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DOE OSTI2021

Modeling of a chain of three plasma accelerator stages with the WarpX electromagnetic PIC code on GPUs

The fully electromagnetic particle-in-cell code WarpX is being developed by a team of the U.S. DOE Exascale Computing Project (with additional non-U.S. collaborators on part of the code) to enable the modeling of chains of tens to hundreds of plasma accelerator stages on exascale supercomputers, for future collider designs. The code is combining the latest algorithmic advances (e.g., Lorentz boosted frame and pseudo-spectral Maxwell solvers) with mesh refinement and runs on the latest computer processing unit and graphical processing unit (GPU) architectures. In this paper, we summarize the strategy that was adopted to port WarpX to GPUs, report on the weak parallel scaling of the pseudo-spectral electromagnetic solver, and then present solutions for decreasing the time spent in data exchanges from guard regions between subdomains. In Sec. IV, we demonstrate the simulations of a chain of three consecutive multi-GeV laser-driven plasma accelerator stages.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

A comprehensive conductivity model for drift and micro-tearing modes

The parallel electrical conductivity is a crucial parameter in the study of the linear stability of drift-modes like the micro-tearing mode (MTM). The conductivity enters by closing the electromagnetic tearing layer equations. Recent progress in the understanding of the pedestal suggests that the MTM could play an important role in its structure and evolution. For this reason, we revisit and improve previous model conductivities. This parameter is generally derived from the linearized drift kinetic equation. In the past literature, it has been computed using either simplified collision operators or neglecting the spatial dependence away from the rational surface. Here, a fully consistent expression for the conductivity that would accurately model the pedestal has not been available. By applying a novel variational procedure and with the full Fokker Plank collision operator, including electron–electron collisions, we compute a closed expression for the parallel electrical conductivity in the form of a rational function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Heterogeneous Computing

To leverage the increasing heterogeneity in modern computing resources, Geant4 incorporates advanced software tools and a task-based framework (G4Tasking) that enables efficient parallelism at event, sub-event, and track levels. Ongoing R&D efforts focus on integrating GPUs into high-energy physics (HEP) simulations, including optical photon simulation with Opticks/NVIDIA OptiX, offloading electromagnetic particle transport using G4HepEM/AdePT and Celeritas, and employing advanced surface-based geometry models such as VecGeom2.0 and ORANGE. As Geant4 continues evolving toward high-performance computing (HPC) and heterogeneous architectures, it remains a key tool for large-scale simulations in HEP and beyond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1992

Multidisciplinary computational aerosciences

By combining CFD with the computational state-of-the-art in structural mechanics, propulsion, aeroacoustics, electromagnetics, etc., multidisciplinary computational aerosciences (MCAS) poses a formidable computational challenge requiring the use of massively parallel machines. Research efforts must accordingly be directed to three areas: (1) parallel architectures, (2) systems software, and (3) applications software; attention is presently given to the last of these, in view of developments at NASA-Ames in solution methodology, physical modeling, and multidisciplinary validation experiments.

Kutler, P.↗

NASA NTRS1993

An efficient formulation of the coupled finite element-integral equation technique for solving large 3D scattering problems

It is often desirable to calculate the electromagnetic fields inside and about a complicated system of scattering bodies, as well as in their far-field region. The finite element method (FE) is well suited to solving the interior problem, but the domain has to be limited to a manageable size. At the truncation of the FE mesh one can either impose approximate (absorbing) boundary conditions or set up an integral equation (IE) for the fields scattered from the bodies. The latter approach is preferable since it results in higher accuracy. Hence, the two techniques can be successfully combined by introducing a surface that encloses the scatterers, applying a FE model to the inner volume and setting up an IE for the tangential fields components on the surface. Here the continuity of the tangential fields is used bo obtain a consistent solution. A few coupled FE-IE methods have recently appeared in the literature. The approach presented here has the advantage of using edge-based finite elements, a type of finite elements with degrees of freedom associated with edges of the mesh. Because of their properties, they are better suited than the conventional node based elements to represent electromagnetic fields, particularly when inhomogeneous regions are modeled, since the node based elements impose an unnatural continuity of all field components across boundaries of mesh elements. Additionally, our approach is well suited to handle large size problems and lends itself to code parallelization. We will discuss the salient features that make our approach very efficient from the standpoint of numerical computation, and the fields and RCS of a few objects are illustrated as examples.

