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Results for “Implicit PIC”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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9 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Local conservation of energy in fully implicit PIC algorithms

We consider the issue of strict, fully discrete local energy conservation for a whole class of fully implicit local-charge- and global-energy-conserving particle-in-cell (PIC) algorithms. Earlier studies demonstrated these algorithms feature strict global energy conservation. However, whether a local energy conservation theorem exists (in which the local energy update is governed by a flux balance equation at every mesh cell) for these schemes is unclear. In this study, we show that a local energy conservation theorem indeed exists. We begin our analysis with the 1D electrostatic PIC model without orbit-averaging, and then generalize our conclusions to account for orbit averaging, multiple dimensions, and electromagnetic models (Darwin). In all cases, a temporally, spatially, and particle-discrete local energy conservation theorem is shown to exist, proving that these formulations (as originally proposed in the literature), in addition to being locally charge conserving and globally energy conserving, are strictly locally energy conserving as well. In contrast to earlier proofs of local conservation in the literature, which only considered continuum time, our result is valid for the fully implicit time-discrete version of all models considered, including important features such as orbit averaging. We demonstrate the local-energy-conservation property numerically with a paradigmatic numerical example.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Addressing key physics problems in high-energy-density plasmas with a novel kinetic simulation capability

Many important physical processes in inertial confinement fusion (ICF) and dense Z-pinch (DZP) experiments require a kinetic (velocity-space-dependent) description. Conventional particle-in-cell (PIC) methods are poorly suited for high-energy-density (HED) plasmas, due to restrictive time-step constraints and the inability to conserve energy. In a previous LDRD (21-FS-048), we demonstrated that a fully implicit PIC formulation overcomes these limitations: it conserves energy even when coupled with Coulomb collision models and can be solved efficiently with large grid cells and large time steps. Thus, it is feasible to use this method to study kinetic effects in ICF and DZP plasmas on hydro-like time and spatial scales. In this follow-on LDRD, we advanced this methodology into a high-fidelity tool for production-scale simulations and used it to answer key questions relevant to ICF and DZP experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Asymptotic-preserving gyrokinetic implicit particle-orbit integrator for arbitrary electromagnetic fields

We extend the asymptotic preserving and energy conserving time integrator for charged-particle motion developed in Ricketson and Chacón (2020) to include finite Larmor-radius (FLR) effects in the presence of electric-field length-scales comparable to the particle gyro-radius (the gyro-kinetic limit). We introduce two modifications to the earlier scheme. The first is the explicit gyro-averaging of the electric field at the half time-step, along with an analogous modification to the current deposition, which we show preserves total energy conservation in implicit PIC schemes. The number of gyrophase samples is chosen adaptively, ensuring proper averaging for large timesteps and the recovery of full-orbit dynamics in the small time-step limit. The second modification is an alternating large and small time-step strategy that ensures the particle trajectory samples gyrophases evenly. We show that this strategy relaxes the time-step restrictions on the scheme, allowing even larger speed-ups than previously achievable. We demonstrate the new method with several single-particle motion tests in a variety of electromagnetic field configurations featuring gyro-scale variation in the electric field. Finally, the results demonstrate the advertised ability to capture FLR effects accurately even when significantly stepping over the gyration time-scale.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
NASA NTRS2016

Extended Magnetohydrodynamics with Embedded Particle-in-Cell Simulation of Ganymede's Magnetosphere

We have recently developed a new modeling capability to embed the implicit particle-in-cell (PIC) model iPIC3D into the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme magnetohydrodynamic (MHD) model. The MHD with embedded PIC domains (MHO-EPIC) algorithm Is a two-way coupled kinetic-fluid model. As one of the very first applications of the MHD-EPIC algorithm, we simulate the Interaction between Jupiter's magnetospherlc plasma and Ganymede's magnetosphere. We compare the MHO-EPIC simulations with pure Hall MHD simulations and compare both model results with Galileo observations to assess the Importance of kinetic effects In controlling the configuration and dynamics of Ganymede's magnetosphere. We find that the Hall MHD and MHO-EPIC solutions are qualitatively similar, but there are significant quantitative differences. In particular. the density and pressure inside the magnetosphere show different distributions. For our baseline grid resolution the PIC solution is more dynamic than the Hall MHD simulation and it compares significantly better with the Galileo magnetic measurements than the Hall MHD solution. The power spectra of the observed and simulated magnetic field fluctuations agree extremely well for the MHD-EPIC model. The MHO-EPIC simulation also produced a few flux transfer events (FTEs) that have magnetic signatures very similar to an observed event. The simulation shows that the FTEs often exhibit complex 3-0 structures with their orientations changing substantially between the equatorial plane and the Galileo trajectory, which explains the magnetic signatures observed during the magnetopause crossings. The computational cost of the MHO-EPIC simulation was only about 4 times more than that of the Hall MHD simulation.

Toth, Gabor↗
DOE OSTI2023

A pseudospectral implicit particle-in-cell method with exact energy and charge conservation

The standard particle-in-cell (PIC) method employs explicit finite-difference (FD) methods (e.g. the leap-frog scheme) for both spatial and temporal integrations. Here, we employ a pseudospectral method for solving the Poisson equation and a fully implicit time integration to achieve exact energy conservation. The advantage of a pseudospectral field solver is its spectral accuracy in solving field solutions. Earlier studies of implicit time integration of PIC FD equations can enforce exact energy exchange between field and particles, resulting in exact energy-conserving schemes. Here, we prove that the exact energy conservation property can be carried over to the pseudospectral scheme. Simultaneously, we provide a solution to ensure a pseudospectral charge continuity equation. We demonstrate the new scheme in a 2D electrostatic PIC code. In conclusion, theoretical results are confirmed via numerical examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Direct implicit and explicit energy-conserving particle-in-cell methods for modeling of capacitively coupled plasma devices

Achieving large-scale kinetic modeling is a crucial task for the development and optimization of modern plasma devices. With the trend of decreasing pressure in applications, such as plasma etching, kinetic simulations are necessary to self-consistently capture the particle dynamics. The standard, explicit, electrostatic, momentum-conserving particle-in-cell method suffers from restrictive stability constraints on spatial cell size and temporal time step, requiring resolution of the electron Debye length and electron plasma period, respectively. This results in a very high computational cost, making the technique prohibitive for large volume device modeling. We investigate the direct implicit algorithm and the explicit energy conserving algorithm as alternatives to the standard approach, both of which can reduce computational cost with a minimal (or controllable) impact on results. These algorithms are implemented into the well-tested EDIPIC-2D and LTP-PIC codes, and their performance is evaluated via 2D capacitively coupled plasma discharge simulations. The investigation reveals that both approaches enable the utilization of cell sizes larger than the Debye length, resulting in a reduced runtime, while incurring only minor inaccuracies in plasma parameters. The direct implicit method also allows for time steps larger than the electron plasma period; however, care must be taken to avoid numerical heating or cooling. It is demonstrated that by appropriately adjusting the ratio of cell size to time step, it is possible to mitigate this effect to an acceptable level.

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↗