DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm

Abstract

The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. A novel, implicit, particle-in-cell based scheme for the hybrid model is derived for fully 3D electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit-averaging for the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allows arbitrary-order shape functions for the particle-mesh interpolations and the application of conservative binomial smoothing. The algorithm is verified for a number of test problems to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme. In particular, there is no indication of unstable growth of the finite-grid instability for a population of cold ions drifting through a uniform spatial mesh, in a set-up where several commonly used non-conservative schemes are highly unstable.

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1477697
Alternate Identifier(s):
OSTI ID: 1756197
Report Number(s):
LA-UR-18-21708
Journal ID: ISSN 0021-9991
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 376; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; hybrid; plasma; particle-in-cell; implicit; conservative; finite grid instability

Citation Formats

Stanier, A., Chacón, L., and Chen, G. A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.09.038.
Stanier, A., Chacón, L., & Chen, G. A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm. United States. https://doi.org/10.1016/j.jcp.2018.09.038
Stanier, A., Chacón, L., and Chen, G. Thu . "A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm". United States. https://doi.org/10.1016/j.jcp.2018.09.038. https://www.osti.gov/servlets/purl/1477697.
@article{osti_1477697,
title = {A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm},
author = {Stanier, A. and Chacón, L. and Chen, G.},
abstractNote = {The quasi-neutral hybrid model with kinetic ions and fluid electrons is a promising approach for bridging the inherent multi-scale nature of many problems in space and laboratory plasmas. A novel, implicit, particle-in-cell based scheme for the hybrid model is derived for fully 3D electromagnetic problems with multiple ion species, which features global mass, momentum and energy conservation. The scheme includes sub-cycling and orbit-averaging for the ions, with cell-centered finite differences and implicit midpoint time advance. To reduce discrete particle noise, the scheme allows arbitrary-order shape functions for the particle-mesh interpolations and the application of conservative binomial smoothing. The algorithm is verified for a number of test problems to demonstrate the correctness of the implementation, the unique conservation properties, and the favorable stability properties of the new scheme. In particular, there is no indication of unstable growth of the finite-grid instability for a population of cold ions drifting through a uniform spatial mesh, in a set-up where several commonly used non-conservative schemes are highly unstable.},
doi = {10.1016/j.jcp.2018.09.038},
journal = {Journal of Computational Physics},
number = ,
volume = 376,
place = {United States},
year = {2018},
month = {9}
}

Journal Article:

Figures / Tables:

Figure 1 Figure 1: Comparison study between an explicit leapfrog-based momentum-conserving scheme (red, see Appendix D.1), a predictor-corrector method (green, see Appendix D.2), and the new implicit conservative algorithm (blue). Top panel: Particle phase space distribution (xp, vxp) at t = 8.8Δx/Cs (400 steps). Second panel: Change in total momentum vs timemore » (the red and blue traces overlap). Third panel: Total energies (ion kinetic + electron thermal) vs time. Bottom panel: Ion-to-electron temperature ratio vs time on a logarithmic scale, with initial$T$i/$T$e = 1/600.« less

Save / Share:

Works referenced in this record:

The link between shocks, turbulence, and magnetic reconnection in collisionless plasmas
journal, June 2014

  • Karimabadi, H.; Roytershteyn, V.; Vu, H. X.
  • Physics of Plasmas, Vol. 21, Issue 6
  • DOI: 10.1063/1.4882875

Role of Ion Kinetic Physics in the Interaction of Magnetic Flux Ropes
journal, October 2015


Low frequency fully kinetic simulation of the toroidal ion temperature gradient instability
journal, August 2017

  • Sturdevant, B. J.; Chen, Y.; Parker, S. E.
  • Physics of Plasmas, Vol. 24, Issue 8
  • DOI: 10.1063/1.4999945

Quasineutral hybrid simulation of macroscopic plasma phenomena
journal, September 1982


