A theoretical model for quantifying the imprinting sensitivity of direct-drive inertial confinement fusion implosions
Shanghai Institute of Laser Plasma（上海激光等离子体研究所）；University of Science and Technology of China（中国科学技术大学）；CAS Key Laboratory of Frontier Physics in Controlled Nuclear Fusion（可控核聚变前沿物理中国科学院重点实验室）；Collaborative Innovation Center of IFSA, Shanghai Jiao Tong University（上海交通大学国际前沿科学创新协同创新中心）
To quantify the sensitivity of diverse implosion designs to laser imprinting, we developed an equivalent perturbation model that maps laser imprinting as the initial target surface perturbation. By incorporating imperfections in target fabrication and thermal smoothing in the plasma, the model shows a reduced implosion sensitivity to laser imprinting, extending the analysis beyond geometric irradiation. The imprinting sensitivity threshold is defined as $\frac{δh_{\text{proxy}}}{δh_{\text{tar}}(0)} = 0.1$, where $δh_{\text{proxy}}$ is the imprinting amplitude and $δh_{\text{tar}}(0)$ is the initial target perturbation amplitude. Radiation-hydrodynamics simulations confirm that when $\frac{δh_{\text{proxy}}}{δh_{\text{tar}(0)}} \leq 0.1$, variations in nonlinear onset time and adiabat remain within 12\% of that with $δh_{\text{tar}}(0)$ alone. Moreover, the imprinting sensitivity is supported by OMEGA experiments. Overall, for linear perturbations of medium-to-high modes in direct-drive, the model enhances our physical understanding of how laser and target perturbations evolve and serves as a simplified tool to optimize implosion performance.
In inertial fusion, one of scientific issues is to reduce an implosion non-uniformity of a spherical fuel target. The implosion non-uniformity is caused by several factors, including the driver beam illumination non-uniformity, the Rayleigh-Taylor instability (RTI) growth, etc. In this paper we propose a new control method to reduce the implosion non-uniformity; the oscillating implosion acceleration dg(t) is created by pulsating and dephasing heavy ion beams (HIBs) in heavy ion inertial fusion (HIF). The dg(t) would reduce the RTI growth effectively. The original concept of the non- uniformit…
High-dimensional inverse design of inertial fusion implosions via differentiable simulation
Centre for Inertial Fusion Studies, The Blackett Laboratory, Imperial College（帝国理工学院惯性聚变研究中心布莱克特实验室）；I-X Centre for AI In Science, Imperial College London（帝国理工学院AI科学I-X中心）；Ergodic LLC（Ergodic有限责任公司）；Pasteur Labs（巴斯德实验室）
The numerical results for the fuel target implosion are presented in order to clarify the target physics in ion beam inertial fusion. The numerical analyses are performed for a direct-driven ion beam target. In the paper the following issues are studied: the beam obliquely incidence on the target surface, the plasma effect on the beam-stopping power, the beam particle energy, the beam time duration, the target radius, the beam input energy and the non-uniformity effect on the fuel target performance. In this paper the beam ions are protons.
