skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Generalized fluid theory including non-Maxwellian kinetic effects

Abstract

The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function. One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed mattermore » or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. Here, the results shown here could provide the insights to break some of the unsolved puzzles of turbulence.« less

Authors:
ORCiD logo [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1376001
Report Number(s):
LLNL-JRNL-696825
Journal ID: ISSN 0022-3778; applab; PII: S0022377817000150
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Plasma Physics
Additional Journal Information:
Journal Volume: 83; Journal Issue: 02; Journal ID: ISSN 0022-3778
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; 70 PLASMA PHYSICS AND FUSION; fusion plasma; magnetized plasmas; plasma confinement

Citation Formats

Izacard, Olivier. Generalized fluid theory including non-Maxwellian kinetic effects. United States: N. p., 2017. Web. doi:10.1017/S0022377817000150.
Izacard, Olivier. Generalized fluid theory including non-Maxwellian kinetic effects. United States. https://doi.org/10.1017/S0022377817000150
Izacard, Olivier. 2017. "Generalized fluid theory including non-Maxwellian kinetic effects". United States. https://doi.org/10.1017/S0022377817000150. https://www.osti.gov/servlets/purl/1376001.
@article{osti_1376001,
title = {Generalized fluid theory including non-Maxwellian kinetic effects},
author = {Izacard, Olivier},
abstractNote = {The results obtained by the plasma physics community for the validation and the prediction of turbulence and transport in magnetized plasmas come mainly from the use of very central processing unit (CPU)-consuming particle-in-cell or (gyro)kinetic codes which naturally include non-Maxwellian kinetic effects. To date, fluid codes are not considered to be relevant for the description of these kinetic effects. Here, after revisiting the limitations of the current fluid theory developed in the 19th century, we generalize the fluid theory including kinetic effects such as non-Maxwellian super-thermal tails with as few fluid equations as possible. The collisionless and collisional fluid closures from the nonlinear Landau Fokker–Planck collision operator are shown for an arbitrary collisionality. Indeed, the first fluid models associated with two examples of collisionless fluid closures are obtained by assuming an analytic non-Maxwellian distribution function. One of the main differences with the literature is our analytic representation of the distribution function in the velocity phase space with as few hidden variables as possible thanks to the use of non-orthogonal basis sets. These new non-Maxwellian fluid equations could initiate the next generation of fluid codes including kinetic effects and can be expanded to other scientific disciplines such as astrophysics, condensed matter or hydrodynamics. As a validation test, we perform a numerical simulation based on a minimal reduced INMDF fluid model. The result of this test is the discovery of the origin of particle and heat diffusion. The diffusion is due to the competition between a growing INMDF on short time scales due to spatial gradients and the thermalization on longer time scales. Here, the results shown here could provide the insights to break some of the unsolved puzzles of turbulence.},
doi = {10.1017/S0022377817000150},
url = {https://www.osti.gov/biblio/1376001}, journal = {Journal of Plasma Physics},
issn = {0022-3778},
number = 02,
volume = 83,
place = {United States},
year = {Wed Mar 29 00:00:00 EDT 2017},
month = {Wed Mar 29 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Plasma Oscillations: II. Kinetic theory of waves in plasmas
journal, June 1964


Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry
journal, May 1992


Electron temperature gradient driven turbulence
journal, May 2000


Limitations of gyrokinetics on transport time scales
journal, April 2008


Fokker-Planck Equation for an Inverse-Square Force
journal, July 1957


Landau fluid models of collisionless magnetohydrodynamics
journal, November 1997


A fast non-Fourier method for Landau-fluid operators
journal, May 2014


Plasma oscillations
journal, July 1959


Detecting non-Maxwellian electron velocity distributions at JET by high resolution Thomson scattering
journal, March 2011


Energetic ion distribution resulting from neutral beam injection in tokamaks
journal, October 1976


Impact of carbon and tungsten as divertor materials on the scrape-off layer conditions in JET
journal, August 2013


Electron Temperature Gradient Turbulence
journal, December 2000


Hamiltonian magnetic reconnection with parallel electron heat flux dynamics
journal, July 2015


Comparison of initial value and eigenvalue codes for kinetic toroidal plasma instabilities
journal, August 1995


GYSELA, a full-f global gyrokinetic Semi-Lagrangian code for ITG turbulence simulations
conference, January 2006

  • Grandgirard, V.; Sarazin, Y.; Garbet, X.
  • THEORY OF FUSION PLASMAS: Joint Varenna-Lausanne International Workshop, AIP Conference Proceedings
  • https://doi.org/10.1063/1.2404543

As hot as it gets
journal, January 2016


Global δf particle simulation of neoclassical transport and ambipolar electric field in general geometry
journal, December 2004


The Boltzmann equation an d the one-fluid hydromagnetic equations in the absence of particle collisions
journal, July 1956

  • Chew, G. F.; Goldberger, M. L.; Low, F. E.
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 236, Issue 1204, p. 112-118
  • https://doi.org/10.1098/rspa.1956.0116

Plasma Physics via Computer Simulation
book, January 1991


An integral equation occuring in plasma oscillations
journal, January 1963


Simulation of neoclassical transport with the continuum gyrokinetic code COGENT
journal, January 2013


Two-dimensional gyrokinetic turbulence
journal, October 2010


Particle simulation of plasmas
journal, April 1983


Integrated modeling applications for tokamak experiments with OMFIT
journal, July 2015


Integrated Modeling of Tokamak Experiments with OMFIT
journal, January 2013


On the theory of stationary waves in plasmas
journal, January 1955


Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
journal, June 1990


Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description
journal, October 2012


Impact of bulk non-Maxwellian electrons on electron temperature measurements (invited)
journal, March 2003


Note onN-dimensional hermite polynomials
journal, December 1949


Large-scale gyrokinetic turbulence simulations: Effects of profile variation
journal, May 1999


A global collisionless PIC code in magnetic coordinates
journal, September 2007


Landau damping and the moments method
journal, September 1967


Gyrokinetic turbulence simulation of profile shear stabilization and broken gyroBohm scaling
journal, May 2002


Gyro-kinetic simulation of global turbulent transport properties in tokamak experiments
journal, September 2006


Asymptotic Theory of the Boltzmann Equation
journal, January 1963


Experimental study of non-thermal electron generation by lower hybrid waves in the ASDEX tokamak
journal, August 1986


Full f gyrokinetic method for particle simulation of tokamak transport
journal, May 2008


Linearized Plasma Oscillations in Arbitrary Electron Velocity Distributions
journal, May 1960


ICRF heating of TFTR plasmas fuelled by deuterium - tritium neutral beam injection
journal, May 1996


Continuum kinetic modeling of the tokamak plasma edge
journal, May 2016


A theory-based transport model with comprehensive physics
journal, May 2007


Measurements and 2-D modeling of recycling and edge transport in discharges with lithium-coated PFCs in NSTX
journal, August 2011


The long and winding road
journal, March 2016


The Gaussian radial basis function method for plasma kinetic theory
journal, October 2015


Works referencing / citing this record:

Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications
journal, September 2017


Anti-symmetric plasma moment equations with conservative discrete counterparts
journal, June 2018


Transport equations in magnetized plasmas for non-Maxwellian distribution functions
journal, October 2018


Incorporating kinetic effects on Nernst advection in inertial fusion simulations
journal, June 2018