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Progress on LMJ targets for ignition

Targets designed to produce ignition on the Laser MegaJoule are presented. The LMJ experimental plans include the attempt of ignition and burn of an ICF capsule with 160 laser beams, delivering up to 1.4MJ and 380TW. New targets needing reduced laser energy with only a small decrease in robustness have then been designed for this purpose. Working specifically on the coupling efficiency parameter, i.e. the ratio of the energy absorbed by the capsule to the laser energy, has led to the design of a rugby-shaped cocktail hohlraum. 1D and 2D robustness evaluations of these different targets shed light on critical points for ignition, that can be traded off by tightening some specifications or by preliminary experimental and numerical tuning experiments.


Introduction
The Laser Mégajoule (LMJ) facility is located at the Commissariat à l'Energie Atomique (CEA) center CESTA near Bordeaux in France. It is part of the French "Simulation Program" and is devoted to laboratory experiments in a large domain of Plasma Physics [1]. It will deliver up to 1.8 MJ and 550 TW of = 0.351 μm light [2]. The standard approach for achieving ignition on the LMJ relies on the indirect drive scheme. Our nominal point design target A1040 is composed of a graded doped plastic capsule in a cylindrical hohlraum; specifications based on current CEA capabilities give a security margin towards modeling uncertainties and technological dispersions. The experimental plans include the attempt of ignition and burn of an ICF capsule with 160 beams in 2 cones (33.2° and 49°), delivering up to 1.4 MJ and 380 TW at 3 . New targets needing reduced laser energy with only a small decrease in robustness have been designed for this purpose. They are presented in section 2. Our strategy is to work specifically on the coupling efficiency parameter, i.e. the ratio of the energy absorbed by the capsule to the laser energy. A rugby-shaped hohlraum is proposed, exhibiting a better coupling efficiency and symmetry control of the implosion than a cylindrical hohlraum for the specific energy balance of the 160-beam configuration [3]. Section 3 details 1D and 2D robustness studies.

Ignition target design
We have designed 300 eV capsules which need less energy with a small decrease of robustness compared to our baseline capsule A1040 [3]. The capsule designs have been first defined by a 0D- Both capsules have the same in flight aspect ratio than the capsule A1040 (about 160 kJ absorbed), which is a signature of the shell break-up risk, while the 1D robustness quantified by the excess in kinetic energy above the ignition threshold is reduced by less than 20%. Figure 1 shows the capsule thicknesses optimized for an uniformly germanium doped plastic ablator, while the LMJ point design is now including gradually doped ablators. As the capsule sensitivity to hydrodynamic instabilities is very dependant on the x-ray spectrum produced by the hohlraum, the ablator thickness and dopant structure need to be optimized for every 2D configuration. Integrated simulations of these capsules have been performed with our 2D hydro-radiative code FCI2, which includes all the target physics except microscopic laser-plasma interactions and highmode hydrodynamic instabilities, badly described by the mesh. The scaling is done for a given ratio of the holhraum equatorial radius over the capsule radius, as this parameter governs the flux uniformity around the capsule. In this 2-cone configuration, the radius of the LEH is taken equal to 1.5 mm for cylindrical hohlraums, to compare to 1.75 mm for the 3-cone design. The gas filling, used to limit the wall motion, is a H2-He equimolar mixture, with a density ranging from 0.8 to 1.3 mg/cc, contained by a polyimid window. Controlling the time-dependent symmetry in this specific 1/2-1/2 balance configuration is more difficult than in the 3-cone configuration. The symmetry control can be obtained by increasing the aspect ratio (half-length over equatorial radius) of the cylinder. An alternative way is to break the inner cone in two, which leads back to a configuration close to the 3-cone one.
All A850 integrated simulations, corresponding to small design variations, produce around 10 MJ yield with an energy budget of 850 kJ and a power laser up to 300 TW. Igniting the A943 capsule in a gold cylindrical hohlraum is still in the budget (1.2 MJ, 360 TW) and produces around 20 MJ. Getting more margin to leave some room for design uncertainties, like laser plasma instabilities (LPI) evaluation, such as backscattering processes, is possible by using either cocktail walls or a rugby shape for the hohlraum, or both. Rugby-shaped hohlraums have been shown to have many advantages over cylindrical hohlraums for the 160-beam configuration [5]. First, minimizing the hohlraum wall surface while keeping the equatorial radius constant improves the coupling efficiency, as approximately half the laser energy is used to heat the walls. But the rugby shape has also a significant advantage for the control of the radiation asymmetry on the capsule with a 1/2-1/2 energy balance. Bending the walls toward the center of the hohlraum, helps increasing the outer ring contribution near the level of the inner ring and leads to a better drive of the capsule. The core at ignition shown in Figure 2 presents around 5% hotspot perturbations, illustrating an adequate symmetry. A laser energy Laser Plasma Instabilities (LPI) may be enhanced in these small targets and their control has to be one of the major requirements of the design process. Two key parameters are the laser intensity and the electronic density inside the hohlraum; these factors can be optimized by playing on the size of the laser focal spot and on the composition and density of the gas filling the hohlraum. Linear growth rates of the Raman (SRS) and Brillouin (SBS) instabilities are evaluated by post-processing the 2D FCI2 simulations with our code PIRANAH. Total amplification is then calculated by integration along the laser beam [6]. The goal is to bring the gain values down to about 10. Work is in progress to lower the SBS by adding a low-Z dopant in the wall, such as boron. Another approach is to work with a lower drive temperature. A 275eV target (BT275 capsule) leading to a larger hohlraum has also been designed with the same laser budget; a key point is then to control its sensitivity to hydrodynamic instabilities ( Figure 3).