The Code O-SUKI is an integrated 2-dimensional (2D) simulation program system for a fuel implosion, ignition and burning of a direct-drive nuclear-fusion pellet in heavy ion beam (HIB) inertial confinement fusion (HIF). The Code O-SUKI consists of the four programs of the HIB illumination and energy deposition program of OK3 (Comput. Phys. Commun. 181, 1332 (2010)), a Lagrangian fluid implosion program, a data conversion program, and an Euler fluid implosion, ignition and burning program. The OK3 computes the multi-HIBs irradiation onto a spherical fuel target. One HIB is divided into many bea…
Improving the description of the equation of state (EoS) of deuterium-tritium (DT) has recently been shown to change significantly the gain of an Inertial Confinement Fusion (ICF) target (Hu et al., PRL 104, 235003 (2010)). We use here an advanced multi-phase equation of state (EoS), based on ab initio calculations, to perform a full optimization of the laser pulse shape with hydrodynamic simulations starting from 19 K in DT ice. The thermonuclear gain is shown to be a robust estimate over possible uncertainties of the EoS. Two different target designs are discussed, for shock ignition and sel…
A novel capsule target design to improve the hot-spot pressure in the high-adiabat implosion for inertial confinement fusion is proposed, where a layer of comparatively high-density material is used as a pusher between the fuel and the ablator. This design is based on our theoretical finding of the stagnation scaling laws, which indicates that the hot spot pressure can be improved by increasing the kinetic energy density $ρ_d V_{imp}^2/2$ ($ρ_d$ is the shell density when the maximum shell velocity is reached, $V_{imp}$ is the implosion velocity.) of the shell. The proposed design uses the high…
The distribution function of suprathermal ions is found to be self-similar under conditions relevant to inertial confinement fusion hot-spots. By utilizing this feature, interference between the hydro-instabilities and kinetic effects is for the first time assessed quantitatively to find that the instabilities substantially aggravate the fusion reactivity reduction. The ion tail depletion is also shown to lower the experimentally inferred ion temperature, a novel kinetic effect that may explain the discrepancy between the exploding pusher experiments and rad-hydro simulations and contribute to…
The design of inertial confinement fusion experiments, alongside improving the development of energy density physics theory and experimental methods, is one of the key challenges in the quest for nuclear fusion as a viable energy source. Recent challenges in achieving a high-yield implosion at the National Ignition Facility (NIF) have led to new interest in considering a much wider design parameter space than normally studied. Here we report an algorithmic approach that can produce reasonable ICF designs with minimal assumptions. In particular we use the genetic algorithm metaheuristic, in whi…
A suite of synthetic nuclear diagnostics has been developed to post-process radiation hydrodynamics simulations performed with the code Chimera. These provide experimental observables based on simulated capsule properties and are used to assess alternative experimental and data analysis techniques. These diagnostics include neutron spectroscopy, primary and scattered neutron imaging, neutron activation, $γ$-ray time histories and carbon $γ$-ray imaging. Novel features of the neutron spectrum have been analysed to infer plasma parameters. The nT and nD backscatter edges have been shown to provi…
We report direct experimental evidence of interspecies ion separation in direct-drive, inertial-confinement-fusion experiments on the OMEGA laser facility. These experiments, which used plastic capsules with D$_2$/Ar gas fill (1% Ar by atom), were designed specifically to reveal interspecies ion separation by exploiting the predicted, strong ion thermo-diffusion between ion species of large mass and charge difference. Via detailed analyses of imaging x-ray-spectroscopy data, we extract Ar-atom-fraction radial profiles at different times, and observe both enhancement and depletion compared to t…
The Code O-SUKI-N 3D is an upgraded version of the 2D Code O-SUKI (Comput. Phys. Commun. 240, 83 (2019)). Code O-SUKI-N 3D is an integrated 3-dimensional (3D) simulation program system for fuel implosion, ignition and burning of a direct-drive nuclear-fusion pellet in heavy ion beam (HIB) inertial confinement fusion (HIF).The Code O-SUKI-N 3D consists of the three programs of Lagrangian fluid implosion program, data conversion program, and Euler fluid implosion, ignition and burning program. The Code O-SUKI-N 3D can also couple with the HIB illumination and energy deposition program of OK3 (Co…
