electrons within the wake is nonlinearly mapped to a discrete final phase space structure of the beam at the location where the electrons are trapped. This phenomenon is theoretically analyzed and examined by three-dimensional particle-in-cell simulations which show that three-dimensional effects limit the wave number of the modulation to between $>2k_0$ and about $5k_0$, where $k_0$ is the wave number of the injection laser. Such a nanoscale bunched beam can be diagnosed by and used to generate coherent transition radiation and may find use in generating high-power ultraviolet radiation upon passage through a resonant undulator.

Figure 1

The nanoscale bunching of injected charge in a laser-driven plasma accelerator. The laser is focused at the $z=0\mathrm{mm}$ plane. (a) Snapshot of the charge density distribution of the background electrons, the $K$-shell electrons of nitrogen, and the laser electric field in the $x$ direction. The red line is the on-axis pseudopotential $\psi$. (b) The distribution of the ionization injected electrons in $({\xi }_i,x_i)$ space. The color represents the time when the electrons are ionized. The red peaks are integrated injected charge in $x_i$, whereas the black is the integrated injected charge for all ${\xi }_i$. (c) The $(\xi ,p_z)$ space at $z=0.5\mathrm{mm}$ for an initial slice indicated by the dashed box in (b). (d) The current profile and the bunching factor at $z=0.5\mathrm{mm}$. (e),(f) show the $(z,x,p_z)$ phase space at $z=0.5\mathrm{mm}$. For the $L_{\text{inj}}=90\mu \mathrm{m}$ case, the ${\mathrm{N}}^{5+}$ ions are distributed from $z=0.038$ to 0.128 mm and $n_{{\mathrm{N}}^{5+}}={10}^{-3}{n}_p$; for the $L_{\text{inj}}=190\mu \mathrm{m}$ case, the ${\mathrm{N}}^{5+}$ ions are distributed from $z=0.038$ to 0.228 mm and $n_{{\mathrm{N}}^{5+}}=5\times {10}^{-4}{n}_p$.

Figure 2

Bunching of electrons when charges are injected by using a relatively low intensity laser pulse in a prescribed and nonevolving wakefield. (a)–(c) The red lines are the bunching factor while scanning the initial ${\overline{\xi }}_i$, and the dashed lines are the analytical results from Eq. (2). (d)–(f) The corresponding Wigner transform of the current profile showing the spatial modulation. The white dashed lines are $k/k_0=2\sqrt{4+{\xi }_i^2}/{\xi }_i$ and the yellow lines are the current profile of the injected charge. Note that (d) is a 1D simulation, and the others are 3D simulations.

Figure 3

An electron driver beam followed by an injection laser propagate to the right in a mixture of preionized plasma and ${\mathrm{He}}^{1+}$ ions ($n_p=1.74\times 10^{17}{\mathrm{cm}}^{-3}$, $n_{{\mathrm{He}}^{1+}}=0.1n_p$). Driver beam: $E_b=1\mathrm{GeV}$, ${\sigma }_r=8.9\mu \mathrm{m}$, ${\sigma }_z=10.6\mu \mathrm{m}$, $I_b=19\mathrm{kA}$. The injection laser is the same as in the case of Fig. 2. (a) Snapshot of the charge density distribution of the background electrons, the second electron of helium, and the laser electric field. The red line is the pseudopotential at the center. (b) The dependence of the final ${\psi }_f$ on the initial ${\psi }_i$ for injected electrons and the bunching factor at $z=0.1\mathrm{mm}$ and $z=0.9\mathrm{mm}$. The color represents the ionization time. The black line represents ${\psi }_f={\psi }_i-1$. (c) The $(z,x,p_z)$ phase space distribution of the trapped electrons at $z=0.9\mathrm{mm}$. The color represents the $z$ position. (d) The current (yellow line) and the corresponding Wigner transform at $z=0.9\mathrm{mm}$. The white line is $k/k_0=2\sqrt{4+{\xi }_i^2}/{\xi }_i$.

Figure 4

The current profile (a) and bunching factor (b) of the trapped electrons by using 200 nm injection laser at $z=1.4\mathrm{mm}$. The red line is the result when $n_{{\mathrm{He}}^{1+}}=0.3n_p$, and the black dashed line is the result when $n_{{\mathrm{He}}^{1+}}=3\times {10}^{-5}{n}_p$. The energy of the electrons is 50 MeV.