Comparison of time-averaged reflectivities from Trident single-hot-spot experiments (triangles) with those from 1D NPIC simulations (diamonds: averaged over time ).
Convergence study of the effect of the number of particles per cell on the SRS reflectivity scaling in Fig. 1. The reflectivity scaling is modeled repeatedly by VPIC using 32 (plus), 64 (asterisk), 128 (diamond), 256 (triangle), 512 (square), and 1000 (cross) particles per cell. With fewer simulation particles, the reflectivity onset is more gradual, occurs at a much higher intensity value, and the saturation level is lower. These effects in the low number of particles per cell simulations are inconsistent with Trident results.
SRS reflectivity vs laser intensity scaling results from 1D PIC simulations for (triangles), 0.34 (squares), 0.45 (diamonds) (the reflectivity is time averaged over an interval of ). A sharp onset of enhanced SRS at a threshold intensity and a saturated level at higher intensities are observed with all the regimes. However, the onset intensity decreases with decreasing , and the saturated level is reduced with increasing .
(Color) The electrostatic spectrum (on a log scale and in color) from a 1D PIC simulation of SRS at a laser intensity of which is just above the onset threshold for enhanced SRS in Fig. 1. The spectrum is averaged over an interval of , during which the electron plasma exhibits a non-Maxwellian tail as shown in the inset. Overlaid are the dispersion roots (solid, dotted, and dashed curves) solved by using the distribution function in the inset. See the text for detailed explanation of the branches.
(Color) The electrostatic spectrum (on a log scale and in color) from a 1D PIC simulation of SRS at a laser intensity of , which is just above the onset threshold for enhanced SRS for the case in Fig. 3. The spectrum is averaged over an interval of , during which the electron plasma exhibit a non-Maxwellian tail as shown in the inset. The solid and dashed curves in black are dispersion roots solved by using the distribution function in the inset. See the text for detailed explanation for the branches.
(Color) The electrostatic spectrum (on log scale and in color) from a 1D PIC simulation of SRS at a laser intensity of which is just above the onset threshold for enhanced SRS for the case in Fig. 3. The spectrum is averaged over an interval of , during which the electron plasma exhibits a non-Maxwellian form as shown in the inset. The solid and dashed curves in black are dispersion roots solved by using the distribution function in the inset, while the dotted curve is the Langmuir root of the initial Maxwellian plasma as a comparison. See text for a detailed explanation of the branches.
(Color) 1D simulation of SRS for the case with a strong laser drive intensity of that corresponds to the saturated level in Fig. 1. Displayed from top to bottom are a typical electron trapping history, snapshots of vector potential of backscattered light, electrostatic wave form, electron phase space distribution, and trapping modified electron velocity distributions at four locations in the region of parametric coupling.
(Color) Spectral dispersion results from the same simulation as Fig. 7. Panel (a) shows a log plot of the electrostatic wave energy in color, exhibiting a spectral streak, a large downshift in frequency with a very narrow increase in . Overlaid are linear dispersion curves for the electrostatic modes, Stokes (solid), unstable (dotted; BAM1) and stable (dashed-dotted; BAM2) BAM obtained from the bump-on-tail electron distribution shown in the lower inset present during the first time-averaged reflectivity pulse. The Langmuir root (dashed) from the initial Maxwellian plasma is also shown for comparison. The upper inset is a representative flat distribution more commonly seen in the middle spatial region during subsequent pulses. Panel (b) is the electromagnetic spectrum . Corresponding to the electrostatic spectral streak in (a) is the excitation of BSRS starting at the matching conditions determined from a Maxwellian plasma and continuing into higher frequencies. The bottom frame (c) shows the time history of instantaneous reflectivity.
(Color) Comparison of dispersion solutions using a bump-on-tail electron distribution (black curves) and a flat distribution (red curves). Displayed are the two electron distributions (upper right frame), frequency vs wave number (upper left), growth rate vs wave number (lower left), and growth rate vs wave phase velocity for the electrostatic modes. The solid curves are for the Stokes mode; its growth region is label with “Streak.” Two BAM roots are included: BAM1 (dotted) is an unstable root whose phase velocities are greater than those of the Streak, while BAM2 (dashed-dotted) is a stable root with overlapping phase velocities as the Streak. An important role of BAM in nonlinear SRS is that as the electron distribution changes to a flat form, the damping rate of BAM2 approaches marginal at its intersection with the Stokes root. This provides a linear plasma response favorable for the nonlinear frequency shift to continue.
(Color) Convergence study with number of particles per cell ranging from 64 to 750 in 2D simulations for SRS at a laser drive intensity of for (ion dynamics are not included). In the top frame (a) overlaid are the time-averaged reflectivity from simulations using 64 (black curve), 128 (blue), 256 (green), 512 (red), and 750 (grey) particles per cell; the latter two simulations agree well. The instantaneous reflectivities from simulations with 128 (blue) and 512 (red) particles per cell are shown in (b). Filamentation and self focusing are stronger in simulations with more particles, as shown by the results in (d) and (e) (512 particles per cell) in which the electrostatic waves extend to a large region and lead to larger SRS reflectivity. In contrast, the electrostatic waves from simulations using fewer particles per cell, as displayed in (c) for the simulation with 128 particles per cell (displayed at a time when the reflectivity has reaches a saturated level), are localized to a small region near the laser entrance (on the left).
(Color) Convergence study with number of particles per cell ranging from 64 to 512 in 2D simulations for SRS and SBS at a laser drive intensity of (ion dynamics are included). The instantaneous reflectivity is shown on the left, the time-averaged, on the right. The sharp peaks in the instantaneous reflectivity are pulses of SRS, while the broad profile results are from SBS. The reflectivity values, especially the time-averaged reflectivities, from these simulations agree well.
(Color) Time-averaged reflectivity (left) from 2D simulations of SRS for (orange and grey curves), 0.24 (blue and grey), 0.29 (green and grey), and 0.34 (red and grey) at a laser intensity of (ion dynamics are not included). The orange, blue, green, and red curves are from simulations with 128 particles per cell, whereas the grey curves are for 512 particles per cell; the inset shows a zoomed-in comparison for the low reflectivity case for . Spectral dispersion (right) for averaged over the period of time during which two time-averaged reflectivity pulses are seen. The spectral streak in 2D has a smaller frequency extent, which compares better to the Trident data.
Spectra from a 2D SRS simulation with during a time interval in which two initial peaks in the time averaged reflectivity are observed. The left frame is a spectrum for the backscattered light wave showing the two separate steps of large scattering. The middle frame is the spectrum obtained directly from the electrostatic field during this time by summing over a range of in the coupling region, while the right frame is obtained from backscattered light spectrum by selecting only the first reflected pulse (the larger burst in the left frame) and mapping back to electrostatic spectrum using energy conservation. The latter procedure can also remove electrostatic components that are not coupled to the backscattered light.
Article metrics loading...
Full text loading...