Fig. 1. (a) Equilibrium hydrodynamic profiles of a 1.5 MJ NIF ignition target during the acceleration phase after evolving for 1 ns using the initialization of the SH model: density from the SH model (black dashed line) and from the SNB model for Kn = 0.01 (blue squares) and Kn = 0.011 (red solid line); v_z from the SH model (black solid line) and from the SNB model for Kn = 0.01 (green squares) and Kn = 0.011 (orange solid line). The local Knudsen number Kn_loc profile (gray solid line) at t = 0 is also plotted. The three purple stars mark the locations of Kn_loc = {0.011, 0.010, 0.009}. (b) Linear growth rates of ARTI from the SH and SNB models for different values of Kn: the SH model for Kn = 0.01 (blue squares) and Kn = 0.011 (black triangles) and the SNB model for Kn = 0.01 (green circles) and Kn = 0.011 (red diamonds). The black triangles and blue squares are superimposed, since the SH model is local and independent of Kn. The theoretical curves are γ=(ATkg−AT2k2Va2/rd)1/2−(1+AT)kVa.²⁰

Fig. 2. (a) Bubble and spike trajectories from the SH and SNB models vs Z_t in the λ = 7 µm, Kn = 0.01 cases, where Zt≡∫0t∫0t′′g(t′)dt′dt′′ is the displacement function commonly used in theoretical descriptions of time-dependent acceleration histories. (b) Ratio of bubble velocities to classical values. The symbols represent the simulations and the curves are from the analytical model given by Eq. (8). (c) Average vorticity inside the bubble volume within a length 1/k below the bubble vertex, as illustrated in Fig. 3(a).

Fig. 3. Simulation results for the 10 μm-SNB case at t = 1.7 ns (Z_t = 180 µm). (a) Density. The volume marked inside the bubble is within 1/k below the bubble tip. (b) Temperature contour with heat flux vectors. (c) Vorticity. (d) Baroclinic source ω̇baro≡−∇P×∇ρ/ρ2. (e) Zoomed-in image of the vorticity and baroclinic source near the RTI interface. The hydrodynamic contours in the SH case are qualitatively similar to those in the SNB case.

Fig. 4. (a) Density profile and the heat flux correction term Q_SNB − Q_SH along the spike axis at t = 2.1 ns (Z_t = 286 µm) in the 7 µm SNB case. The density profile of the SH case at the same time is plotted as the dash-dotted line for comparison. Q_SNB and Q_SH are calculated using the density and temperature profiles from the SNB model. (b) Dependence of the volume-averaged baroclinic source −∇P × ∇ρ/ρ² on the dimensionless quantity kL_spike for both SH and SNB simulations.