Cwik, T.↗

DOE OSTI2025

New Results on Communication- and Memory-Aware Load Balancing Model and Algorithms

While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe “work” in a distributed system: computation, communication, and memory. Our model enables an optimizer to explore complex tradeoffs in task placement, such as augmented parallelism, at the expense of data replication increasing memory usage. We propose a fully distributed, heuristic-based load balancing optimization algorithm, and demonstrate that it quickly finds close-to-optimal solutions. We formalize the complex optimization problem as a mixed-integer linear program, and compare it to our strategy. Finally, we show that when applied to an electromagnetics code, our approach obtains up to 2.3x speedups for the imbalanced execution.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

High-Fidelity Arc-Discharge Model for Hydrogen-Plasma-Smelting-Reduction of Iron Ore

Electrification and use of renewable hydrogen is currently a necessity for decarbonizing the iron-and-steel industry. In this regard, hydrogen plasma smelting reduction (HPSR) is a novel pathway that is being explored for reduction of iron ore. HPSR provides several decarbonization merits compared to conventional blast furnaces. Firstly, the use of renewable hydrogen drastically reduces the CO2 emissions compared to the use of coke. Secondly, renewable electricity in the form of a thermal plasma for making reactive hydrogen species (radicals, ions) are more efficient at reducing iron ore compared to neutral H2. Thirdly, a molten product compatible with downstream processes is obtained from the intense heat transfer from the plasma. However, the scale-up of this technology requires fundamental exploration of hydrogen plasma dynamics and its interaction with complex solid material that include phase changing iron-ore and slag. In this work, we present a first principles continuum scale model for thermal plasmas in Ar/H2 gas mixtures typically used for HPSR. The thermal plasma governing equations for mass, momentum and energy with Lorentz force and Joule heating source terms are solved along with electromagnetic equations for electrostatic and magnetic vector potential. Our solver will be based on Pele, a suite of reacting flow solvers designed for advanced scientific computing architectures (Henry De Frahan et al., Proceedings of SIAM Parallel Processing, 13-25, 2024), and will utilize adaptive mesh generation for enhanced resolutions at locations of intense physicochemical interactions. This study will present the impact of Ar to H2 ratios on excited/dissociated hydrogen species concentrations, plasma temperature and conductivity along with the impact of outgassed species (water, metal vapor, O, OH radicals) from ore surface on gas phase chemistry. Furthermore, the heat and species flux to the surface will be quantified as a function of applied voltages in a transferred arc configuration.

hydrogen plasma↗

DOE OSTI2022

Integrating a ponderomotive guiding center algorithm into a quasi-static particle-in-cell code based on azimuthal mode decomposition

High fidelity modeling of plasma based acceleration (PBA) requires the use of three dimensional, fully nonlinear, and kinetic descriptions based on the particle-in-cell (PIC) method. In PBA an intense particle beam or laser (driver) propagates through a tenuous plasma whereby it excites a plasma wave wake. Three-dimensional PIC algorithms based on the quasi-static approximation (QSA) have been successfully applied to efficiently model the interaction between relativistic charged particle beams and plasma. In a QSA PIC algorithm, the plasma response to a charged particle beam or laser driver is calculated based on forces from the driver and self-consistent forces from the QSA form of Maxwell's equations. These fields are then used to advance the charged particle beam or laser forward by a large time step. Since the time step is not limited by the regular Courant-Friedrichs-Lewy (CFL) condition that constrains a standard 3D fully electromagnetic PIC code, a 3D QSA PIC code can achieve orders of magnitude speedup in performance. Recently, a new hybrid QSA PIC algorithm that combines another speedup technique known as an azimuthal Fourier decomposition has been proposed and implemented. This hybrid algorithm decomposes the electromagnetic fields, charge and current density into azimuthal harmonics and only the Fourier coefficients need to be updated, which can reduce the algorithmic complexity of a 3D code to that of a 2D code. Modeling the laser-plasma interaction in a full 3D electromagnetic PIC algorithm is very computationally expensive due the enormous disparity of physical scales to be resolved. In the QSA the laser is modeled using the ponderomotive guiding center (PGC) approach. We describe how to implement a PGC algorithm compatible for the QSA PIC algorithms based on the azimuthal mode expansion. Here this algorithm permits time steps orders of magnitude larger than the cell size and it can be asynchronously parallelized. Details on how this is implemented into the QSA PIC code that utilizes an azimuthal mode expansion, QPAD, are also described. Benchmarks and comparisons between a fully 3D explicit PIC code (OSIRIS), as well as a few examples related to laser wakefield acceleration, are presented.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1985

