Implosion of a directly driven inertial confinement fusion capsule can be affected by laser-plasma instability. At relatively high laser intensities the laser energy dispersed in electron plasma wave converts a fraction of the laser energy into hot electrons that, by heating the compressed Deuterium–Tritium fuel, increases the temperature and the isentropic parameter while decreases the density. All these effects worsen the implosion process by increasing the ignition energy. Furthermore, it was found that the penetration deep of the alpha particles is also modified by changes in temperature and density, and consequently the amount of mass of the high-density fuel shell heated by alpha particles increases between 15 and 50

In the deceleration phase of an Inertial Confinement Fusion capsule implosion Rayleigh-Taylor hydrodynamic instability can affect or even quench the ignition and thermonuclear burn wave propagation. This instability tends to mix the inner hot plasma with the cold and dense plasma shell providing a mixing layer where nuclear fusion reactions are inhibited. The 1D hydrodynamics code Multi-IFE has been used to simulate the implosion of a direct-drive high-gain laser-capsule design and the temporal evolution of the average radius and thickness of the mixing layer have been estimated. To mimic the effect of the reduced reaction rate, the fuel reactivity in the mixing layer is artificially set to zero thus inhibiting the burn wave propagation throughout it nullifying the energy gain. In order to overcome this negative effect, secondary short and powerful laser pulse is added, shortening this way the deceleration phase, which in turn reduces the thickness of the mixing layer. A study has been carried out to identify the optimal secondary laser pulse that recovers the high energy gain.

An Omega-like beam configuration is considered where the 60-beam layout can be separated into two independent sub-configurations with 24 and 36 laser beams, each minimizing direct drive illumination non-uniformity. Two different laser focal spot profiles, one associated with each configuration, are proposed to apply the zooming technique in order to increase the laser-target coupling efficiency. This approach is used by 1D hydrodynamics simulations of the implosion of a direct-drive capsule characterized by a relatively large aspect ratio A = 7 and an optimized laser pulse shape delivering a maximum of 30 TW and 30 kJ, with different temporal pulse shapes in each of the two sets of beams. It is shown that zooming allows for an optimistic 1D thermonuclear energy gain greater than one while without zooming the thermonuclear gain remains largely below one. While this is incompatible with the as-built Omega laser, it provides a promising option for a future intermediate-energy direct drive laser system.

The OMEGA installation is separated into two independent sub-configurations with 24 and 36 laser beams each one minimising direct drive illumination non-uniformity. Two different laser focal spots associated one to each configuration are proposed to apply the zooming technique in order to increase the laser-target coupling efficiency. This approach is used by 1D hydrodynamics simulations of the implosion of a direct-drive capsule characterised by a relatively large aspect ratio A = 7 and an optimized laser pulse shape delivering a maximum of 30 TW and 30 kJ. It is shown that zooming allows for a 1D-thermonuclear energy gain greater than one while without zooming the thermonuclear gain remains largely below one.

In Inertial Confinement Fusion the ignition of the Deuterium–Tritium fuel and the self-sustained thermonuclear burn-wave propagation depend on several factors among them the reaction rate, product of the number densities of the reactants and the thermal reactivity of the fusion reaction. Different mechanisms could affect the reactivity and modify the final thermonuclear gain leading to a failure of ignition. Here, it is analysed the effect of a fuel reaction rate degraded by a given factor $$\upchi ~< ~1$$ on the kinetic energy needed to reach fuel ignition and thermonuclear burn-out. Ignition and burnout thresholds are firstly defined in the metrics of reactivity factor $$\upchi $$ and homothetic scaling curves. Then a parametric variation of $$\upchi $$ shows that a reduction of 10% (20%) on the reaction rate approximately implies a 15% (50% respectively) increase in the kinetic energies thresholds.

