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At least 181 records · Page 10

Final Report on Project “Micro-Misted Plasmas”

The key subject of this program was an examination of droplet evaporation kinetics in conjunction with plasma characteristics. Specifically, we undertook a careful investigation of the physical interactions between microscopic droplets of evaporating liquids and low pressure environments (including plasmas) by both experiment and simulation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Brief Description of the Kokkos implementation of the SNAP potential in ExaMiniMD.

Within the EXAALT project, the SNAP [1] approach is being used to develop high accuracy potentials for use in large-scale long-time molecular dynamics simulations of materials behavior. In particular, we have developed a new SNAP potential that is suitable for describing the interplay between helium atoms and vacancies in high-temperature tungsten[2]. This model is now being used to study plasma-surface interactions in nuclear fusion reactors for energy production. The high-accuracy of SNAP potentials comes at the price of increased computational cost per atom and increased computational complexity. The increased cost is mitigated by improvements in strong scaling that can be achieved using advanced algorithms [3].

74 ATOMIC AND MOLECULAR PHYSICS↗

The Multiphysics on Advanced Platforms Project

In 2015, the Lawrence Livermore National Laboratory started development of next-generation multiphysics simulation capabilities for the National Nuclear Security Administration under the Advanced Technologies Development and Mitigation (ATDM) element of the Advanced Simulation and Computing program in collaboration with the Exascale Computing Project (ECP). A key driver for this effort across the NNSA tri-lab was the emergence of advanced high performance computing (HPC) architectures based on heterogeneous compute capabilities, including GPU based systems, as part of the national drive toward exascale computing platforms at multiple Department of Energy (DOE) facilities. Developing a multiphysics code capable of meeting the various simulation needs of the NNSA as defined by the current generation of integrated codes (or ICs), initially developed as part of the Accelerated Strategic Computing Initiative (ASCI) program beginning in 1996, and able to scale to the current 100 petaflop class pre-exascale systems, as well the forthcoming exaflop class computers, is a daunting challenge. To accomplish this ambitious goal, LLNL has embraced two key themes: use of high-order numerical methods and a modular approach to code development. The LLNL next generation effort is organized under the Multi-Physics on Advanced Platforms Project (MAPP). A foundational component of MAPP is the Axom computer science (CS) toolkit which provides infrastructure for the development of modular, performance portable, multi-physics application codes. MARBL is a next-generation application code built on the Axom base to address the modeling needs of the high energy density physics (HEDP) community for simulating high-explosive, magnetic or laser driven experiments such as inertial confinement fusion (ICF), pulsed-power magneto-hydrodynamics (MHD), equation of state (EOS) and material strength studies as part of the NNSA’s stockpile stewardship program (SSP).

97 MATHEMATICS AND COMPUTING↗

Collaborative Research: Parametric Instabilities of Alfven Waves in Low‐beta Plasmas

Alfven waves are of fundamental importance in magnetized plasmas. This project aims to advance our understanding of the basic physics of the parametric instabilities of Alfven waves using advanced computer simulations. The results will have implications for important processes in the heliosphere involving Alfven waves, such as coronal heating and solar wind heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

LLNL FESP Theory Highlights: August 2024

The 2024 ABOUND SciDAC and BOUT++ combined workshop was held August 5-9 th 2024 at the University of California Livermore Collaboration Center (UCLC) in Livermore. Bringing together leading scientists and researchers from across the globe, this pivotal event focused on advancing plasma physics and boundary plasma dynamics within the context of fusion energy research. Key discussions throughout the meeting highlighted significant advancements in the BOUT++ framework, including enhanced simulations of small Edge Localized Modes (ELMs) and the initiation of integrating the integration of the 5D GEM gyrokinetic turbulence core code with the 2D SOLPS-ITER boundary transport code. These developments are crucial for managing heat loads in fusion reactors and supporting the longevity of plasma-facing components. The event also featured a session on Inter-SciDAC Collaborations, where principal investigators from multiple U.S. FES SciDAC tokamak projects explored opportunities for cross-collaboration. Additionally, the meeting showcased cutting-edge advancements in GPU acceleration and AI/ML technologies, poised to drive the next generation of fusion research. In his closing remarks, Dr. Xueqiao Xu emphasized the importance of the collaborative efforts and discussions that took place, noting their potential to shape future breakthroughs in fusion energy. The event underscored the global nature of the BOUT++ collaboration, with contributions from over 57 institutions worldwide. The 2024 BOUT++ and ABOUND Joint Hybrid Meeting continues to drive forward the research and innovations needed to achieve fusion energy, setting the stage for future collaboration and discovery.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cold Plasma IC Report

