Modeling the solid-to-plasma transition for laser imprinting in direct-drive inertial confinement fusion

Laser imprinting possesses a potential danger for low-adiabat and high-convergence implosions in direct-drive inertial confinement fusion (ICF). Within certain direct-drive ICF schemes, a laser picket (prepulse) is used to condition the target to increase the interaction efficiency with the main pulse. Whereas initially the target is in a solid state (of ablators such as polystyrene) with specific electronic and optical properties, the current state-of-the-art hydrocodes assume an initial plasma state, which ignores the detailed plasma formation process. To overcome this strong assumption, a model describing the solid-to-plasma transition, eventually aiming at being implemented in hydrocodes, is developed. It describes the evolution of main physical quantities of interest, including the free electron density, collision frequency, absorbed laser energy, temperatures, and pressure, during the first stage of the laser-matter interaction. The results show that a time about 100 ps is required for the matter to undergo the phase transition, the initial solid state thus having a notable impact on the subsequent plasma dynamics. The nonlinear absorption processes (associated to the solid state) are also shown to have an influence on the thermodynamic quantities after the phase transition, leading to target deformations depending on the initial solid state. The negative consequences for the ICF schemes consist in shearing of the ablator and possibly preliminary heating of the deuterium-tritium fuel.

Figure 1

Evolution of the collision frequency as a function of electron temperature in (a) the equilibrium case ($T_e=T_{\mathrm{il}}$) and (b) for two constant ion-lattice temperatures of 0.1 eV and 0.5 eV. In all cases $n_{\mathrm{fe}}={10}^{22}{\mathrm{cm}}^{-3}$.

Figure 2

Evolution of the laser intensity as a function of time. The second part of the pulse is not shown because simulations are stopped before.

Figure 3

Evolution of (a) the electron density, (b) the temperatures, and (c) the collision frequency as a function of time on the front surface ($z=0$).

Figure 4

Contour plots of laser intensity (top), electron temperature (middle), and collision frequency (bottom) as a function of time and the laser propagation axis $z$. The laser starts at $z=0$ (target surface) and propagates along the $z$ direction.

Figure 5

At $t=90$ ps, evolution of (a) the laser intensity, (b) free electron density, (c) electron and ion-lattice temperatures, and (d) collision frequency as a function of the propagation distance $z$.

Figure 6

Evolution of the electron pressure as a function of time at $z=8\mu m$ in the center of a speckle. Various laser parameters are used.

Figure 7

Evolution of the electron pressure as a function of the laser propagation distance $z$ and the radial coordinate of a speckle, at $t=90$ ps. The maximum intensity in space and time is ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 8

At $t=90$ ps on the CH-DT interface ($z=8\mu \text{m}$), evolution of the electron pressure as a function of the radial coordinate. The maximum incident intensity in time and space is ${10}^{14}\mathrm{W}/{\mathrm{cm}}^2$.