Simulations Of Implosions Research Articles

Spectroscopic analysis of Cu wire array implosions on the refurbished Z generator

Experimental investigations of pinches on the refurbished Z (ZR) generator using Cu arrays have been initiated and more are planned for the near future. Significant X-ray emissions in the K-shell from moderately high atomic number plasmas such as Cu generate extreme interest. However, the production of these hard photons from high Z materials comes with a price. There is substantial loss of radiative yield due to stripping through many electrons present in high Z materials to reach to the H- or He-like ionization stages. Production of hard X-rays for materials with atomic number higher than Cu such as Kr is very difficult and theoretical predictions are even more uncertain. Previous experimental efforts using Cu as a plasma pinch load are encouraging and promote further investigations of this element on the refurbished Z machine for achieving photon energies higher than 5 keV and obtaining sufficient radiative yield. We will analyze the ionization dynamics and generate Cu spectrum using the temperature and density conditions obtained from 1-D non-LTE radiation hydrodynamics simulations of Cu wire array implosions on ZR. These results will be compared with K- and L-shell experimental spectrum of shot Z 1975. Theoretical K- and L-shell spectroscopy provides validation of atomic and plasma modeling when compared to available experimental data and also provides useful diagnostics for the plasma parameters. Our self-consistently generated non-LTE collisional-radiative model employs an extensive atomic level structure and data for all dominant atomic processes that are necessary to model accurately the pinch dynamics and the spectroscopic details of the emitted radiation.

A new exceptional points method with application to cell-centered Lagrangian schemes and curved meshes

The aim of this paper is the numerical simulation of compressible hydrodynamic strong implosions, which take place for instance in Inertial Confinement Fusion. It focuses in particular on two crucial issues, for such calculations: very low CFL number at the implosion center and approximation error on the initial geometry. Thus, we propose an exceptional points method, which is translation invariant and suitable to curved meshes. This method is designed for cell-centered Lagrangian schemes (GLACE [8,13,14], EUCCLHYD [25–29]). Several numerical examples on significant test cases are presented to show the relevance of our approach.

First-principles equation-of-state table of deuterium for inertial confinement fusion applications

Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations rely on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical or chemical EOS models become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure, and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density ({\rho}R), and neutron yield, which are significantly different from the SESAME simulations.

On the transport coefficients of hydrogen in the inertial confinement fusion regime

Ab initio molecular dynamics is used to compute the thermal and electrical conductivities of hydrogen from 10 to 160 g cm–3 and temperatures up to 800 eV, i.e., thermodynamical conditions relevant to inertial confinement fusion (ICF). The ionic structure is obtained using molecular dynamics simulations based on an orbital-free treatment for the electrons. The transport properties were computed using ab initio simulations in the DFT/LDA approximation. The thermal and electrical conductivities are evaluated using Kubo–Greenwood formulation. Particular attention is paid to the convergence of electronic transport properties with respect to the number of bands and atoms. These calculations are then used to check various analytical models (Hubbard’s, Lee–More’s and Ichimaru’s) widely used in hydrodynamics simulations of ICF capsule implosions. The Lorenz number, which is the ratio between thermal and electrical conductivities, is also computed and compared to the well-known Wiedemann–Franz law in different regimes ranging from the highly degenerate to the kinetic one. This allows us to deduce electrical conductivity from thermal conductivity for analytical model. We find that the coupling of Hubbard and Spitzer models gives a correct description of the behavior of electrical and thermal conductivities in the whole thermodynamic regime.