This past year we completed the simulation campaign in support of our magnetospheric cold plasma research project. This project aimed to develop the next-generation particle instruments to measure the properties of the cold particle populations in the Earth’s magnetosphere.

58 GEOSCIENCES↗

Collaborative Research: Tomographic imaging of laser-plasma structures

The interaction of intense short laser pulses with ionized gases, or plasmas, underlies many applications such as acceleration of elementary particles, production of energy by laser fusion, generation of x-ray and far-infrared “terahertz” pulses for medical and materials probing, remote sensing of explosives and pollutants, and generation of guide stars. Such laser-plasma interactions create tiny electron density structures (analogous to the wake behind a boat) inside the plasma in the shape of waves, bubbles and filaments that move at the speed of light, and evolve as they propagate. Prior to recent work by the PI of this proposal, detailed knowledge of such structures came exclusively from intensive computer simulations. Now “snapshots” of these elusive, light-velocity structures can be taken in the laboratory using dynamic variant of holography, the technique used to produce ID cards and DVDs, and dynamic variant of tomography, the technique used in medicine to image internal bodily organs. These fast visualization techniques are important for understanding, improving and scaling the above-mentioned applications of laser-plasma interactions. In this project, we accomplished three things: 1) We took holographic pictures of a laser-driven plasma-wave in the act of accelerating electrons to high energy, and used computer simulations to understand the pictures. 2) Using results from this experiment to optimize the performance of the accelerator, and the brightness of x-rays that it emits. These x-rays will be useful for medical and materials science applications. 3) We made technical improvements to the holographic technique that enables us to see finer details in the recorded pictures. Four refereed journal papers were published, and two students earned PhDs and moved on to scientific careers in US National Laboratories based on their work under this project.

43 PARTICLE ACCELERATORS↗

Data-driven linear time advance operators for the acceleration of plasma physics simulation

In this study, we demonstrate the application of data-driven linear operator construction for time advance with a goal of accelerating plasma physics simulation. We apply dynamic mode decomposition (DMD) to data produced by the nonlinear SOLPS-ITER (Scrape-off Layer Plasma Simulator - International Thermonuclear Experimental Reactor) plasma boundary code suite in order to estimate a series of linear operators and monitor their predictive accuracy via online error analysis. We find that this approach defines when these dynamics can be represented by a sequence of approximate linear operators and is essential for providing consistent projections when compared to an unconstrained application. For linear diffusion and advection–diffusion fluid test problems, we construct and apply operators within explicit and implicit time advance schemes, demonstrating that stability can be robustly guaranteed in each case. We further investigate the use of the linear time advance operators within several integration methods including forward Euler, backward Euler, and the matrix exponential. The application of this method to simulation data from SOLPS-ITER, with varying levels of Markov chain Monte Carlo numerical noise, shows that constrained DMD operators yield a capability to identify, extract, and integrate a (slow) subset of the present timescales. Example applications show that for projected speedup factors of [Formula: see text], and [Formula: see text], a mean relative error of 3%, 5%, and 8% and maximum relative error less than 20% are achievable, which appears acceptable for typical SOLPS-ITER steady-state simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Physics-constrained, low-dimensional models for magnetohydrodynamics: First-principles and data-driven approaches