In direct-drive inertial confinement fusion implosion, the absorption of the laser light with the plasma corona can be affected by laser-plasma instabilities. Among them, the two-plasmon-decay instability converts part of the laser energy in accelerated electrons and reduces the incoming laser power. These electrons propagate and deposit their energy providing undesired fuel preheating that increases the fuel adiabat and makes it difficult to compress which negatively affects the capsule performance. Hydrodynamic numerical calculations of a direct-drive capsule that include a Monte Carlo package to account for the propagation of the hot-electrons have been performed. It turned out that the effect on the implosion depends on the kind of the electron energy distributions. Here, exponential and Maxwellian energy distributions have been considered and it is shown that Maxwellian distribution induces stronger preheating of the fuel than the exponential and makes more difficult the reach of the ignition condition and thermonuclear burn wave propagation. It is also found that hot-electrons with kinetic energies greater than 200 keV are primarily responsible of the degradation of the output fusion energy.

This work aims to analyse the possibility of directly driven imploding spherical targets in order to create a source of energetic particles (neutrons, protons, alphas, tritium and 3 He ions) for the Laser MégaJoule facility. D 3 He gas-filled spherical SiO 2 glass pellets, irradiated by an absorbed laser intensity of 10 14 W cm −2 or 10 15 W cm −2 have been considered. Depending on the absorbed laser intensity and the amount of the ablated glass layer two distinct regimes have been identified: a massive pusher and an exploding pusher . Both regimes are analysed in terms of hydrodynamics and fast particle spectra. Energetic particle time-resolved spectra are calculated and used to infer ionic temperatures and total areal densities. A parametric study has been performed by varying the shell thickness and target inner radius for both laser absorbed intensities.

In inertial confinement fusion, ignition conditions of the thermonuclear deuterium–tritium fusion reactions depend on the electron thermal heat conduction that affects the hot-spot mass accretion and energy balance. One-dimensional hydrodynamic calculations have been performed to simulate the implosion of a capsule directly irradiated by laser beams. For these calculations, the laser-capsule configuration has been scaled using homothetic transformations to scan the transition to ignition while keeping the implosion velocity constant. The electronic heat conduction has been modified by two alternative ways: (i) the classical Spitzer heat flux has been harmonically limited to the free streaming limit using a flux limit factor φ, and (ii) the classical Spitzer coefficient is reduced by a multiplicative factor α < 1. A change of the thermal conductivity affects the performances of the implosion and it can be beneficial or harmful. Parametric studies have been performed for both alternatives, looking for the kinetic energy threshold that generates a unitary energy gain as a function of parameters φ or α, respectively. These studies show how the energy threshold is modified by acting on the heat flux and that there is a minimum ignition energy that can be tuned by appropriately reducing the heat conduction. A simple qualitative model is developed to understand the relation between energy threshold and heat conduction.

Three-dimensional (3D) hydrodynamic numerical simulations of laser driven thin-shell gas-filled microballoons have been carried out using the computer code MULTI-3D [Ramis et al., Phys. Plasmas 21, 082710 (2014)]. The studied configuration corresponds to experiments carried at the ORION laser facility [Hopps et al., Plasma Phys. Controlled Fusion 57, 064002 (2015)]. The MULTI-3D code solves single-temperature hydrodynamics, electron heat transport, and 3D ray tracing with inverse bremsstrahlung absorption on unstructured Lagrangian grids. Special emphasis has been placed on the genuine 3D effects that are inaccessible to calculations using simplified 1D or 2D geometries. These include the consequences of (i) a finite number of laser beams (10 in the experimental campaign), (ii) intensity irregularities in the beam cross-sectional profiles, (iii) laser beam misalignments, and (iv) power imbalance between beams. The consequences of these imperfections have been quantified by post-processing the numerical results in terms of capsule nonuniformities (synthetic emission and absorption images) and implosion efficiency (convergence ratio and neutron yield). Statistical analysis of these outcomes allows determination of the laser tolerances that guarantee a given level of target performance.