Design of High-Neutron-Yield, Polar-drive targets for diagnostic activation experiments on the NIF

Polar-drive (PD) target implosions have been designed for neutron diagnostic development on the NIF. These experiments use thin, room-temperature glass shells filled with low pressures of DT. Initial target implosions on the NIF will produce DT yields in the range of a few 1014 neutrons. The predicted yields are consistent with earlier data (1014 neutrons at 30 kJ) and recent PD scoping experiments performed on OMEGA. The experiments will use existing x-ray-drive phase plates with judicious repointing and defocusing to drive the implosions as uniformly as possible. These implosions have been modeled with three codes: LILAC, to optimize the 1-D design; SAGE, to optimize the pointing uniformity; and DRACO, to predict the yield from 2-D implosion simulations. Current simulation results indicate that the required yields will be obtained using up to 200-kJ UV light formed into a 1500-ps Gaussian pulse. Large-diameter glass shells (∼1500-μm OD) are under development and fabrication at General Atomics. As tritium and environmental conditions evolve, similar target designs, with larger diameters and higher laser energies, are expected to produce thermonuclear yields approaching 1016 neutrons.

Calibrating mix models for NIF tuning

Mixing may play a role in early "tuning" implosions at the National Ignition Facility (NIF), intended for optimizing target geometry and laser operating parameters prior to the first ignition shots. Turbulent transport models allow mixing to be represented in integrated capsule-plus-hohlraum simulations, so that its effects can be predicted. Such models typically have many adjustable coefficients, so it is important to calibrate the coefficients systematically, whether by comparison to experiments, theory, or detailed higher fidelity simulations. We have begun by comparing to results from high-resolution 2D multimode simulations of a NIF Rev3 CH(Ge) ignition capsule, using the time-varying angle-averaged radial profiles of ion species composition as the calibration reference. 1D implosion simulations are performed with either of two turbulence models, and the models are calibrated so that the 1D composition profiles roughly match the 2D reference profiles at a sequence of five times near the end of the implosion. Details of the reference profiles, however, such as non-monotonicity resulting from structures in the flow, cannot be represented by these models. Parameter searches, besides identifying optimal sets of model coefficients, also exhibit model sensitivity to parameter variations.

Strong Coupling and Degeneracy Effects in Inertial Confinement Fusion Implosions

Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of ρ=0.002-1596 g/cm3 and T=1.35 eV-5.5 keV. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density (ρR), and neutron yield relative to SESAME simulations.

Computational investigation of the magneto-Rayleigh–Taylor instability in Z-pinch implosions

The instability evolvement induced by single mode and random density seeds have been investigated by using the Magnetics Atom Radiation Electron Dynamics (MARED) code, which is a two dimensional, three temperature, radiation magnetohydrodynamic Lagrangian code developed for the Z-pinch implosion simulation. The instability development during each stage (linear, weak nonlinear, and nonlinear) and its corresponding characteristics are studied with single-mode seeds. The evolvement of the dominant mode and its final wavelength are revealed through the development of seeds composed of modes covering the “whole” spectrum or just a “band-type” range of it. In addition, the relationship between the initial perturbation amplitude and the final x-ray output are also discussed. Through these discussions, the MARED code is found able to reproduce the primary dynamic characteristics of the Z-pinch implosions and the development of the instability qualitatively agrees with the theoretical analyses and experimental observations, which shows us a modest expectation of the broad coverage of the future application.

A Laser Based Fusion Test Facility

The Fusion Test Facility (FTF) is a high repetition rate ignition facility that would bridge the gap between single shot facilities (such as NIF and LMJ) and a fully functioning laser fusion power plant. It would allow development of science and technologies so that follow-on power plants could have predictable performance. The FTF would need to have enough fusion power, about 100 MW, to rigorously test materials and components for the power plants. Because inertial fusion provides a “point” source for neutrons, it can provide very high fluxes for test objects placed close to the target, while the reaction chamber walls remain at conservatively large distances. Simulations indicate that direct-drive designs can achieve 100 MW fusion power with laser energies well below 1 MJ with a 5 Hz driver. High-resolution 2-D simulations of high-velocity direct-drive implosions utilizing a Krypton-Fluoride (KrF) laser give gains of >60× at 500 kJ, and shock-ignited targets may allow higher gains at even lower driver energy. Utilizing designs that require relatively small driver energy is the most straightforward path to reducing cost and development time for a practical laser fusion energy power plant. A program to develop an FTF would build upon the science and technologies developed in the existing National Ignition Campaign and the High Average Power Laser (HAPL) program, as well as the magnetic fusion technology program.

