Basic mechanism for CBET: (a) two crossing laser beams with frequencies and wave vectors drive a beat wave with frequency , wave vector , and phase velocity in the frame of the plasma ( V is the plasma flow velocity); (b) the ponderomotive force from the beat wave drives a density modulation in the plasma and hence a refractive index modulation, traveling at vk ; (c) if , the refractive index modulation acts as a Bragg cell scattering one laser beam in the direction of the other (i.e., energy transfer); being able to control vk , e.g., via the frequency shift between the beams, allows to set the direction of power transfer (via the sign) and its amplitude (via the proximity of vk to cs ).
NIF geometry: 192 laser beams grouped in 48 quadruplets or “quads” enter the cylindrical “hohlraum” cavity through the LEHs at both ends of the hohlraum. The “inner beams,” at 23.5° and 30° from the hohlaum axis and hitting the hohlraum wall near the waist, are shown in red, whereas the “outer beams,” at 44.5° and 50° from axis, are shown in blue and hit near the LEH. Also shown is a polar view of the 24 quads from the upper hemisphere; the number next to each quad is its azimuthal angle in degree. The zoomed-in view of one of the quads shows the “checkerboard” polarization arrangement of the 4 beams in a quad.
(a) Phase velocities of the 276 beat waves created by crossing pairs of quads, from the 24 quads overlapping at each LEH of a NIF hohlraum (z is the hohlraum axis; 148 of the beat waves actually have no phase velocity since they are created by quads with similar wavelengths); (b) amplitudes of the density fluctuations created by the beat waves; (c) electrostatic potentials driven by the beat waves (normalized to ); (d) gain rates for each of the 24 quads (such that ), ordered against the azimuthal angle of the quads in the NIF chamber (cf. Fig. 2 ).
Distribution function (log scale, arbitrary units) of the hydrogen and carbon ions of a C5H12 plasma at t = 0 (when both species are initially Maxwellian with the same temperature, ) and after 500 ps, plotted as a function of the longitudinal velocity vz (along the hohlraum axis) and the transverse velocity . The green dots represent the beat waves' phase velocities (cf. Fig. 3(a) ). Due to the symmetry around the hohlraum axis on NIF (cf. Fig. 2 ), each green dot marks the position of 4 beat waves symmetrically distributed every 90° in azimuth, and the particle distribution function is essentially axisymmetric around the hohlraum axis.
(a) Ion temperature (defined in the local Maxwellian limit, i.e., ) for the carbon and hydrogen ions in a C5H12 plasma with an initial ion temperature Ti = 0.8 keV for the hydrogen and carbon ions; (b) average CBET gain rate for a NIF inner quad for a C5H12 plasma and a pure He plasma.
Average gain rate for a NIF inner quad m ( is the contribution from each other crossing quad n, given by Eq. (21) ), as a function of , the wavelength shift between inner and outer beams, calculated at four different times t = 0, 0.2, 0.5, and 1 ns. The calculation is done using the reduced fluid model described in the Appendix; the area highlighted in yellow represents the typical NIF operational range of , between 5 and 9 Å.
(a) Initial ion temperature calculated by the LASNEX code at peak laser power for the upper half of a NIF hohlraum; (b) ion heating rate (in keV/ns) calculated by our quasi-linear model; (c) initial flow velocity along z (hohlraum axis) calculated by LASNEX at the same time, and (d) acceleration of the flow due to momentum deposition. The green contour represents the density isocontour.
(a) Phase velocities of the 276 beat waves for the case where , with ; (b) resulting flow acceleration along z, , showing an expected deceleration of the flow at the LEH ( , whereas the initial flow velocity is positive, as seen in Fig. 7(c) ).
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