Recent implosion experiments performed at the OMEGA laser facility reported by Casey et al.[1], displayed an anomalously low dd proton yield and a high tt neutron yield as compared to dt fusion reactions, explained as a stratification of the fuel in the implosion core. We suggest that in the com- pression stage the fuel is out of equilibrium. Ions are inward accelerated to a velocity v0 independent on the particle type. Yield ratios are simply given by the ratios of fusion cross-sections obtained at the same velocity. A 'Hubble' type model gives also a reasonable description of the data. These…
In this review paper on heavy ion inertial fusion (HIF), the state-of-the-art scientific results are presented and discussed on the HIF physics, including physics of the heavy ion beam (HIB) transport in a fusion reactor, the HIBs-ion illumination on a direct-drive fuel target, the fuel target physics, the uniformity of the HIF target implosion, the smoothing mechanisms of the target implosion non- uniformity and the robust target implosion. The HIB has remarkable preferable features to release the fusion energy in inertial fusion: in particle accelerators HIBs are generated with a high driver…
In inertial confinement fusion the target implosion non-uniformity is introduced by a driver beams' illumination non-uniformity, a fuel target alignment error in a fusion reactor, the target fabrication defect, et al. For a steady operation of a fusion power plant the target implosion should be robust against the implosion non-uniformities. In this paper the requirement for the implosion uniformity is first discussed. The implosion uniformity should be less than a few percent. A study on the fuel hotspot dynamics is also presented and shows that the stagnating plasma fluid provides a significa…
We study the cusp configuration of pre-seeded magnetic field for laser-driven flux-compression. The proposed configuration provides better particle confinement than that in Ref. [O.V. Gotchev et al., Journal of Fusion Energy 27 (2008) 25-31.] thereby leading to better magnetic insulation of hot fusion plasma. We develop the model that takes into account (i) magnetized target implosion, (ii) magnetic flux compression; (iii) particle losses from magnetic trap. The key parameter governing the process is the ratio of the implosion time to the particle loss 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 and J. Meyer-ter-Vehn, Comp. Phys. Comm. 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 implo…
We report first direct experimental evidence of interspecies ion separation in direct-drive ICF experiments performed at the OMEGA laser facility via spectrally, temporally and spatially resolved imaging x-ray-spectroscopy data [S. C. Hsu et al., EPL 115, 65001 (2016)]. These experiments were designed based on the expectation that interspecies ion thermo-diffusion would be strongest for species with large mass and charge difference. The targets were spherical plastic shells filled with D2 and a trace amount of Ar (0.1% or 1% by atom). Ar K-shell spectral features were observed primarily betwee…
We present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov-Fokker-Planck (VFP) simulation of an inertial confinement fusion (ICF) capsule implosion. The approach relies on extending a recent mass, momentum, and energy conserving phase-space moving-mesh adaptivity strategy to spherical geometry. In configuration space, we employ a mesh motion partial differential equation (MMPDE) strategy while, in velocity space, the mesh is expanded/contracted and shifted with the plasma's evolving temperature and drift velocity. The mesh motion is dealt with by transforming the unde…
Here we present the application of an advanced Sparse Gaussian Process based machine learning algorithm to the challenge of predicting the yields of inertial confinement fusion (ICF) experiments. The algorithm is used to investigate the parameter space of an extremely robust ICF design for the National Ignition Facility, the `Simplest Design'; deuterium-tritium gas in a plastic ablator with a Gaussian, Planckian drive. In particular we show that i) GPz has the potential to decompose uncertainty on predictions into uncertainty from lack of data and shot-to-shot variation, ii) permits the incorp…
The first simulations employing a kinetic treatment of both fuel and shell ions to model inertial confinement fusion experiments are presented, including results showing the importance of kinetic physics processes in altering fusion burn. A pair of direct drive capsule implosions performed at the OMEGA facility with two different gas fills of deuterium, tritium, and helium-3 are analyzed. During implosion shock convergence, highly non-Maxwellian ion velocity distributions and separations in the density and temperature amongst the ion species are observed. Diffusion of fuel into the capsule she…
The different behaviours of deuterium (D) and tritium (T) in the hot spot of marginally-igniting cryogenic DT inertial-confinement fusion (ICF) targets are investigated with an ion Fokker-Planck model. With respect to an equivalent single-species model, a higher density and a higher temperature are found for T in the stagnation phase of the target implosion. In addition, the stagnating hot spot is found to be less dense but hotter than in the single-species case. As a result, the fusion reaction yield in the hot spot is significantly increased. Fusion neutron diagnostics of the implosion find …