Integrated simulations of implosion, electron transport, and heating for direct-drive fast-ignition targets

A thorough understanding of future integrated fast-ignition experiments combining compression and heating of high-density thermonuclear fuel requires hybrid (fluid+particle) simulations of the implosion and ignition process. Different spatial and temporal scales need to be resolved to model the entire fast-ignition experiment. The two-dimensional (2D) axisymmetric hydrocode DRACO [P. B. Radha et al., Phys. Plasmas 12, 056307 (2005)] and the 2D/three-dimensional hybrid particle-in-cell code LSP [D. R. Welch et al., Nucl. Instrum. Methods Phys. Res. A 464, 134 (2001)] have been integrated to simulate the implosion and heating of direct-drive, fast-ignition fusion targets. DRACO includes the physics required to simulate compression, ignition, and burn of fast-ignition targets. LSP simulates the transport of hot electrons from the place where they are generated to the dense fuel core where their energy is absorbed. The results from integrated simulations of cone-in-shell CD targets designed for fast-ignition experiments on OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997); C. Stoeckl et al., Fusion Sci. Technol. 49, 367 (2006)] are presented. Target heating and neutron yields are computed. The results from LSP simulations of electron transport in solid-density plastic targets are also presented. They confirm an increase in the electron divergence angle with the laser intensity in the current experiments. The self-generated resistive magnetic field is found to collimate the hot-electron beam and increase the coupling efficiency of hot electrons with the target. Resistive filamentation of the hot-electron beam is also observed.

Laboratory planetary science studies using intense heavy ion beams at FAIR: The HEDgeHOB collaboration

In this paper we propose a novel experimental scheme, named LAboratory PLAnetary Sciences (LAPLAS), to study interiors of the giant planets in our solar system as well as exoplanets. This scheme involves low-entropy compression of a test material like hydrogen or ice that is imploded in a multi-layered cylindrical target driven by an intense heavy ion beam. Two-dimensional hydrodynamic simulations of implosion of a typical LAPLAS target assuming beam parameters that will be available at the future Facility for Antiprotons and Ion Research (FAIR) at Darmstadt, are reported, that demonstrate the feasibility of this scheme. Moreover, it is shown that the target implosion will be robust and will be stable towards hydrodynamic instabilities. This work has been done within the framework of the High Energy Density Matter Generated by Heavy Ion Beams (HEDgeHOB) collaboration.

Simulations of electron transport and ignition for direct-drive fast-ignition targets

The performance of high-gain, fast-ignition fusion targets is investigated using one-dimensional hydrodynamic simulations of implosion and two-dimensional (2D) hybrid fluid-particle simulations of hot-electron transport, ignition, and burn. The 2D/3D hybrid-particle-in-cell code LSP [D. R. Welch et al., Nucl. Instrum. Methods Phys. Res. A 464, 134 (2001)] and the 2D fluid code DRACO [P. B. Radha et al., Phys. Plasmas 12, 056307 (2005)] are integrated to simulate the hot-electron transport and heating for direct-drive fast-ignition targets. LSP simulates the transport of hot electrons from the place where they are generated to the dense fuel core where their energy is absorbed. DRACO includes the physics required to simulate compression, ignition, and burn of fast-ignition targets. The self-generated resistive magnetic field is found to collimate the hot-electron beam, increase the coupling efficiency of hot electrons with the target, and reduce the minimum energy required for ignition. Resistive filamentation of the hot-electron beam is also observed. The minimum energy required for ignition is found for hot electrons with realistic angular spread and Maxwellian energy-distribution function.