Electromagnetic ion beam instabilities: Comparison of one- and two-dimensional simulations
journal, January 1986


Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics
journal, February 2014


Magnetic field and density fluctuations at perpendicular supercritical collisionless shocks
journal, January 1988


Current Advance Method and Cyclic Leapfrog for 2D Multispecies Hybrid Plasma Simulations
journal, May 1994


Re-forming supercritical quasi-parallel shocks: 1. One- and two-dimensional simulations
journal, January 1990

  • Thomas, V. A.; Winske, D.; Omidi, N.
  • Journal of Geophysical Research, Vol. 95, Issue A11
  • DOI: 10.1029/JA095iA11p18809

Magnetic self-organization in Hall-dominated magnetorotational turbulence
journal, July 2013

  • Kunz, Matthew W.; Lesur, Geoffroy
  • Monthly Notices of the Royal Astronomical Society, Vol. 434, Issue 3
  • DOI: 10.1093/mnras/stt1171

Use of a hybrid code to model the Earth's magnetosphere
journal, February 1995

  • Swift, Daniel W.
  • Geophysical Research Letters, Vol. 22, Issue 3
  • DOI: 10.1029/94GL03082

A global method of solving the electron-field equations in a zero-inertia-electron-hybrid plasma simulation code
journal, December 1980


A robust method for handling low density regions in hybrid simulations for collisionless plasmas
journal, October 2014

  • Amano, Takanobu; Higashimori, Katsuaki; Shirakawa, Keisuke
  • Journal of Computational Physics, Vol. 275
  • DOI: 10.1016/j.jcp.2014.06.048

A second-order semi-implicit method for hybrid simulation
journal, July 2013


An implicit δf particle-in-cell method with sub-cycling and orbit averaging for Lorentz ions
journal, July 2016

  • Sturdevant, Benjamin J.; Parker, Scott E.; Chen, Yang
  • Journal of Computational Physics, Vol. 316
  • DOI: 10.1016/j.jcp.2016.04.036

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm
journal, August 2011


The energy conserving particle-in-cell method
journal, August 2011


Energy-conserving numerical approximations for Vlasov plasmas
journal, August 1970


A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions
journal, July 2016


Geometric integration of the Vlasov-Maxwell system with a variational particle-in-cell scheme
journal, August 2012

  • Squire, J.; Qin, H.; Tang, W. M.
  • Physics of Plasmas, Vol. 19, Issue 8
  • DOI: 10.1063/1.4742985

Variational formulation of particle algorithms for kinetic plasma simulations
journal, July 2013


Hamiltonian splitting for the Vlasov–Maxwell equations
journal, February 2015

  • Crouseilles, Nicolas; Einkemmer, Lukas; Faou, Erwan
  • Journal of Computational Physics, Vol. 283
  • DOI: 10.1016/j.jcp.2014.11.029

Canonical symplectic particle-in-cell method for long-term large-scale simulations of the Vlasov–Maxwell equations
journal, December 2015


GEMPIC: geometric electromagnetic particle-in-cell methods
journal, July 2017

  • Kraus, Michael; Kormann, Katharina; Morrison, Philip J.
  • Journal of Plasma Physics, Vol. 83, Issue 4
  • DOI: 10.1017/S002237781700040X

Nonphysical noises and instabilities in plasma simulation due to a spatial grid
journal, December 1972


On energy and momentum conservation in particle-in-cell plasma simulation
journal, July 2016


Gridless finite-size-particle plasma simulation
journal, February 2001


Finite grid instability and spectral fidelity of the electrostatic Particle-In-Cell algorithm
journal, October 2016


Finite-Grid Instability in Quasineutral Hybrid Simulations
journal, April 1995


Hybrid simulations of magnetic reconnection with kinetic ions and fluid electron pressure anisotropy
journal, March 2016

  • Le, A.; Daughton, W.; Karimabadi, H.
  • Physics of Plasmas, Vol. 23, Issue 3
  • DOI: 10.1063/1.4943893