Primary and secondary nuclear fusion reaction yields in a spherical and uniform Deuterium-Deuterium fuel plasma have been calculated via Monte-Carlo simulations. An iterative procedure has been used to correlate the fuel areal density and temperature to the yields. It is shown that, once is measured the time-evolution of the reaction yields for an imploding capsule, the method provides the areal density, electronic temperature, density, and radius of the fuel as a function of time.

The alpha-particle energy deposition mechanism modifies the ignition conditions of the thermonuclear Deuterium-Tritium fusion reactions, and constitutes a key issue in achieving high gain in Inertial Confinement Fusion implosions. One-dimensional hydrodynamic calculations have been performed with the code Multi-IFE [R. Ramis, J. Meyer-ter-Vehn, Comput. Phys. Commun. 203, 226 (2016)] to simulate the implosion of a capsule directly irradiated by a laser beam. The diffusion approximation for the alpha energy deposition has been used to optimize three laser profiles corresponding to different implosion velocities. A Monte-Carlo package has been included in Multi-IFE to calculate the alpha energy transport, and in this case the energy deposition uses both the LP [C.K. Li, R.D. Petrasso, Phys. Rev. Lett. 70, 3059 (1993)] and the BPS [L.S. Brown, D.L. Preston, R.L. Singleton Jr., Phys. Rep. 410, 237 (2005)] stopping power models. Homothetic transformations that maintain a constant implosion velocity have been used to map out the transition region between marginally-igniting and high-gain configurations. The results provided by the two models have been compared and it is found that – close to the ignition threshold – in order to produce the same fusion energy, the calculations performed with the BPS model require about 10% more invested energy with respect to the LP model.

Hot-spot path in the thermodynamic space(rho(R), T-i)(hs) is investigated for direct-drive scaled-target family covering a huge interval of kinetic energy on both sides of kinetic threshold for ignition. Different peak implosion velocities and two initial aspect ratios have been considered. It is shown that hot spot follows almost the same path during deceleration up to stagnation whatever the target is. As attended, after stagnation, a clear distinction is done between non-, marginally-, or fully igniting targets. For the last, ionic temperature can reach very high values when the thermonuclear energy becomes very high.

The implosion uniformity of a directly driven spherical inertial confinement fusion capsule is considered within the context of the Laser Mégajoule configuration. Two-dimensional (2D) hydrodynamic simulations have been performed assuming irradiation with two laser beam cones located at 49° and 131° with respect to the axis of symmetry. The laser energy deposition causes an inward shock wave whose surface is tracked in time, providing the time evolution of its non-uniformity. The illumination model has been used to optimize the laser intensity profiles used as input in the 2D hydro-calculations. It is found that a single stationary laser profile does not maintain a uniform shock front over time. To overcome this drawback, it is proposed to use two laser profiles acting successively in time, in order to dynamically stabilize the non-uniformity of the shock front.

An axially symmetric laser beam configuration irradiating a spherical capsule has been considered in the context of inertial confinement fusion (ICF). The laser beams are located at co-latitudes 49° and 131° and mimic the quad positions in the second cone of the Laser Mégajoule Facility. The capsule is directly irradiated by the laser beams whose energy deposition generates a nearly spherical shock wave. Two-dimensional hydrodynamic numerical simulations have been performed to analyse the non-uniformity of the shock wavefront launched inward throughout the target. Different laser intensity profiles, calculated by the illumination model, have been tested. The performance, in terms of shock non-uniformity, has been compared, and it is found that with an appropriate choice of the laser intensity profile it is possible to control the shock non-uniformity at early times.

A direct-drive shock ignition scheme in the context of the Laser MegaJoule facility has been considered. The irradiation uniformity provided by two laser beam configurations using a total of 10 or 20 quads to drive the first compression phase has been analyzed. Firstly, a numerical method is used to optimize the laser intensity profiles in the context of the illumination approximation model; then these profiles are used to calculate the irradiation non-uniformity of a spherical target of radius r 0 = 1000 μm assuming the beam uncertainties: power imbalance 5%, pointing error 50 μm and target positioning 20 μm. These uncertainties deteriorate the quality of the irradiation increasing considerably the irradiation non-uniformity; moreover, it is found that the pointing error provides the major contribution to the degradation of the irradiation. A strategy to mitigate the negative effect induced by the beam uncertainties is proposed. It consists in using a composite profile in each beam: a first large and flat intensity profile provides a background that reduces pointing error and target positioning effects, whilst a second overlapping profile optimizes the illumination irradiation. It is found that the introduction of the flat background with an intensity of 55% with respect to the maximum intensity reduces by about 40% the non-uniformity of the irradiation due to beam uncertainties.

