Production of relativistic electrons at subrelativistic laser intensities

Relativistic electron temperatures were measured from kilojoule, subrelativistic laser-plasma interactions. Experiments show an order of magnitude higher temperatures than expected from a ponderomotive scaling, where temperatures of up to 2.2 MeV were generated using an intensity of $1\times {10}^{18}\mathrm{W}/{\mathrm{cm}}^2$. Two-dimensional particle-in-cell simulations suggest that electrons gain superponderomotive energies by stochastic acceleration as they sample a large area of rapidly changing laser phase. We demonstrate that such high temperatures are possible from subrelativistic intensities by using lasers with long pulse durations and large spatial scales.

Figure 1

(a) Diagram of the experimental setup with ARC beamlets incident on a gold prism target. (b) Polar view of the target.

Figure 2

Electron measurements from (${90}^{\circ },{78}^{\circ }$) (a) and (${90}^{\circ },{315}^{\circ }$) (b) viewing angles. $1\sigma$ error bounds are shown in shaded regions. Dashed lines are single-exponential temperature fits between 1.5 MeV and the detection limit.

Figure 3

(a) Electron density at $\tau =-3$ ps with $n_c/4$ and $n_c$ contours drawn in red and black, respectively (peak intensity occurs at $\tau =0$ ps). (b) Laser intensity at the same time step. (c) Example trajectory of an electron with a two times ponderomotive final energy and $n_c/10$ contour shown in addition to those in (a). Electron motion is incoherent and rapid energy gains occur as it moves transversely across a changing laser phase. 100 fs time steps are labeled. (d) Histogram of transverse path length for electrons with energies above 180 keV.

Figure 4

(a) Input laser intensity (red) for the high-intensity case and cycle-averaged laser intensity on the simulation grid (black). An increase is observed due to self-focusing inside density filaments. Self-focusing occurs in both intensity simulations. (b) Simulated time-integrated and time-resolved ($\pm 0.1$ ps) electron spectra for the high-intensity case.

Figure 5

Measured and simulated electron temperatures. Square and circle markers differentiate ARC data at (${90}^{\circ },{78}^{\circ }$) and (${90}^{\circ },{315}^{\circ }$) lines of sight, respectively, and are placed at the mean peak intensity of the four beamlets. Horizontal error bars are uncertainty in calculated intensity. For ARC data, error includes scatter in delivered beamlet intensities. Confidence ranges in temperature include uncertainty in measurement and fit. The Pukhov scaling is only shown at intensities considered in their study, above ${10}^{18}\mathrm{W}/{\mathrm{cm}}^2$.