An improved time-dependent nonlocal electron heat-flux model and its verification by laser-driven Al foil acceleration experiment

• Improved nonlocal electron heat-flux model valid from degenerate warm dense matter to fully ionized plasmas.
• The model avoids commonly used constant ad hoc thermal flux limiting in regions having steep temperature gradients.
• Improved model has been self-consistently coupled to a two-dimensional radiation hydrodynamics code.
• Experimental verification of the improved nonlocal heat flux model via laser-driven Al foil acceleration experiment.
• Improved model gives better match with our experimental results (terminal velocity of the accelerated Al foils).

In hydrodynamics simulation of laser driven systems, the time-dependent nonlocal electron heat-flux models predict the saturation (flux inhibition) and delocalization of the heat-flux automatically. Therefore it avoids commonly used time and space-independent ad hoc flux limiting. Previously proposed analytical nonlocal heat-flux model of Luciani et al. [Phys. Rev. Lett., 51, p-1664, (1983)] which fits the results of numerical Fokker–Planck calculations is simple and straight forward to implement in a fluid code. The proposed expression, however, is a convolution of Spitzer–Harm heat-flux with a delocalization kernel which depends on classical electron collision mean free path. This is rigorously valid for high temperature non-degenerate plasmas. However, in laser driven systems, the energy transport due to electron thermal conduction is important in regions between the critical density and ablation surface where the plasma is mostly degenerate. We have improved this nonlocal heat-flux model by using a wide-range electron collision frequency model valid from warm-dense matter (degenerate plasmas) to fully ionized plasmas. The effect of this improved nonlocal heat-flux model on the free-surface velocity of laser-accelerated Al foils of thickness 2–10 μm is studied by using a two-dimensional radiation hydrodynamics code. The simulated free surface velocities are compared with our experimental results for laser intensities in the range 4 × 1013–3 × 1014 W/cm2. Preliminary analysis shows that the simulation results obtained with improved nonlocal heat-flux model yields better agreement with our experimental values.