MHD processes during the cascade development of the neck and hot spot in an X-pinch

Results are presented from two-dimensional MHD simulations of X-pinch implosion. The simulations were performed in the (r, z) and (x, y) geometries for homogeneous (dense plasma) and heterogeneous (core-corona) loads. The formation of a minidiode, the development of a neck and an X-radiating hot spot, and the influence of the plasma corona on the implosion dynamics of the dense X-pinch plasma were investigated. For through simulations, the conical neck model was used, whereas a detailed analysis of the X-ray burst was performed in the parabolic neck model. The MHD processes occurring during the implosion of oblique shock waves and the onset of instability of the plasma column were examined. It is found that, due to the quasi-periodic character of these processes, the neck compression proceeds in a cascade fashion. The plasma state in a hot spot just before the break of the neck is analyzed, and the possibility of generating fast particle beams is considered.

Target design for high-density non-spherical implosion in fast ignition

A high ρR core which is formed by non-spherical cone-guided implosion is required in fast ignition. Contrary to the central-hot-spot scheme, high temperature is not necessary in the implosion process. Therefore, relatively slow implosion design could be effective using a massive shell target. In this work, two-dimensional simulations of such slow implosions are performed to achieve high ρR core. In the result, the higher ρRmax can be obtained if the target mass is increased. In this study, an implosion with a foot pulse laser is examined also. In the initial phase, during the foot pulse irradiation, ablated plasma affects the gold cone surface, and the gold plasma expands, which leads pernicious effect on the implosion process.

Direct-indirect hybrid mode implosion in heavy ion inertial fusion

A direct-indirect hybrid implosion mode is proposed and discussed in heavy ion beam (HIB) inertial confinement fusion (HIF) in order to release sufficient fusion energy in a robust manner. On the other hand, the HIB illumination non-uniformity depends strongly on a target displacement dz from the centre of a fusion reactor chamber. In a direct-driven implosion mode, dz of ~ 20 μm was tolerable, and in an indirect-implosion mode, dz of ~ 100 μm was allowable. In the direct-indirect mixture mode target, a low-density foam layer is inserted, and the radiation energy is confined in the foam layer. In the foam layer the radiation transport is expected to smooth the HIB illumination non-uniformity in the lateral direction. Two-dimensional implosion simulations are performed, and show that the HIB illumination non-uniformity is well smoothed in the direct-indirect hybrid-mode target. Our simulation results present that a large pellet displacement of ~ a few hundred μm is allowed in order to obtain a sufficient fusion energy output in HIF.

Fast ignitor target studies for the HiPER project

Target studies for the proposed High Power Laser Energy Research (HiPER) facility [M. Dunne, Nature Phys. 2, 2 (2006)] are outlined and discussed. HiPER will deliver a 3ω (wavelength λ=0.35μm), multibeam, multi-ns pulse of about 250kJ and a 2ω or 3ω pulse of 70–100kJ in about 15ps. Its goal is the demonstration of laser driven inertial fusion via fast ignition. The baseline target concept is a direct-drive single shell capsule, ignited by hot electrons generated by a conically guided ultraintense laser beam. The paper first discusses ignition and compression requirements, and presents gain curves, based on an integrated model including ablative drive, compression, ignition and burn, and taking the coupling efficiency ηig of the igniting beam as a parameter. It turns out that ignition and moderate gain (up to 100) can be achieved, provided that adiabat shaping is used in the compression, and the efficiency ηig exceeds 20%. Using a standard ponderomotive scaling for the hot electron temperature, a 2ω or 3ω ignition beam is required to make the hot electron range comparable to the desired size of the hot spot. A reference target family is then presented, based on one-dimensional fluid simulation of compression, and two-dimensional fluid and hybrid simulations of fast electron transport, ignition, and burn. The sensitivity to compression pulse shape, as well as to hot electron source location, hot electron range, and beam divergence is also discussed. Rayleigh–Taylor instability at the ablation front has been addressed by a model and a perturbation code. Simplified simulations of code-guided target implosions have also been performed.

