Electron Self-Injection and Trapping into an Evolving Plasma Bubble

The blowout (or bubble) regime of laser wakefield acceleration is promising for generating monochromatic high-energy electron beams out of low-density plasmas. It is shown analytically and by particle-in-cell simulations that self-injection of the background plasma electrons into the quasistatic plasma bubble can be caused by slow temporal expansion of the bubble. Sufficient criteria for the electron trapping and bubble’s expansion rate are derived using a semianalytic nonstationary Hamiltonian theory. It is further shown that the combination of bubble’s expansion and contraction results in monoenergetic electron beams.

Figure 1

Electron trapping by an expanding ultrarelativistic (${\gamma }_0=66.1$) bubble. (a)–(c) Dynamics of particles with three impact parameters. Trapped particle with $k_p{y}_0=5.6$ (red solid line) satisfies $\Delta H<-1$. Untrapped particles: $k_p{y}_0=5.73$ (green dashed line) and $k_p{y}_0=5.4$ (blue dash-dotted line). (a) Particle orbits, (b) evolution of the particles’ energies, (c) evolution of the Hamiltonian. (d) Variation rate of the $\delta H/ϵ$ (black line) and the slippage time $T_{\mathrm{slip}}$ [green (light gray) line] for the unperturbed orbits.

Figure 2

Defocusing of a 2 PW, 100 fs laser pulse in the $n_0=4\times {10}^{17}{\mathrm{cm}}^{-3}$ plasma causes expansion of the bubble and electron self-injection. Electron density (grayscale) and laser intensity [isocontour at $e^{-2}$ of the peak, red (dark gray)] from the 3D VLPL (a),(b) and WAKE simulations (c),(d) at 0.7 mm (left) and 1.3 mm (right) from the plasma border. Dots in (c),(d): test electron radial positions.

Figure 3

(a) Longitudinal momentum of electrons after 1.3 mm propagation. Black: VLPL macroparticles from Fig. 2b; red (gray): WAKE test electrons from Fig. 2d. (b) Normalized Hamiltonian for WAKE test electrons as a function of their energy [red (gray)] and initial position (black).

Figure 4

Bubble size variation and shortening the electron bunch due to the bubble contraction. (a)–(c) Electron density in grayscale and isocontour of laser intensity in red (dark gray) at (a) $x=0.68\mathrm{mm}$, (b) $1.046\mathrm{mm}$, and (c) $1.32\mathrm{mm}$. (d) Variation of the bubble length over the propagation distance; red (dark gray) dots mark the positions of snapshots.

Figure 5

Acceleration of the quasimonoenergetic electron bunch generated due to the bubble contraction in the simulation of Fig. 4. (a) Longitudinal phase space of electrons for (black) $x=1.046\mathrm{mm}$, [red (light gray)] 1.32 mm, and blue (dark gray)] 1.77 mm. (b) Electron energy spectrum for $x=1.32\mathrm{mm}$ [red (light gray)] and 1.77 mm [blue (dark gray)].