Plasmas are highly nonlinear and multiscale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these reduced models hold promise for understanding key physical mechanisms, efficient computation, and real-time optimization and control. Galerkin models, obtained by projection of the MHD equations onto a truncated modal basis, and data-driven models, obtained by modern machine learning and system identification, can furnish this gap in the lower levels of the model hierarchy. This work develops a reduced-order modeling framework for compressible plasmas, leveraging decades of progress in projection-based and data-driven modeling of fluids. We begin by formalizing projection-based model reduction for nonlinear MHD systems. To avoid separate modal decompositions for the magnetic, velocity, and pressure fields, we introduce an energy inner product to synthesize all of the fields into a dimensionally consistent, reduced-order basis. Next, we obtain an analytic model by Galerkin projection of the Hall-MHD equations onto these modes. We illustrate how global conservation laws constrain the model parameters, revealing symmetries that can be enforced in data-driven models, directly connecting these models to the underlying physics. We demonstrate the effectiveness of this approach on data from high-fidelity numerical simulations of a three-dimensional spheromak experiment. Finally, this manuscript builds a bridge to the extensive Galerkin literature in fluid mechanics and facilitates future principled development of projection-based and data-driven models for plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

An interprojection sensor fusion approach to estimate blocked projection signal in synchronized moving grid-based CBCT system

Purpose: A preobject grid can reduce and correct scatter in cone beam computed tomography (CBCT). However, half of the signal in each projection is blocked by the grid. A synchronized moving grid (SMOG) has been proposed to acquire two complimentary projections at each gantry position and merge them into one complete projection. That approach, however, suffers from increased scanning time and the technical difficulty of accurately merging the two projections per gantry angle. Herein, the authors present a new SMOG approach which acquires a single projection per gantry angle, with complimentary grid patterns for any two adjacent projections, and use an interprojection sensor fusion (IPSF) technique to estimate the blocked signal in each projection. The method may have the additional benefit of reduced imaging dose due to the grid blocking half of the incident radiation. Methods: The IPSF considers multiple paired observations from two adjacent gantry angles as approximations of the blocked signal and uses a weighted least square regression of these observations to finally determine the blocked signal. The method was first tested with a simulated SMOG on a head phantom. The signal to noise ratio (SNR), which represents the difference of the recovered CBCT image to the original image without the SMOG, was used to evaluate the ability of the IPSF in recovering the missing signal. The IPSF approach was then tested using a Catphan phantom on a prototype SMOG assembly installed in a bench top CBCT system. Results: In the simulated SMOG experiment, the SNRs were increased from 15.1 and 12.7 dB to 35.6 and 28.9 dB comparing with a conventional interpolation method (inpainting method) for a projection and the reconstructed 3D image, respectively, suggesting that IPSF successfully recovered most of blocked signal. In the prototype SMOG experiment, the authors have successfully reconstructed a CBCT image using the IPSF-SMOG approach. The detailed geometric features in the Catphan phantom were mostly recovered according to visual evaluation. The scatter related artifacts, such as cupping artifacts, were almost completely removed. Conclusions: The IPSF-SMOG is promising in reducing scatter artifacts and improving image quality while reducing radiation dose.

61 RADIATION PROTECTION AND DOSIMETRY↗

Advanced gasifier and water gas shift technologies for low cost coal conversion to high hydrogen syngas

The Gas Technology Institute (GTI) and team members RTI International (RTI), Coanda Research and Development, and Nexant, are developing and maturing a portfolio of technologies to meet the United States Department of Energy (DOE) goals for lowering the cost of producing high hydrogen syngas from coal for use in carbon capture power and coal-to-liquids/chemicals. This project matured an advanced pilot-scale gasifier, with scalable and commercially traceable components, to readiness for use in a first-of-a-kind commercially-relevant demonstration plant on the scale of 500-1,000 tons per day (TPD). This was accomplished through cold flow simulation of the gasifier quench zone transition region at Coanda and through an extensive hotfire gasifier test program on highly reactive coal and high ash/high ash fusion temperature coals at GTI. RTI matured an advanced water gas shift process and catalyst to readiness for testing at pilot plant scale through catalyst development and testing, and development of a preliminary design basis for a pilot scale reactor demonstrating the catalyst. A techno-economic analysis was performed by Nexant to assess the potential benefits of the gasifier and catalyst technologies in the context of power production and methanol production. This analysis showed an 18%reduction in cost of power and a 19%reduction in cost of methanol relative to DOE reference baseline cases.

