Engineering topics
Taitano, William
Publications and source records attributed to Taitano, William.
iFP simulations for Omega experiments studying implosions about the cryogenic vapor pressure of 0.3 mg/cc [Slides]
Abstract not provided.
Coupled radiation transport and plasma physics for ICF simulations [Slides]
Describing high-temperature plasmas requires inclusion of several nonlinear coupled physics, including ion kinetics - for each isotope species present in the plasma, electron kinetics, thermal radiative transfer (TRT), electromagnetic description, and nuclear reactions (fusion burn). Simulating plasmas in ICF hohlraums aims to solve kinetic ions (particles), fluid electrons, energetic electrons, electromagnetics, kinetic radiation (MG DP solver), and laser-plasma interactions.
An Eulerian Vlasov-Fokker–Planck algorithm for spherical implosion simulations of inertial confinement fusion capsules
Here, we present a numerical algorithm that enables a phase-space adaptive Eulerian Vlasov–Fokker–Planck (VFP) simulation of inertial confinement fusion (ICF) capsule implosions. 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 underlying VFP equations into a computational (logical) coordinate, with the resulting inertial terms carefully discretized to ensure conservation. To deal with the spatial and temporally varying dynamics in a spherically imploding system, we have developed a novel nonlinear stabilization strategy for MMPDE in the configuration space. The strategy relies on a nonlinear optimization procedure that optimizes between mesh quality and the volumetric rate change of the mesh to ensure both accuracy and stability of the solution. Implosions of ICF capsules are driven by several boundary conditions: (1) an elastic moving wall boundary; (2) a time-dependent Maxwellian Dirichlet boundary; and (3) a pressure-driven Lagrangian boundary. Of these, the pressure-driven Lagrangian boundary driver is new to our knowledge. The implementation of our strategy is verified through a set of test problems, including the Guderley and Van-Dyke implosion problems — the first-ever reported using a Vlasov–Fokker–Planck model.
Simulating and comparing cryogenic ICF capsule implosions in iFP and xRAGE
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Impact of Kinetic fuel Ions on Inferred Ion Temperatures from Neutron Spectra
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A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver
In this work, we develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.
Physics of the implosion up until the time of ignition in a revolver (triple-shell) capsule
Here, a revolver is designed to have two dynamical fuel implosion stages to reach ignition: a shock phase in which the fuel is pre-heated up until the shock collapses at the capsule center, followed by an adiabatic compression phase to ignition. This picture assumes ideal hydrodynamics. Employing the state-of-the-art, hybrid (kinetic-ion/fluid electron), multi-ion Vlasov-Fokker-Planck code, iFP, along with semi-analytic predictions from ideal hydrodynamics in spherical geometry, we confirm this two phase picture—resolving some outstanding questions in Revolver design along the way. Although we find that shock kinetic effects and non-ideality are present in the course of the implosion, these effects do not change the overall dynamics (which is well described by ideal hydrodynamics theory). Additionally, we put the assumption of adiabaticity, for the post-collapse phase, to the test. Finally, we verify the ideal hydro-conjecture that the shock collapse (fuel) convergence is ~2.12 given a single shock, and we confirm that the convergence is about 2.5 in the case of two shocks—in agreement with previous radiation-hydrodynamics simulations.
High-Order Low Order Nonlinear Convergence Accelerator for the Rosenbluth-Fokker-Planck Collision Operator and Applications to ICF
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Implicit, manifold-preserving numerical representations and solvers for multiscale kinetic simulations of plasmas
Presentation Conclusions: We have derived manifold-preserving algorithms for kinetic plasma simulation; Collisionless (PIC): we have solved the 40-year-old algorithmic challenge of developing accurate implicit PIC algorithms; Collisional (VFP): we have demonstrated a truly multiscale algorithm that has enabled routine simulation of ICF spherical capsule implosions with a few hundred cores for a couple of days.; In both cases: Strict conservation properties have been shown to be critical for long-term accuracy.; Significant algorithmic acceleration has been achieved by using nested asymptotic models.; We have seen similar benefits in other applications
Observations of Multiple Nuclear Reaction Histories and Fuel-Ion Species Dynamics in Shock-Driven Inertial Confinement Fusion Implosions
Fuel-ion species dynamics in DT 3 He-gas-filled Inertial Confinement Fusion implosion is quantitatively assessed for the first time using simultaneously measured D 3 He and DT reaction histories. Here, these reaction histories are measured with the Particle X-ray Temporal Diagnostic, which captures the relative timing between different nuclear burns with unprecedented precision (~10 ps). The observed 50±10 ps earlier D 3 He reaction history timing (relative to DT) cannot be explained by average-ion hydrodynamic simulations, and is attributed to fuel-ion species separation between the D, T, and 3 He ions during shock convergence and rebound. At the onset of the shock burn, inferred 3 He/T fuel ratio in the burn region using the measured reaction histories is much higher as compared to the initial gas-fill ratio. As T and 3 He have the same mass but different charge, these results indicate that the charge-to-mass ratio plays an important role in driving fuel-ion species separation during strong shock propagation.