Coupling of newborn ions to the solar wind by electromagnetic instabilities and their interaction with the bow shock

The process by which the solar wind assimilates newly ionized atoms is important for understanding the presence of planetary or interstellar helium in the solar wind, the dynamics of the Active Magnetospheric Particle Tracer Explorers (AMPTE) lithium releases in front of the earth's bow shock, and the formation of cometary tails. In this paper is examined how newborn ions can be coupled to the solar wind in the direction parallel to the magnetic field by means of electromagnetic instabilities driven by the distribution of newborn ions. The linear properties of three instabilities are analyzed and compared with numerical solutions of the linear dispersion equation, while their nonlinear behavior is followed by means of computer simulation to obtain the characteristic time for the pickup process. With a primary emphasis on the AMPTE lithiuim releases, various degrees of realism are introduced into the calculations to model the upstream conditions and the intersection of the lithium with the bow shock. It is shown that a time-dependent shock model is needed to correctly reproduce the amount of lithium which is transmitted through the shock and that the resulting lithium ion distribution is still likely to be subject to the same type of instabilities in the magnetosheath. Applications of these results to comets, in particular the artificial comet expected to be generated by the AMPTE barium release in the magnetosheath, is also briefly discussed.

Winske, D.↗

NASA NTRS1994

Proton and helium cyclotron anisotropy instability thresholds in the magnetosheath

Both the protons and the helium ions of the terrestrial magnetosheath typically display T (sub perpendicular) greater than T (sub parallel), where perpendicular to and parallel to denote directions perpendicular and parallel to the background magnetic field. Observations of the highly compressed magnetosheath show an inverse correlation between these ion temperature anisotropies and the parallel proton beta. Computer simulations have demonstrated that these correlations are due to wave-particle scattering by electromagnetic ion cyclotron anisotropy instabilities. These correlations correspond to linear theory thresholds of the proton cyclotron and the helium cyclotron instabilities. This paper uses linear Vlasov theory and the assumption of a constant maximum growth rate to obtain closed-form expressions for these thresholds as a function of the relative helium density and the parallel proton beta in a parameter model of the magnetosheath.

Gary, S. Peter↗

DOE OSTI2019

Electromagnetic wave propagation based upon spectral-element methodology in dispersive and attenuating media

SUMMARY We build on mathematical equivalences between Maxwell’s wave equations for an electromagnetic medium and elastic seismic wave equations. This allows us to readily model Maxwell’s wave propagation in the spectral-element codes SPECFEM2D and SPECFEM3D, written for acoustic, viscoelastic and poroelastic seismic wave propagation, providing the ability to handle complex geometries, inherent to finite-element methods and retaining the strength of exponential convergence and accuracy due to the use of high-degree polynomials to interpolate field functions on the elements, characteristic to spectral-element methods (SEMs). Attenuation and dispersion processes related to the frequency dependence of dielectric permittivity and conductivity are also included using a Zener model, similar to shear attenuation in viscoelastic media or viscous diffusion in poroelastic media, and a Kelvin–Voigt model, respectively. Ability to account for anisotropic media is also discussed. Here, we limit ourselves to certain dielectric permittivity tensor geometries, in order to conserve a diagonal mass matrix after discretization of the system of equations. Doing so, simulation of Maxwell’s wave equations in the radar frequency range based on SEM can be solved using explicit time integration schemes well suited for parallel computation. We validate our formulation with analytical solutions. In 2-D, our implementation allows for the modelling of both a transverse magnetic (TM) mode, suitable for surface based reflection ground penetration radar type of applications, and a transverse electric (TE) mode more suitable for crosshole and vertical radar profiling setups. Two 2-D examples are designed to demonstrated the use of the TM and TE modes. A 3-D example is also presented, which allows for the full TEM solution, different antenna orientations, and out-of-plane variations in material properties.