In a bounce-free spherical hydrodynamic implosion, the post-stagnation hot core plasma does not expand against the imploding flow. Such an implosion scheme has the advantage of improving the dwell time of the burning fuel, resulting in a higher fusion burn-up fraction. The existence of bounce-free spherical implosions is demonstrated by explicitly constructing a family of self-similar solutions to the spherically symmetric ideal hydrodynamic equations. When applied to a specific example of plasma liner driven magneto-inertial fusion, the bounce-free solution is found to produce at least a fact…
2D and 3D numerical simulations with the adaptive mesh refinement Eulerian radiation-hydrocode RAGE at unprecedented spatial resolution are used to investigate the connection between drive asymmetry and the generation of turbulence in the DT fuel in a simplified inertial-confinement fusion (ICF) implosion. Long-wavelength deviations from spherical symmetry in the pressure drive lead to the generation of coherent vortical structures in the DT gas and it is the three-dimensional instability of these structures that in turn leads to turbulence and mix. The simulations sug-gest that this mechanism…
A pulse shape designer for direct drive inertial confinement fusion has been developed, it aims at high compression of the fusion fuel while keeping hydrodynamics instability within tolerable level. Fast linear analysis on implosion instability enables the designer to fully scan the vast pulse configuration space at a practical computational cost, machine learning helps to summarize pulse performance into an implicit scaling metric that promotes the pulse shape evolution. The designer improves its credibility by incorporating various datasets including extra high-precision simulations or exper…
In laser-drive ICF, hybrid drive (HD) combined direct drive (DD) and indirect drive (ID) offers a smoothed HD pressure $P_{HD}$, far higher than the ablation pressure in ID and DD, to suppress hydrodynamic instabilities. In this letter, simulations of a new robust HD ignition target show that maximal HD pressure as high as $P_{HD} \sim$ 650 Mbar driven by a novel "bulldozer" effect is achieved, resulting in nonstagnation hotspot ignition at the convergence ratio $C_r \sim $23, and finally, fusion energy gain $\sim$ 10 in total laser energy = 1.42 MJ. Two-dimensional simulations have confirmed …
The sensitivity of inertial confinement fusion implosions of the type performed on the National Ignition Facility (NIF) to low-mode flux asymmetries has been investigated numerically. It is shown that large-amplitude, low-order mode shapes (Legendre polynomial P4), resulting from associated low order flux asymmetries, cause spatial variations in capsule and fuel momentum that prevent the DT ice layer from being decelerated uniformly by the hot spot pressure. This reduces the transfer of kinetic to internal energy of the central hot spot, thus reducing neutron yield. Furthermore, synthetic gate…
An indirect-direct hybrid-drive work-dominated hotspot ignition scheme for inertial confinement fusion is proposed: a layered fuel capsule inside a spherical hohlraum with an octahedral symmetry is compressed first by indirect-drive soft-x rays (radiation) and then by direct-drive lasers in last pulse duration. In this scheme, an enhanced shock and a follow-up compression wave for ignition with pressure far greater than the radiation ablation pressure are driven by the direct-drive lasers, and provide large pdV work to the hotspot to perform the work-dominated ignition. The numerical simulatio…
In inertial confinement fusion, the scientific issues include the generation and transport of driver energy, the pellet design, the uniform target implosion physics, the realistic nuclear fusion reactor design, etc. In this paper, we present a pellet injection into a power reactor in heavy ion inertial fusion. We employ a magnetic correction method to reduce the pellet alignment error in heavy ion inertial fusion reactor chamber, including the gravity, the reactor gas drag force and the injection errors. We found that the magnetic correction device proposed in this paper is effective to constr…
One of the best methods in inertial confinement fusion (ICF) is the concept of central spark ignition, consisting of two distinct regions named as hot and cold regions and formed by hydro-dynamical implosion of fuel micro-sphere central spark ignition method in inertial fusion and fuel pellet design condition in fusion power plant has been investigated and fuel gain for isochoric model in this method is calculated. We have shown the effects of different physical parameters of inertial fusion on fuel gain and optimized limit for fuel density and fuel pellet radius has been calculated.
