Electron Acceleration in Cavitated Channels Formed by a Petawatt Laser in Low-Density Plasma

The spectra of energetic electrons produced by a laser interaction with underdense plasma have been measured at intensities $>3\times {10}^{20}\mathrm{W}{\mathrm{cm}}^{-2}$. Electron energies in excess of 300 MeV have been observed. Measurements of the transmitted laser spectrum indicate that there is no correlation between the acceleration of electrons and plasma wave production. Particle-in-cell simulations show that the laser ponderomotive force produces an ion channel. The interaction of the laser field with the nonlinear focusing force of the channel leads to electron acceleration. The majority of the electrons never reach the betatron resonance but those which gain the highest energies do so. The acceleration process exhibits a strong sensitivity to initial conditions with particles that start within a fraction of a laser wavelength following completely different trajectories and gaining markedly different energies.

Figure 1

Three example electron energy spectra observed at various background electron densities for laser intensity $\sim 3\times {10}^{20}\mathrm{W}{\mathrm{cm}}^{-2}$.

Figure 2

(a) The transmitted laser spectra corresponding to the electron spectra in Fig. 1. (b) The effective temperature of the electron beam (black squares) and side band amplitude normalized to the signal at ${\omega }_0$ (gray diamonds) as a function of electron density. The lines in (b) are a visual aid only.

Figure 3

(a) Laser envelope, (b) channel focusing force, $F_y=E_y-B_z$, (c) $p_x$-$x$ phase space of electrons, (d) ${\Gamma }_y^{1/2}=(\int 2p_y{E}_{y}dt{)}^{1/2}$ vs $\gamma$ of the electrons and (e) $p_x$-$p_y$ phase space from a simulation at $n=0.01$ $n_c={10}^{19}{\mathrm{cm}}^{-3}$ after 1.2 ps of propagation.

Figure 4

Trajectories of four typical test particles left column $y$ and $p_x$ vs $t$, right column $p_y$-$p_x$ trajectory.