58 GEOSCIENCES↗

DOE OSTI2024

Topanga: A kinetic ion plasma code for large-scale ionospheric simulations on magnetohydrodynamic timescales

Topanga is a kinetic ion code developed for simulating large-scale plasma phenomena in the Earth's ionosphere on magnetohydrodynamic timescales. It is a domain-decomposed parallel code that runs on high-performance computing platforms. Features of Topanga include spherical geometry for simplified boundary conditions and computational efficiency; a hybrid plasma model with inertia-less fluid electrons, kinetic ions, and an electric field specified via an Ohm's law; a Maxwell-FDTD (finite difference time domain) plasma model which retains the displacement current in Maxwell's equations and models electron currents in the ionosphere with a tensor conductivity; sponge-layer boundary conditions for absorption of electromagnetic and plasma waves incident on the domain boundaries; and a novel mixed-implicit algorithm for evolving the EM fields inside the Maxwell-FDTD region that is stable over many orders of magnitude in the electron–ion collision frequency. We verify the numerical methods used in Topanga on a pair of test problems. The first test involves modeling a three-dimensional collisionless shock using the hybrid set of equations. The second test involves modeling a spherical TEM mode in vacuum using the Maxwell-FDTD set of equations. Finally, we demonstrate how using the combined set of hybrid and Maxwell-FDTD equations to model the Starfish Prime high-altitude nuclear test recovers a “missing” EM signal on the ground that is not present when using only the hybrid set of equations. The magnitude of this signal in the simulation containing the Maxwell-FDTD region agrees well with the E3a portion of the magnetohydrodynamic electromagnetic pulse from Starfish Prime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Advancement of hybrid fluid-kinetic modeling for HEDP and ICF science

We report on the development progress of a hybrid fluid-kinetic code for simulating fluids and plasmas in a wide range of environments, such as laser–matter interactions, inertial confinement fusion, magnetic confinement fusion, and pulsed power. The suite of numerical tools under development utilizes heterogeneous computer architectures and leverages the benefits of particle–based simulation techniques. By working to combine the kinetic particle-in-cell (PIC) model with a particle-based fluid simulation technique, such as smoothed particle hydrodynamics, we are developing a flexible framework capable of accurately modeling complex flows within and between kinetic and fluid regimes. The TriForce code is under development as a C++ framework for parallel, 3D, particle-based, hybrid ﬂuid-kinetic plasma simulations. The ﬂuid half of TriForce will be based upon the meshless smoothed-particle-hydrodynamics (SPH) approach, well-suited for shear, mixing, and turbulence, whereas the kinetic half resembles a traditional particle-in-cell (PIC) code; other particle-based approaches to fluid modeling that do use a mesh are also possible to use and are under investigation. Maxwell’s electromagnetic field equations are solved either via explicit or implicit algorithms or approximated via resistive magnetohydrodynamics (MHD) using an Ohm’s law and resulting induction equation (extended MHD is under development). A primary goal of enabling direct comparisons, from the same code, between results from the variants of MHD and implicit electromagnetic solutions is to improve our fundamental understanding of systems with magnetic ﬁelds. The code is under development to recover results from both radiation-MHD and fully kinetic codes in those limits, and is continuing to be developed from other follow-on grants to operate in between where both descriptions may co-exist and interact. For certain applications, it is desired for a simulation to contain ﬂuid ions and electrons as well as kinetic ions and electrons. Typically, it is too computationally intensive to model a full-scale ICF or HEDP experiment fully kinetically since many cycles are expended with very small time steps on modeling the ﬂuid part of a material that is well treated by the ﬂuid approximation. In this case, many traditional PIC particles can be replaced with a single ﬂuid particle representing the thermal part of the distribution function, and there are fewer needed kinetic particles, which describe the non-thermal part and can be sub-cycled relative to the ﬂuid particle advance. Furthermore, a pure ﬂuid code may, depending on the problem, simply lack many physically important details that are beyond the scope of its reduced approximations and assumptions. In this report, we summarize the objectives achieved in the development of the collisional and kinetic half of the code, and the physics problems to which the code has been applied in the areas of advanced and innovative fusion concepts, pulsed power, and magneto-inertial fusion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Parallel Simulation of Beam Dynamics in Particle Accelerators [Slides]