This paper describes a technique for identifying trends in performance degradation for inertial confinement fusion implosion experiments. It is based on reconstruction of the implosion core with a combination of low- and mid-mode asymmetries. This technique was applied to an ensemble of hydro-equivalent deuterium-tritium implosions on OMEGA that achieved inferred hot-spot pressures ~56+/-7 Gbar [S. Regan et al., Phys. Rev. Lett. 117, 025001 (2016)]. All the experimental observables pertaining to the core could be reconstructed simultaneously with the same combination of low and mid modes. This…
Direct-drive is an important approach to achieving the ignition of inertial confinement fusion. To enhance implosion performance while keeping the risk of hydrodynamic instability at a low level, we have designed a procedure to optimize the parameters of the target doped with mid- or high-$Z$ atoms. In the procedure, a one-dimensional implosion can be automatically simulated, while its implosion performance and high-dimensional instability are integrally evaluated at the same time. To find the optimal doping parameters, the procedure is performed in the framework of global optimization algorit…
A Hybrid Scheme to Achieve Highest Implosion Performance on the OMEGA Laser
Laboratory for Laser Energetics, University of Rochester（罗切斯特大学激光能量学实验室）；Department of Mechanical Engineering, University of Rochester（罗切斯特大学机械工程系）；Department of Physics and Astronomy, University of Rochester（罗切斯特大学物理与天文系）
The new interpretation of the known results of simulation of the turbulent regime at the time before stagnation stage of the fusion implosion is stated. For this aim the universal turbulence energy spectrum obtained by the authors with a scaling law -8/3, which corresponds to the exact solution of one-dimensional Euler equations for the dynamics of a compressible medium, is used. It is stated that the scaling law -8/3 has more relevance in comparison with the Kolmogorov spectrum of -5/3 in the inertial sub-range of scales for the compressible turbulence at this stage of fusion implosion. A pos…
Magnetization of inertial confinement implosions is a promising means of improving their performance, owing to the potential reduction of energy losses within the target and mitigation of hydrodynamic instabilities. In particular, cylindrical implosions are useful for studying the influence of a magnetic field thanks to their axial symmetry. Here we present experimental results from cylindrical implosions on the OMEGA-60 laser using a 40-beam, 14.5 kJ, 1.5 ns drive and an initial seed magnetic field of B0=24 T along the axis of the targets, compared with reference results without an imposed B-…
Inertial Confinement Fusion is a promising option to provide massive, clean, and affordable energy for mankind in the future. The present status of research and development is hindered by hydrodynamical instabilities occurring at the intense compression of the target fuel by energetic laser beams. A recent patent combines advances in two fields: detonations in relativistic fluid dynamics and radiative energy deposition by plasmonic nano-shells. The compression of the target pellet can be moderate and rapid volume ignition is achieved by a laser pulse, which is as short as the penetration time …
Two-dimensional space-resolved temperature and density images of an inertial confinement fusion (ICF) implosion core have been diagnosed for the first time. Argon-doped, direct-drive ICF experiments were performed at the Omega Laser Facility and a collection of two-dimensional space-resolved spectra were obtained from an array of gated, spectrally resolved pinhole images recorded by a multi-monochromatic x-ray imager. Detailed spectral analysis revealed asymmetries of the core not just in shape and size but in the temperature and density spatial distributions, thus characterizing the core with…
Engineering features are known to cause jets of ablator material to enter the fuel hot-spot in inertial confinement fusion implosions. The Biermann battery mechanism wraps them in self-generated magnetic field. We show that higher-Z jets have an additional thermoelectric magnetic source term that is not present for hydrogen jets, verified here through a kinetic simulation. It has similar magnitude to the Biermann term. We then include this in an extended magneto-hydrodynamics approach to post-process an xRAGE radiation-hydrodynamic implosion simulation. The simulation includes an accurate mode…
The effects of laser-plasma interactions (LPI) on the dynamics of inertial confinement fusion hohlraums is investigated via a new approach that self-consistently couples reduced LPI models into radiation-hydrodynamics numerical codes. The interplay between hydrodynamics and LPI -- specifically stimulated Raman scatter (SRS) and crossed-beam energy transfer (CBET) -- mostly occurs via momentum and energy deposition into Langmuir and ion acoustic waves. This spatially redistributes energy coupling to the target, which affects the background plasma conditions and thus modifies laser propagation. …