Modern Multiscale Methods for the Vlasov-Fokker-Planck Equation with Applications to ICF
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Diffusion-driven Fluid Dynamics in Ideal Gases and Plasmas
The classical transport theory based on Chapman-Enskog methods provides self-consistent approximations for the kinetic flux of mass, heat, and momentum in a fluid limit characterized with a small Knudsen number. The species mass fluxes relative to the center of mass, or “diffusive fluxes,” are expressed as functions of known gradient quantities with kinetic coefficients evaluated using similar analyses for mixtures of gases or plasma components. The sum over species of the diffusive mass fluxes is constrained to be zero in the Lagrange frame, and thus results in a non-zero molar flux leading to a pressure perturbation. At an interface between two species initially in pressure equilibrium, the pressure perturbation driven by the diffusive molar flux induces a center of mass velocity directed from the species of greater atomic mass towards the lighter atomic mass species. As the ratio of the species particle masses increases, this center of mass velocity carries an increasingly greater portion of the mass across the interface and for a particle mass ratio greater than about two, the center of mass velocity carries more mass than the gradient driven diffusion flux. Early time transients across an interface between two species in a 1D plasma regime and initially in equilibrium are compared using three methods; a fluid code with closure in a classical transport approximation, a particle in cell simulation, and an implicit Fokker-Planck solver for the particle distribution functions. The early time transient phenomenology is shown to be similar in each of the computational simulation methods, including a pressure perturbation associated with the stationary “induced” component of the center of mass velocity which decays to pressure equilibrium during diffusion. At early times, the diffusive process generates pressure and velocity waves which propagate outward from the interface and are required to maintain momentum conservation. The energy in the outgoing waves dissipates as heat in viscous regions, and it is hypothesized that these diffusion driven waves may sustain fluctuations in less viscid finite domains after reflections from the boundaries. Finally, these fluid dynamic phenomena are similar in gases or plasmas and occur in flow transients with a moderate Knudsen number. The analysis and simulation results show how the kinetic flux, represented in the fluid transport closure, directly modifies the mass averaged flow described with the Euler equations.
A Multiscale, Conservative, Implicit 1D-2V Multispecies Vlasov-Fokker-Planck Solver for ICF Capsule Implosion Simulations
No abstract provided.
Multiscale high-order/low-order (HOLO) algorithms and applications
We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
In this paper, we propose an adaptive velocity-space discretization scheme for the multi-species, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass-, momentum-, and energy-conserving. Unlike most earlier studies, our approach normalizes the velocity-space coordinate to the temporally varying individual plasma species' local thermal velocity, v th (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v th -ratio-based expansion of the Rosenbluth potentials that only requires the computation of several velocity-space integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocity-grid adaptivity and asymptotic expansions delivers many orders-of-magnitude savings in mesh resolution requirements compared to a single, static uniform mesh.
Applying nonlinear diffusion acceleration to the neutron transport k-Eigenvalue problem with anisotropic scattering
High-order/low-order (or moment-based acceleration) algorithms have been used to significantly accelerate the solution to the neutron transport k-eigenvalue problem over the past several years. Recently, the nonlinear diffusion acceleration algorithm has been extended to solve fixed-source problems with anisotropic scattering sources. In this paper, we demonstrate that we can extend this algorithm to k-eigenvalue problems in which the scattering source is anisotropic and a significant acceleration can be achieved. Lastly, we demonstrate that the low-order, diffusion-like eigenvalue problem can be solved efficiently using a technique known as nonlinear elimination.