A numerical method providing the optimal laser intensity profiles for a direct-drive inertial confinement fusion scheme has been developed. The method provides an alternative approach to phase-space optimization studies, which can prove computationally expensive. The method applies to a generic irradiation configuration characterized by an arbitrary number NB of laser beams provided that they irradiate the whole target surface, and thus goes beyond previous analyses limited to symmetric configurations. The calculated laser intensity profiles optimize the illumination of a spherical target. This paper focuses on description of the method, which uses two steps: first, the target irradiation is calculated for initial trial laser intensities, and then in a second step the optimal laser intensities are obtained by correcting the trial intensities using the calculated illumination. A limited number of example applications to direct drive on the Laser MegaJoule (LMJ) are described.

Analysis of low initial aspect ratio direct-drive target designs is carried out by varying the implosion velocity and the fuel mass. Starting from two different spherical targets with a given 300 µg-DT mass, optimization of laser pulse and drive power allows to obtain a set of target seeds referenced by their peak implosion velocities and initial aspect ratio (A = 3 and A = 5). Self-ignition is achieved with higher implosion velocity for A = 5-design than for A = 3-design. Then, rescaling is done to extend the set of designs to a huge amount of mass, peak kinetic energies and peak areal densities. Self-ignition kinetic energy threshold Ek is characterized by a dependance of Ek ∼ vβ with β-values which depart from self-ignition models. Nevertheless, self-ignition energy is seen lower for smaller initial aspect ratio. An analysis of Two-Plasmons Decay threshold and Rayleigh–Taylor instability e-folding is carried out and it is shown that two-plasmon decay threshold is always overpassed for all designs. The hydrodynamic stability analysis is performed by embedded models to deal with linear and non-linear regime. It is found that the A = 5-designs are always at the limit of disruption of the shell.

The illumination uniformity provided during the initial imprinting phase of the laser foot pulse in a direct drive scenario at the Laser MegaJoule facility has been analyzed. This study analyzes the quality of the illumination of a spherical capsule and concerns the uniformity of the first shock generate in the absorber of an Inertial Confinement Fusion capsule. Four configurations making use of all or some of the 80 laser beams organized in the 20 quads of the cones at 49° and 131° with respect to the polar axis have been considered in order to assemble the foot pulse. Elliptical and circular super-gaussian laser intensity profiles taking into account beam-to-beam power imbalance (10%), pointing error (50 μm), and target positioning (20 μm) have been considered. It has been found that the use of the Polar Direct Drive technique can in some cases reduce the irradiation non-uniformity by a factor as high as 50%. In all cases, elliptical profile provides better results in comparison with the circular one and it is shown that the minimum of the non-uniformity is also a function of the capsule radius.

The symmetry of a Direct-Drive (DD) irradiation scheme has been analyzed by means of three-dimensional (3D) simulations carried out by the code MULTI (R. Ramis et al., Comput. Phys. Commun. 49, 475 (1988)) that includes hydrodynamics, heat transport, and 3D laser ray-tracing. The implosion phase of a target irradiated by the Laser Megajoule (LMJ) facility in the context of the Shock Ignition scheme has been considered. The LMJ facility has been designed for Indirect-Drive, and by this reason that the irradiation scheme must be modified when used for DD. Thus, to improve the implosion uniformity to acceptable levels, the beam centerlines should be realigned and the beam power balance should be adjusted. Several alternatives with different levels of complexity are presented and discussed.