Electron acceleration at oblique angles via stimulated Raman scattering at laser irradiance $>{10}^{16}\mathrm{W}{\mathrm{cm}}^{-2}\mu {\mathrm{m}}^2$

The generation of hot, directional electrons via laser-driven stimulated Raman scattering (SRS) is a topic of great importance in inertial confinement fusion (ICF) schemes. Little recent research has been dedicated to this process at high laser intensity, in which back, side, and forward scatter simultaneously occur in high energy density plasmas, of relevance to, for example, shock ignition ICF. We present an experimental and particle-in-cell (PIC) investigation of hot electron production from SRS in the forward and near-forward directions from a single speckle laser of wavelength ${\lambda }_0=1.053\mu \mathrm{m}$, peak laser intensities in the range $I_0=0.2–1.0\times {10}^{17}{\mathrm{Wcm}}^{-2}$ and target electron densities between $n_e=0.3–1.6\%n_c$, where $n_c$ is the plasma critical density. As the intensity and density are increased, the hot electron spectrum changes from a sharp cutoff to an extended spectrum with a slope temperature $T=34\pm 1\mathrm{keV}$ and maximum measured energy of 350 keV experimentally. Multidimensional PIC simulations indicate that the high energy electrons are primarily generated from SRS-driven electron plasma wave phase fronts with k vectors angled $\sim {50}^{\circ }$ with respect to the laser axis. These results are consistent with analytical arguments that the spatial gain is maximized at an angle which balances the tendency for the growth rate to be larger for larger scattered light wave angles until the kinetic damping of the plasma wave becomes important. The efficiency of generated high energy electrons drops significantly with a reduction in either laser intensity or target electron density, which is a result of the rapid drop in growth rate of Raman scattering at angles in the forward direction.

Figure 1

(a) Schematic displaying the experimental configuration, where EPPS is the electron spectrometer. An example density map measured by the interferometer is shown, for a peak laser intensity $I_0=2\times {10}^{16}{\mathrm{Wcm}}^{-2}$ and pressure P = 400 psi. The electron density ($n_e$) is shown as a percentage of the critical density ($n_c$). (b) Measured $n_e$ as a function of $P$ obtained from multiple interferograms for $I_0=2\times {10}^{16}{\mathrm{Wcm}}^{-2}$. The dashed black line is a linear fit to the data intercepting at $n_e=0$, with the fit parameters labeled.

Figure 2

(a)–(c) Electron spectra recorded by the electron spectrometer for five values of plasma electron density ($n_e$) and peak laser intensities ($I_0$) equal to (a) $I_0=6\times {10}^{16}{\mathrm{Wcm}}^{-2}$, (b) $I_0=4\times {10}^{16}{\mathrm{Wcm}}^{-2}$, and (c) $I_0=2\times {10}^{16}{\mathrm{Wcm}}^{-2}$. A temperature fit to each spectrum was performed, with the hot electron slope temperature ($T$) labeled next to the corresponding spectrum. The fit was performed in the range bound by the colored dashed vertical lines, where the electron temperature can be accurately described by a single temperature dependence. Note that the data series shown in (a)–(c) corresponds to the legend shown in (a). (d) Maximum electron energy (${\varepsilon }_{\max }$) and (e) total energy contained in the accelerated electron population per solid angle ($\mathrm{\Omega }$) as a function of $n_e$ for the three values of $I_0$ explored experimentally.

Figure 3

(a)–(c) Electron plasma wave activity (laser propagating from left to right, entering at $x=0$) for a peak laser intensity $I_0=1\times {10}^{17}{\mathrm{Wcm}}^{-2}$ at $t=4.3\mathrm{ps}$ for electron densities: (a) $n_e=0.5\%n_c$, (b) $n_e=1.0\%n_c$, and (c) $n_e=1.6\%n_c$, with electrons of energy $\varepsilon >150\mathrm{keV}$ overlaid as red circles. For clarity only 10% of these electrons are displayed in (c). (d) Net electron spectra of all electrons present in the simulation domain at $t=4.3\mathrm{ps}$. The slope temperatures are given in (d) for the high energy portion of the spectra (minimum computed energy indicated by the dashed lines). (e) Histogram of electron density for the $n_e=1.6\%n_c$ case, for all electrons accelerated at an angle equal to $8^{\circ }\pm 1^{\circ }$—similar to the collection angle of the electron spectrometer used experimentally. (f) Summation of the electron density shown in (e) for the whole simulated time.

Figure 4

Wave number spectrum of the longitudinal electric field ($E_x$) for peak laser intensity $I_0=1\times {10}^{17}{\mathrm{Wcm}}^{-2}$ and electron density $n_e=1.6\%n_c$ at time $t=2.4\mathrm{ps}$, showing the angular dependence of the near-forward SRS and the spectrum present for other laser plasma instabilities. The red semicircle shows wave numbers in the lower half plane for which an electron plasma wave would satisfy k-matching conditions with an incident and scattered light wave.

Figure 5

(a) Electron phase space plot for a peak laser intensity $I_0=1\times {10}^{17}{\mathrm{Wcm}}^{-2}$ and electron density $n_e=1.6\%n_c$ at time $t=4.3\mathrm{ps}$, showing the angular dependence of the accelerated electrons. The plasma wave angle ($\theta$) is shown for the oblique wave. (b) Separate electron spectra (at $t=4.3\mathrm{ps}$) showing those electrons accelerated due to forward SRS and those accelerated by near-forward SRS. Slope temperatures ($T$) are given; in the case of forward SRS-driven electrons the dashed red line indicates the cutoff energy the fit is performed to. In the case of oblique electrons, the dashed black line indicates the starting energy in the fit protocol.

Figure 6

(a) Spatial growth rate of the electron plasma wave (EPW) as a function of plasma wave angle for the three electron densities used in the simulations ($0^{\circ }$ refers to the angle of laser propagation) and peak laser intensity $I_0={10}^{17}{\mathrm{Wcm}}^{-2}$. (b) Laser intensity and electron density map of the spatial growth rate of the EPW for the full domain investigated experimentally, at the angle of maximum growth rate for each case.