01 COAL, LIGNITE, AND PEAT↗

SciDAC - Center for Plasma Edge Simulation - Project Summary

Final Technical Report: Center for Plasma Edge Simulation (CPES) Principal Investigator: Scott Parker, University of Colorado, Boulder Description/Abstract First-principle simulations of edge pedestal micro-turbulence are performed with the global gyrokinetic turbulence code GEM for both low and high confinement tokamak plasmas. The high confinement plasmas show a larger growth rate, but nonlinearly a lower particle and heat flux. Numerical profiles are obtained from the XGC0 neoclassical code. XGC0/GEM code coupling is implemented under the EFFIS (“End-to-end Framework for Fusion Integrated Simulation”) framework. Investigations are underway to clearly identify the micro-instabilities in the edge pedestal using global and flux-tube gyrokinetic simulation with realistic experimental high confinement profiles. We use both experimental profiles and those obtained using the EFFIS XGC0/GEM coupled code framework. We find there are three types of instabilities at the edge: a low-n, high frequency electron mode, a high-n, low frequency ion mode, and possibly an ion mode like kinetic ballooning mode (KBM). Investigations are under way for the effects of the radial electric field. Finally, we have been investigating how plasmas dominated by ion-temperature gradient (ITG) driven turbulence, how cold Deuterium and Tritium ions near the edge will naturally pinch radially inward towards the core. We call this mechanism “natural fueling.” It is due to the quasi-neutral heat flux dominated nature of the turbulence and still applies when trapped and passing kinetic electron effects are included. To understand this mechanism, examine the situation where the electrons are adiabatic, and there is an ion heat flux. In such a case, lower energy particles move inward and higher energy particles move outward. If a trace amount of cold particles are added, they will move inward.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Relativistic Modeling Capabilities in Perseus Extended MHD Simulation Code for HED Plasmas

This project is submitted in response to DE-FOA-0001153, and will be carried out by Dr. Charles Seyler and Dr. Nathaniel Hamlin as post doc under the direction of Professor Seyler. The objectives are to enable PERSEUS to self-consistently model relativistic high-energy-density (HED) laboratory and astrophysical phenomena. Electrons and ions in a plasma are generally modeled either as fluids using a two-fluid code, like PERSEUS, or as particles using a Particle-In- Cell (PIC) code. Nonrelativistic PERSEUS solves the two-fluid equations, formulated in terms of a generalized Ohm’s law (GOL), so as to model about nine orders of magnitude in density variation using a local semi-implicit method. Relativistic PERSEUS preserves this structure and therefore retains these advantageous properties, enabling it to model a broader range of relativistic HED phenomena than previous codes. We have also overcome a major technical challenge associated with solving a relativistic system of equations relating conserved quantities (momentum, energy, etc.) to primitive variables (density, velocity, and pressure). We have thus far developed a relativistic version of PERSEUS and demonstrated that it recovers expected nonrelativistic results. We are currently using relativistic PERSEUS to model two HED phenomena, namely laser-plasma interactions and X-pinches, both of which show spectroscopic evidence of relativistic electrons. In an X-pinch, a section of wire carrying sufficiently large current forms a plasma column that pinches down to a point-like source, generating X-rays for use in radiographic imaging. Laser-plasma interactions have been simulated using PIC codes, and we use their results as a benchmark for comparison. However, neither PIC codes nor existing two-fluid schemes can simulate X-pinches, due to the broad range of densities which have thus far made such a simulation computationally prohibitive. In both laser-plasma interaction and Xpinch simulations, we have observed relativistic phenomena that PERSEUS could not previously model. This includes relativistic channeling of a laser into an over-dense deuterium gas (i.e. induced transparency), consistent with PIC simulation results, along with energetic electrons and ions following an X-pinch and likely accompanied by strong X-ray emission, consistent with experimental observations of energetic X-rays. This proposal includes our latest simulation results. We will improve computational efficiency with techniques that allow the use of a less refined numerical grid. This will enable extensions to three-dimensional geometries. We will improve modeling of laser-plasma interactions and X-pinches, including radiative transport processes, in order to improve comparisons with PIC simulations and experimental diagnostics. We will also model power loss through electrode surface plasmas in magnetically insulated transmission lines (MITLs). We will model relativistic astrophysical phenomena in both astrophysical and HED regimes, which could shed light on the validity of laboratory astrophysics for certain problems. These phenomena are currently modeled using PIC codes and existing relativistic two-fluid codes, neither of which can model the range of length scales of which relativistic PERSEUS is capable. There is strong potential for this project to have a broad impact on both the astrophysical and laboratory plasma communities. In the laboratory community, our work is applicable to those concerned with laser-plasma interactions such as laser-driven fusion, and those in the dense Z pinch community concerned with X-pinches and electrode surface plasmas. An improved understanding of the mechanisms of hard (i.e. high-energy) X-ray generation will likely make important contributions toward the use of X-pinches for radiography through the harnessing or mitigation of hard X-rays, depending on the application. The modeling of electrode surface plasmas, including vacuum electron flow, will improve our understanding of power loss to various loads.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Second order gyrokinetic theory for particle-in-cell codes