Particle accelerators are among the most versatile and important tools of scientific discovery. The Nation's accelerators are responsible for a wealth of advances in materials science, chemistry, the biosciences, particle physics, and nuclear physics. They also have important applications to national security, the environment, energy, medicine, and on the quality of people's lives. LANL has a long history of making pioneering contributions to Accelerator Science including key contributions to the field of Computational Accelerator Physics. These include the development of early beam dynamics codes with space charge (such as PARMILA and PARMELA), the development of rf cavity codes and magnet codes (including Poisson and Superfish), and the development and distribution of codes to the accelerator community through the Los Alamos Accelerator Code Group. LANL researchers also helped pioneer the development of massively parallel space-charge codes. In project t22_accelsim we have moved beyond electrostatic models of collective effects (i.e., solving the Poisson equation in the bunch frame) to fully electromagnetic models based on the Lienard-Wiechert formalism. This approach enables the large-scale simulation of radiation production and collective effects in high brightness electron beams. This is highly relevant to LANL given its future goal of developing an X-ray Free Electron Laser (XFEL). It also directly impacts a LANL LDRD project to develop an undulator-based non-invasive beam profile monitor for beams created in laser-plasma accelerator systems.

43 PARTICLE ACCELERATORS↗

NASA NTRS1973

Lunar electromagnetic scattering. II - Magnetic fields and transfer functions for parallel propagation

Magnetic field and transfer function amplitudes, resulting from a transverse electromagnetic wave in the interplanetary medium scattering from the moon and its diamagnetic cavity, are presented. Calculations are made using an asymmetric scattering theory for a spherical two-layer model of the lunar electrical conductivity profile and a nonconducting cylindrical model of the downstream lunar plasma void. Both the field and transfer function magnitudes are calculated as functions of position on the surface of the moon for frequencies relevant to the observations of the lunar surface and orbiting magnetometers. The amplitudes of the magnetic field components on the cavity boundary are also computed as functions of frequency and distance downstream from the lunar limb. Comparisons of the results are made with those of (1) spherically symmetric descriptions of lunar electromagnetic scattering, (2) the quasi-static approximation to asymmetric scattering theory, and (3) observations of the scattering phenomenon by lunar surface and orbiting magnetometers.

Schubert, G.↗

NASA NTRS1989

Computer simulations of cosmic-ray diffusion near supernova remnant shock waves

A plasma simulation model was used to study the resonant interactions between streaming cosmic-ray ions and a self-consistent spectrum of Alfven waves, such as might exist in the interstellar medium upstream of a supernova remnant shock wave. The computational model is a hybrid one, in which the background interstellar medium is an MHD fluid and the cosmic-rays are discrete kinetic particles. The particle sources for the electromagnetic fields are obtained by averaging over the fast cyclotron motions. When the perturbed magnetic field is larger than 10 percent of the background field, the macro- and microphysics are no longer correctly predicted by quasi-linear theory. The particles are trapped by the waves and show sharp jumps in their pitch-angles relative to the background magnetic field, and the effective ninety-degree scattering time for diffusion parallel to the background magnetic field is reduced to between 5 and 30 cyclotron periods. Simulation results suggest that Type 1 supernova remnants may be the principal sites of cosmic ray acceleration.

Max, C. E.↗

NASA NTRS2000

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

Oliker, Leonid↗

DOE OSTI2021

A multi-dimensional Child–Langmuir law for any diode geometry

While prior theoretical studies of multi-dimensional space-charge limited current (SCLC) assumed emission from a small patch on infinite electrodes, none have considered emission from an entire finite electrode. In this paper, we apply variational calculus (VC) and conformal mapping, which have previously been used to derive analytic solutions for SCLC density (SCLCD) for nonplanar one-dimensional geometries, to obtain mathematical relationships for any multi-dimensional macroscopic diode with finite cathode and anode. We first derive a universal mathematical relationship between space-charge limited potential and vacuum potential for any diode and apply this technique to determine SCLCD for an eccentric spherical diode. We then apply VC and the Schwartz–Christoffel transformation to derive an exact equation for SCLCD in a general two-dimensional planar geometry with emission from a finite emitter. Particle-in-cell simulations using VSim agreed within 4%–13% for a range of ratios of emitter width to gap distance using the thinnest electrodes practical for the memory constraints of our hardware, with the difference partially attributed to the theory's assumption of infinitesimally thin electrodes. After generalizing this approach to determine SCLCD for any orthogonal diode as a function of only the vacuum capacitance and vacuum potential, we derive an analytical formulation of the three-dimensional Child–Langmuir law for finite parallel rectangular and disk geometries. These results demonstrate the utility for calculating SCLCD for any diode geometry using vacuum capacitance and vacuum potential, which are readily obtainable for many diode geometries, to guide experiment and simulation development.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