Gain curves and hydrodynamic simulations of ignition and burn for direct-drive fast-ignition fusion targets

Hydrodynamic simulations of realistic high-gain fast-ignition targets are performed, including one-dimensional simulations of the implosion and two-dimensional simulations of ignition by a collimated electron beam and burn propagation. These simulations are used to generate gain curves for fast-ignition direct-drive inertial confinement fusion. The minimum energy required for ignition is computed for fast-electron beams with a monoenergetic or Maxwellian distribution, generated by a constant or Gaussian laser pulse. It is found that realistic fast-ignition targets can be ignited by monoenergetic collimated electron beams with a radius of 20μm, duration of 10ps, and energy of 15kJ. Simulations using ponderomotive temperature scaling for fast electrons and Gaussian laser pulses predict a minimum laser energy for ignition of 235kJ (105kJ) for the energy conversion efficiency from the laser to fast electrons 0.3 (0.5) and the wavelength of 1.054μm. Such large energies are required because ultra-intense lasers are predicted to generate very energetic (multi-MeV) electrons with stopping distance exceeding the target size. The fast-electron energy, the stopping distance and the minimum energy required for ignition can be reduced using frequency-doubled laser pulses. Simulations of idealized cone targets are also performed in order to determine a lower bound of the gain deterioration due to the cone.

Expansion shock waves in the implosion process from a time-reversible molecular-dynamics simulation of a dual explosion process

Why does not an expansion shock wave exist in a gaseous medium in nature? The reason has been widely believed to be the irreversibility in nature, while an obvious demonstration for this belief has not been accomplished yet. In order to resolve the question from a microscopic viewpoint, an implosion process dual to an explosion process was investigated by means of the molecular-dynamics method (MD). To this aim, we employed a “bit-reversible algorithm (Bit MD)” that was completely time-reversible in a microscopic viewpoint and was free from any round-off error. Here we show that, through a dual implosion simulation (i.e., a time-reversible simulation of the explosion), a kind of expansion shock wave is successfully formed in the Bit MD simulation. Furthermore, we show that when the controlled noise is intentionally added to the Bit MD, the expansion shock wave disappears dramatically and turns into an isentropic expansion wave, even if the noise is extremely small. Since the controlled noise gives rise to the irreversibility in the Bit MD simulation, it can be concluded that the irreversibility in the system prohibits the expansion shock wave from appearing in the system.

Direct–indirect mixed implosion mode in heavy ion inertial fusion

In order to realize an effective implosion, beam illumination non-uniformity on a fuel target must be suppressed less than a few percent. In this study, a direct–indirect mixture implosion mode is proposed and discussed in heavy ion beam (HIB) inertial confinement fusion (HIF) in order to release sufficient fusion energy in a robust manner. On the other hand, the HIB illumination non-uniformity depends strongly on a target displacement dz from the center of a fusion reactor chamber. In a direct-driven implosion mode, dz of ∼20 μm was tolerable, and in an indirect-implosion mode, dz of ∼100 μm was allowable. In the direct–indirect mixture mode target, a low-density foam layer is inserted, and the radiation energy is confined in the foam layer. In the foam layer, the radiation transport is expected to smooth the HIB illumination non-uniformity in the lateral direction. Two-dimensional implosion simulations are performed, and show that the HIB illumination non-uniformity is well smoothed in the direct–indirect mixture target. Our simulation results present that a large pellet displacement of approximately a few hundred microns is allowed in order to obtain a sufficient fusion energy output in HIF.

Some new discretization and adaptation and multigrid methods for 2-D 3-T diffusion equations

In the simulation of laser-driven implosion of a fuel capsule in inertial confinement fusion experiments, a system of two-dimensional diffusion equations coupled with electron, iron and photon temperature are widely used to approximately describe the process of energy across multiple materials and the exchange of energy among electrons, irons and photons. The numerical solution of such equations is always challenging because of its strong nonlinear phenomena and strong discontinuous interfaces. In this article, we design a symmetric finite volume method, develop the corresponding preconditioning technique, and propose a mesh adaptation algorithm based on Hessian matrix and a two-grid method. Using these new methods, we demonstrate that the energy conservation error and computation efficiency of the integrated algorithm are much better than classical method.