For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. As recently reported, a burning plasma state, where the alpha-heating in the plasma is the primary source of heating, was achieved in laboratory experiments. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin ``burn propagation'' into surrounding cold fuel, enabling the possibility of high energy gain. While ``scientific breakeven'' (i.e. unity target gain) has not yet been achieved, this talk reports the first controlled fusion experiment on the National Ignition Facility to produce capsule gain greater than unity (here 5.8) and reach ignition by many different formulations of the Lawson criterion. In the talk, we will discuss some key basic physics inertial confinement fusion (ICF) principles behind the burning plasma and ignition results as well as discuss future challenges.

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Lawson Criterion for Ignition Exceeded In An Inertial Fusion Experiment

White dwarfs represent the final state of evolution for most stars1–3. Certain classes of white dwarfs pulsate4,5, leading to observable brightness variations, and analysis of these variations with theoretical stellar models probes their internal structure. Modelling of these pulsating stars provides stringent tests of white dwarf models and a detailed picture of the outcome of the late stages of stellar evolution6. However, the high-energy-density states that exist in white dwarfs are extremely difficult to reach and to measure in the laboratory, so theoretical predictions are largely untested at these conditions. Here we report measurements of the relationship between pressure and density along the principal shock Hugoniot (equations describing the state of the sample material before and after the passage of the shock derived from conservation laws) of hydrocarbon to within five per cent. The observed maximum compressibility is consistent with theoretical models that include detailed electronic structure. This is relevant for the equation of state of matter at pressures ranging from 100 million to 450 million atmospheres, where the understanding of white dwarf physics is sensitive to the equation of state and where models differ considerably. The measurements test these equation-of-state relations that are used in the modelling of white dwarfs and inertial confinement fusion experiments7,8, and we predict an increase in compressibility due to ionization of the inner-core orbitals of carbon. We also find that a detailed treatment of the electronic structure and the electron degeneracy pressure is required to capture the measured shape of the pressure–density evolution for hydrocarbon before peak compression. Our results illuminate the equation of state of the white dwarf envelope (the region surrounding the stellar core that contains partially ionized and partially degenerate non-ideal plasmas), which is a weak link in the constitutive physics informing the structure and evolution of white dwarf stars9. Researchers have measured the equation of state of hydrocarbon in a high-density regime, which is necessary for accurate modelling of the oscillations of white dwarf stars.

A measurement of the equation of state of carbon envelopes of white dwarfs

The effects of hydrocarbon reactions and diamond precipitation on the internal structure and evolution of icy giant planets such as Neptune and Uranus have been discussed for more than three decades1. Inside these celestial bodies, simple hydrocarbons such as methane, which are highly abundant in the atmospheres2, are believed to undergo structural transitions3,4 that release hydrogen from deeper layers and may lead to compact stratified cores5–7. Indeed, from the surface towards the core, the isentropes of Uranus and Neptune intersect a temperature–pressure regime in which methane first transforms into a mixture of hydrocarbon polymers8, whereas, in deeper layers, a phase separation into diamond and hydrogen may be possible. Here we show experimental evidence for this phase separation process obtained by in situ X-ray diffraction from polystyrene (C8H8)n samples dynamically compressed to conditions around 150 GPa and 5,000 K; these conditions resemble the environment around 10,000 km below the surfaces of Neptune and Uranus9. Our findings demonstrate the necessity of high pressures for initiating carbon–hydrogen separation3 and imply that diamond precipitation may require pressures about ten times as high as previously indicated by static compression experiments4,8,10. Our results will inform mass–radius relationships of carbon-bearing exoplanets11, provide constraints for their internal layer structure and improve evolutionary models of Uranus and Neptune, in which carbon–hydrogen separation could influence the convective heat transport7.Diamonds precipitate from methane under the intense pressures of the atmospheres of Neptune and Uranus. Here, a laser shock experiment on a hydrocarbon sample shows that diamonds may require ten times as much pressure to precipitate as was previously thought.

Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions

We put together a first-principles equation of state (FPEOS) database for matter at extreme conditions by combining results from path integral Monte Carlo and density functional molecular dynamics simulations of the elements H, He, B, C, N, O, Ne, Na, Mg, Al, and Si as well as the compounds $\mathrm{LiF}, {\mathrm{B}}_{4}\mathrm{C}, \mathrm{BN}, {\mathrm{CH}}_{4}, {\mathrm{CH}}_{2}, {\mathrm{C}}_{2}{\mathrm{H}}_{3}, \mathrm{CH}, {\mathrm{C}}_{2}\mathrm{H}, \mathrm{MgO}, \mathrm{and} {\mathrm{MgSiO}}_{3}$. For all these materials, we provide the pressure and internal energy over a density-temperature range from $\ensuremath{\sim}0.5$ to 50 g ${\mathrm{cm}}^{\ensuremath{-}3}$ and from $\ensuremath{\sim}{10}^{4}$ to ${10}^{9}$ K, which are based on $\ensuremath{\sim}5000$ different first-principles simulations. We compute isobars, adiabats, and shock Hugoniot curves in the regime of $\mathrm{L}$- and $\mathrm{K}$-shell ionization. Invoking the linear mixing approximation, we study the properties of mixtures at high density and temperature. We derive the Hugoniot curves for water and alumina as well as for carbon-oxygen, helium-neon, and CH-silicon mixtures. We predict the maximal shock compression ratios of ${\mathrm{H}}_{2}\mathrm{O},$ ${\mathrm{H}}_{2}{\mathrm{O}}_{2},$ ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}, \mathrm{CO}, \mathrm{and} {\mathrm{CO}}_{2}$ to be 4.61, 4.64, 4.64, 4.89, and 4.83, respectively. Finally we use the FPEOS database to determine the points of maximum shock compression for all available binary mixtures. We identify mixtures that reach higher shock compression ratios than their end members. We discuss trends common to all mixtures in pressure-temperature and particle-shock velocity spaces. In the Supplemental Material, we provide all FPEOS tables as well as computer codes for interpolation, Hugoniot calculations, and plots of various thermodynamic functions.

First-principles equation of state database for warm dense matter computation.

We present the design of the first igniting fusion plasma in the laboratory by Lawson's criterion that produced 1.37 MJ of fusion energy, Hybrid-E experiment N210808 (August 8, 2021) [Phys. Rev. Lett. 129, 075001 (2022)10.1103/PhysRevLett.129.075001]. This design uses the indirect drive inertial confinement fusion approach to heat and compress a central "hot spot" of deuterium-tritium (DT) fuel using a surrounding dense DT fuel piston. Ignition occurs when the heating from absorption of α particles created in the fusion process overcomes the loss mechanisms in the system for a duration of time. This letter describes key design changes which enabled a ∼3-6× increase in an ignition figure of merit (generalized Lawson criterion) [Phys. Plasmas 28, 022704 (2021)1070-664X10.1063/5.0035583, Phys. Plasmas 25, 122704 (2018)1070-664X10.1063/1.5049595]) and an eightfold increase in fusion energy output compared to predecessor experiments. We present simulations of the hot-spot conditions for experiment N210808 that show fundamentally different behavior compared to predecessor experiments and simulated metrics that are consistent with N210808 reaching for the first time in the laboratory "ignition."

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Design of an inertial fusion experiment exceeding the Lawson criterion for ignition.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1453&context=ameslab_manuscripts

P. Zhang

Papers

A Review of Equation-of-State Models for Inertial Confinement Fusion Materials