Magnetic fields spontaneously grow at unstable interfaces around hot-spot asymmetries during inertial confinement fusion implosions. Although difficult to measure, theoretical considerations and numerical simulations predict field strengths exceeding 5kT in current national ignition facility experiments. Magnetic confinement of electrons then reduces the hot-spot heat loss by >5%. We demonstrate this via magnetic post-processing of two-dimensional xRAGE hydrodynamic simulation data at bang time. We then derive a model for the self-magnetization, finding that it varies with the square of the st…
We report the first measurement of the $^{10}{\rm B}(α,n)^{13}{\rm N}$ reaction in a polar-direct-drive exploding pusher (PDXP) at the National Ignition Facility (NIF). This work is motivated by the need to develop alternative mix diagnostics, radiochemistry being the focus here. The target is composed of a $65/35\,\rm at.\,\%$ deuterium-tritium (DT) fill surrounded by a roughly $30\,μ\rm m$ thick beryllium ablator. The inner portion of the beryllium ablator is doped with $10\,\rm at.\,\%$ of $^{10}{\rm B}$. Radiation-hydrodynamics calculations were performed in 1D to optimize both the remaini…
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
The design space for inertial confinement fusion (ICF) experiments is vast and experiments are extremely expensive. Researchers rely heavily on computer simulations to explore the design space in search of high-performing implosions. However, ICF multiphysics codes must make simplifying assumptions, and thus deviate from experimental measurements for complex implosions. For more effective design and investigation, simulations require input from past experimental data to better predict future performance. In this work, we describe a cognitive simulation method for combining simulation and exper…
Investigating the potential benefits of the use of magnetic fields in Inertial Confinement Fusion (ICF) experiments has given rise to new experimental platforms like the Magnetized Liner Inertial Fusion (MagLIF) approach at the Z-machine (Sandia National Laboratories), or its laser-driven equivalent at OMEGA (Laboratory for Laser Energetics). Implementing these platforms at MJ-scale laser facilities, such as the Laser MegaJoule (LMJ) or the National Ignition Facility (NIF), is crucial to reaching self-sustained nuclear fusion and enlarges the level of magnetization that can be achieved through…
To indirectly evaluate the asymmetry of the radiation drive under limited measurement conditions in inertial confinement fusion research, we have proposed an integral method to approximate the three-dimensional self-radiation distribution of the compressed plasma core using only four pinhole images from a single laser entrance hole at a maximum projection angle of 10°. The simultaneous algebraic reconstruction technique (SART) that uses spatial constraints provided by the prior structural information and the central pinhole image is utilized in the simulation. The simulation results showed tha…
Inertial Confinement Fusion is a promising option to provide massive, clean, and affordable energy for humanity in the future. The present status of research and development is hindered by hydrodynamic instabilities occurring at the intense compression of the target fuel by energetic laser beams. A recent proposal Csernai et al. (2018) combines advances in two fields: detonations in relativistic fluid dynamics and radiative energy deposition by plasmonic nano-shells. The initial compression of the target pellet can be eliminated or decreased, not to reach instabilities. A final and more energe…
We identify the desired characteristics and parameters of a beta>1 magnetized plasma, possibly with highly tangled, open field lines, that could be a suitable target to be compressed to fusion conditions by a spherically imploding plasma liner [S. C. Hsu et al., IEEE Trans. Plasma Sci. 40, 1287 (2012)] formed by merging hypersonic plasma jets. This concept is known as plasma-jet-driven magneto-inertial fusion (PJMIF). We set requirements on the target and liner such that (a) compressional heating dominates over thermal transport in the target, and (b) magnetic amplification due to compression …
Presented is a semi-analytic model of magnetized liner inertial fusion (MagLIF). This model accounts for several key aspects of MagLIF, including: (1) preheat of the fuel (optionally via laser absorption); (2) pulsed-power-driven liner implosion; (3) liner compressibility with an analytic equation of state, artificial viscosity, internal magnetic pressure, and ohmic heating; (4) adiabatic compression and heating of the fuel; (5) radiative losses and fuel opacity; (6) magnetic flux compression with Nernst thermoelectric losses; (7) magnetized electron and ion thermal conduction losses; (8) end …