Demonstration of Anisotropic Fluid Closure Capturing the Kinetic Structure of Magnetic Reconnection
journal, September 2012


The island coalescence problem: Scaling of reconnection in extended fluid models including higher-order moments
journal, November 2015

  • Ng, Jonathan; Huang, Yi-Min; Hakim, Ammar
  • Physics of Plasmas, Vol. 22, Issue 11
  • DOI: 10.1063/1.4935302

Rigorous charge conservation for local electromagnetic field solvers
journal, March 1992


Charge conservation in electromagnetic PIC codes; spectral comparison of Boris/DADI and Langdon-Marder methods
journal, November 1997


Exact charge conservation scheme for Particle-in-Cell simulation with an arbitrary form-factor
journal, April 2001


Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004


A Flexible Inner-Outer Preconditioned GMRES Algorithm
journal, March 1993

  • Saad, Youcef
  • SIAM Journal on Scientific Computing, Vol. 14, Issue 2
  • DOI: 10.1137/0914028

Orbit-averaged implicit particle codes
journal, March 1982


Accurate Numerical Solution of Charged Particle Motion in a Magnetic Field
journal, February 1995


Heuristic stability theory for finite-difference equations
journal, June 1968


Curvature-compensated convective transport: SMART, A new boundedness- preserving transport algorithm
journal, June 1988

  • Gaskell, P. H.; Lau, A. K. C.
  • International Journal for Numerical Methods in Fluids, Vol. 8, Issue 6
  • DOI: 10.1002/fld.1650080602

A linear dispersion relation for the hybrid kinetic-ion/fluid-electron model of plasma physics
journal, July 2016


Numerical simulation of nonoscillatory mirror waves at the Earth's magnetosheath
journal, January 1986

  • Price, Channon P.; Swift, Daniel W.; Lee, Lou-Chuang
  • Journal of Geophysical Research, Vol. 91, Issue A1
  • DOI: 10.1029/JA091iA01p00101

Ion anisotropy instabilities in the magnetosheath
journal, February 1993

  • Gary, S. Peter; Fuselier, Stephen A.; Anderson, Brian J.
  • Journal of Geophysical Research: Space Physics, Vol. 98, Issue A2
  • DOI: 10.1029/92JA01844

Observation of mirror waves downstream of a quasi-perpendicular shock
journal, February 1989

  • Hubert, D.; Perche, C.; Harvey, C. C.
  • Geophysical Research Letters, Vol. 16, Issue 2
  • DOI: 10.1029/GL016i002p00159

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge
journal, March 2001

  • Birn, J.; Drake, J. F.; Shay, M. A.
  • Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3
  • DOI: 10.1029/1999JA900449

A fully nonlinear characteristic method for gyrokinetic simulation
journal, January 1993

  • Parker, S. E.; Lee, W. W.
  • Physics of Fluids B: Plasma Physics, Vol. 5, Issue 1
  • DOI: 10.1063/1.860870

A Particle-in-cell Method with Adaptive Phase-space Remapping for Kinetic Plasmas
journal, January 2011

  • Wang, B.; Miller, G. H.; Colella, P.
  • SIAM Journal on Scientific Computing, Vol. 33, Issue 6
  • DOI: 10.1137/100811805

Current sheet bifurcation and collapse in electron magnetohydrodynamics
journal, November 2009

  • Zocco, A.; Chacón, L.; Simakov, Andrei N.
  • Physics of Plasmas, Vol. 16, Issue 11
  • DOI: 10.1063/1.3264102

Fluid vs. kinetic magnetic reconnection with strong guide fields
journal, October 2015

  • Stanier, A.; Simakov, Andrei N.; Chacón, L.
  • Physics of Plasmas, Vol. 22, Issue 10
  • DOI: 10.1063/1.4932330

A 2D high-β Hall MHD implicit nonlinear solver
journal, July 2003


Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.