The main idea of the gyrokinetic dynamical reduction consists in a systematical removal of the fast scale motion (the gyromotion) from the dynamics of the plasma, resulting in a considerable simplification and a significant gain of computational time. The gyrokinetic Maxwell–Vlasov equations are nowadays implemented in for modeling (both laboratory and astrophysical) strongly magnetized plasmas. Different versions of the reduced set of equations exist, depending on the construction of the gyrokinetic reduction procedure and the approximations performed in the derivation. The purpose of this article is to explicitly show the connection between the general second order gyrokinetic Maxwell–Vlasov system issued from the modern gyrokinetic theory and the model currently implemented in the global electromagnetic Particle-in-Cell code ORB5. Necessary information about the modern gyrokinetic formalism is given together with the consistent derivation of the gyrokinetic Maxwell–Vlasov equations from first principles. The variational formulation of the dynamics is used to obtain the corresponding energy conservation law, which in turn is used for the verification of energy conservation diagnostics currently implemented in ORB5. This work fits within the context of the code verification project VeriGyro currently run at IPP Max-Planck Institut in collaboration with others European institutions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Collaborative Research: Enabling multi-scale studies of magnetic reconnection with interpretable data-driven models

The development of accurate reduced descriptions and improved closures for magnetic reconnection is an important and a long‐standing challenge in plasma physics. The four‐fluid approach, and associated closures, that were investigated have the potential to improve the accuracy of plasma fluid models, capturing physical effects which would otherwise require a kinetic description. If successful, this approach could have an important impact for the modeling of laboratory and space plasmas. The major goals of this project were to develop new machine learning (ML) tools based on sparse and symbolic regression techniques, and to extract interpretable and generalizable reduced models (e.g., in the form of partial differential equations - PDEs) from data generated by first principles plasma simulations. Preserving interpretability of such data‐driven models is key to addressing the long‐standing theoretical and numerical challenges. Prior proof‐of‐principle studies have demonstrated the enormous potential of this approach, by recovering the well‐established hierarchy of plasma equations (from Vlasov to MHD) from data produced by particle‐in‐cell (PIC) simulations. Our goal in this project was to extend and apply these new tools to construct better kinetic closures for magnetic reconnection; to derive better models of particle injection and acceleration by this fundamental plasma process; and to use this understanding to accelerate the development of multi‐scale plasma algorithms. While our immediate focus was on the problem of magnetic reconnection, the tools that were will developed are general and applicable to other areas of plasma physics, and more broadly to many‐body phenomena. We anticipate that the development of these multi‐scale models will have a significant impact across different areas of plasma science, from fusion to space and astrophysical plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A simulation-based model for understanding the time dependent x-ray drive asymmetries and error bars in indirectly driven implosions on the National Ignition Facility

