Schematic of the laser-beam configurations on (a) OMEGA EP, (b) OMEGA planar, and (c) OMEGA spherical. On OMEGA EP experiments, the polarizations of the beams are from vertical [inset (a)], and on OMEGA experiments the beams used polarization smoothing.
Hot-electron fraction ( ) as a function of vacuum overlapped laser intensity. Single, two, and four correspond to OMEGA EP planar experiments where the beams are linearly polarized; 18 (60) corresponds to OMEGA planar (spherical) experiments where the beams have polarization smoothing. For each configuration, the overlapped intensity is given by the vacuum intensity of the laser beams on the target surface. The dashed lines are drawn to guide the eye. In each case, the overlapped intensity at quarter-critical density is about half the vacuum overlapped intensity. For the eighteen beam configuration, at an overlapped intensity of , the signal was lower than the diagnostic detection threshold (red arrow).
(a) The common-wave region for two beams is given by a plane that bisects the wave vectors ( ) of the laser beams (red plane). (b) A common EPW can be driven only by multiple laser beams that share the same angle to the common-wave vector ( ) in order to satisfy the dispersion relation for each daughter EPW ( ).
(a) 3-D representation of the maximum growth rate for a single beam with polarization smoothing (gray hyperboloids). Multiple beams with polarization smoothing can couple through the common wave along the common-wave line ( , red dashed line) at an angle . (b) Normalized single-beam with polarization smoothing growth rate in the plane ( ). The Landau cutoff ( , where k is the maximum value between and ) for is represented with a black dashed line. The normalized multiple-beam growth rate is equal to the single-beam growth rate along . (c) Normalized multiple-beam growth rate calculated along the common-wave line for (solid red line), (dashed red line), and (dotted red line). The cutoff for small and large corresponds to the Landau cutoff calculated for .
The hot-electron fraction is plotted as a function of the common-wave gain for each experimental configuration tested. The errors bars shown are a result of the uncertainties in the laser beam intensities, and the temporal variation in the hydrodynamic conditions after the plasma has reached steady state.
The projection of the common-wave vector in the plane ( ) for a single beam with polarization smoothing (PS).
List of parameters defining the common-wave gain that were varied during the experiments. is the number of beams that share an equivalent angle with the common electron-plasma wave [see Eq. (3) ] with the largest growth rate, is in units of and is in units of .
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