1D robustness
Exhaustive robustness studies [7] have been conducted on the targets to estimate the yield sensitivity to target fabrication, modeling uncertainties and experimental tuning. The various 1D sources of uncertainties have been combined in order to give a net error budget. These sources are small enough that by themselves they do not significantly affect the yield, but a combination of them can be harmful for ignition. The dominant error among the 22 parameters studied was shown to be the total ablator thickness, which provided guidance for target fabrication and led us to tighter specifications. Considerable effort has been done by the CEA target fabrication laboratory on the thickness and doping accuracy control of the ablator shell [8], lowering their contribution to the error budget to acceptable values. The next five main sources of error all come from experimental tuning, and they cannot be improved only by tightening specifications. The Fusion Campaign is elaborated in order to bring them down.

Controlling hydrodynamic instabilities
The tolerable roughness of the different interfaces of the capsules is determined by the use of different capsule-only simulations.
For sufficiently small initial amplitudes (still large enough to dominate the numerical noise), the evolution of a perturbed interface can be obtained with a simulation-based linear analysis, by combining numerical growth rates with an assumed initial spectrum of perturbations. Haan's saturation model [9] is then used to estimate the final deformations at the end of the acceleration phase. As these simulations cannot tell us by how much the capsule yield is affected, they are complemented with multimode calculations having a realistic power spectrum (modes 12 to 200) and a variable multiplier on the nominal roughness, in order to find the cliff in performance.
The tolerable roughness of the external surface of the plastic shell, leading to 75% of the nominal yield is estimated by these simulations to be between 70 and 150 nm, depending on the capsule. This leaves a reasonable security margin compared to the 20 nm state of the art of the CEA target lab [8]. The tolerable roughness of the internal surface of the solid DT shell (high modes only) is less than 1 μm for all designs.
Complete parametric studies presented on Figure 3 were done with uniformly germanium doped plastic ablator, as its sensitivity to hydrodynamic instabilities can be considered as a lower limit compared to what is obtained with gradually doped ablators. A gradually doped ablator can indeed strongly limit the development of the perturbations, but it has to be finely adapted to the capsule drive, and more specifically to the hohlraum x-ray spectrum, which is not very well known. Work is in progress on a laminated ablator, made of a succession of doped and undoped plastic layers. This multilayered design makes use of the stabilizing effect of anisotropic diffusion on the ablative Rayleigh-Taylor instability, and is now tested experimentally on Omega [10].

Conclusion
Different ICF targets have been designed to achieve ignition on the Laser MegaJoule. The rugbyshaped hohlraum appears as a natural candidate to save energy and achieve ignition with the specific 160-beam configuration. Controlling the laser-plasma instabilities in the hohlraum is now part of the design process, as it stays a major drawback in these small hohlraums. Robustness evaluations of the different targets are compulsory for the definition of mature designs. Integrated simulations of the complete designs are performed to set requirements for the details of the hohlraum. Important effort has gone into designing the capsules in order to optimize their hydrodynamic stability; tolerable roughnesses are then set by 2D capsule-only simulations. Sensitivity studies have shown the importance of the experimental tuning, than can be partially prepared by experiments on other laser facilities and by preliminary experiments on surrogate targets, as THD capsules.