Time-dependent low-mode asymmetries are believed to play a leading role in limiting the performance of current inertial confinement fusion implosions on the National Ignition Facility (NIF) [E. I. Moses et al., Phys. Plasmas 16, 041006 (2009)]. These long wavelength modes are initiated and driven by asymmetries in the x-ray flux from the hohlraum; however, the underlying hydrodynamics of the implosion also act to modify and amplify these asymmetries. Here we present here a simulation-based model connecting the time-dependent drive asymmetry seen by the capsule to the measured inflight and hot spot symmetries. This approach is based on a Green's function analysis for which we evaluate the response of the capsule to impulses of drive asymmetry at a series of times. Our model sheds new light on the sensitivity to the drive asymmetry of an imploded capsule, giving a new tool for design. Inverting the problem and finding the drive asymmetry needed to match the experimental data allow us to tightly constrain the drive asymmetry seen by the capsule, providing an error estimate on the result. Doing so, we are able to point out when and how the complex hohlraum simulations start to deviate from what they should obtain to match the experimental data. Ultimately, we project to use this model to make some experimental recommendations to fix the time-dependent low-mode asymmetry of indirectly driven implosions and identify additional measurements to further constrain the asymmetries with a view to improving target design on the NIF.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Wide-Bandgap Semiconductor Amplifiers for Fusion Plasma Heating and Control

This paper discusses power electronics developed under the ARPA-E GAMOW program to support nuclear fusion power production. The goal of this project was to develop and assess the potential for wide-bandgap (WBG) semiconductor devices in power electronics to enable high-efficiency and high-voltage solid-state systems for fusion plasma generation, heating, and control. The power electronics use an architecture in which multiple high-power boards can be combined to produce megawatt-level power, where using multiple boards provides high reliability. Two main areas of power electronics boards are developed in this project for fusion plasma heating and control applications: (1) pulse generation and control and (2) radiofrequency generation. The first area is for boards capable of driving high-voltage millisecond pulses at high duty cycles. The envisioned application of these pulses is in plasma control of magnetohydrodynamic instabilities, plasma position, and edge-localized modes. Pulse-width modulation allows for the implementation of a wide variety of linear and nonlinear control systems. The boards developed for this project could actuate control coils based on digital input signals and can be parallelized to provide megawatts of output power. The design of the pulse generator is a low-side load switch. A load switch was designed and constructed that utilized 2-kV-rated field-effect transistor (FET)-based cascodes developed by Qorvo under this project to perform initial testing of these cascodes. The second area is being implemented using class E amplifiers with WBG devices and a reactance steering network to handle inductive or capacitive plasma loads. Applications include ion cyclotron resonance heating (ICRH) and high-harmonic fast-wave (HHFW) heating. A class E reactance steering network is demonstrated in modeling and experiment with a resistive-inductive load that models an inductively-coupled plasma. Power combining of boards with class E reactance steering networks is also simulated and demonstrated experimentally, to enable scaling up to high power. Modeling of high-power-density cooling and remaining useful life is conducted to enable reliable, effectively cooled high-power electronics for fusion applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

The Development of Kinetic and Radiation Hydrodynamics Modeling of Thermonuclear Burn Propagation in Isochoric p - 11 B Through the Support of the INFUSE Program

The report summarizes DOE INFUSE-supported work between HB11 Energy and the University of Rochester’s TriForce Institute to improve computational modeling of advanced fusion fuels, especially proton–boron-11 (p- 11 B). The project extended the TriForce particle-in-cell/Monte Carlo collision code to include physics needed for dense, high-temperature p- 11 B burn studies, including p- 11 B fusion reactions, three-alpha-particle reaction products, relativistic Coulomb collisions, large-angle nuclear scattering, bremsstrahlung radiation, inverse bremsstrahlung absorption, and photon transport. The upgraded models were verified against focused physics tests and against known deuterium–tritium burn behavior. The study then used one-dimensional spherical simulations to estimate the conditions required for thermonuclear burn propagation in isochoric p- 11 B fuel. The calculations found that burn propagation is possible in the model, but only under very extreme hot-spot conditions, such as about 7000 g/cm 3 at 500 keV or 9000 g/cm 3 at 300 keV for a 20-micron hot spot. These conditions are much more demanding than current demonstrated inertial confinement fusion hot spots. The report concludes that the INFUSE collaboration successfully advanced kinetic and radiation modeling capabilities for p- 11 B fusion and provided useful estimates of ignition requirements. However, the simulated fuel gains remain below what would be needed for practical inertial fusion energy, and further work is needed to reconcile differences among kinetic, radiation-hydrodynamic, and analytic models and to identify more achievable target designs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