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Title: Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications

Abstract

Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolaï, and Busquet’s [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the heliummore » gas-fill by a factor of ~2 despite predicting the peak heat flux to within 16%.« less

Authors:
ORCiD logo [1];  [2];  [3]; ORCiD logo [3];  [4]; ORCiD logo [5];  [3]; ORCiD logo [1]; ORCiD logo [1];  [6];  [3];  [3];  [1]
  1. Univ. of York (United Kingdom). Department of Physics, York Plasma Institute
  2. Imperial College, London (United Kingdom). Plasma Physics Group, Blackett Laboratory
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  4. Max-Planck-Institute for Plasma Physics (Germany)
  5. Chalmers University of Technology (Sweden). Department of Physics
  6. Science and Technology Facilities Council (STFC), Oxford (United Kingdom). Rutherford Appleton Lab. (RAL)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1393324
Alternate Identifier(s):
OSTI ID: 1378821
Report Number(s):
LLNL-JRNL-727659
Journal ID: ISSN 1070-664X
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 24; Journal Issue: 9; Journal ID: ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Brodrick, Jonathan P., Kingham, R. J., Marinak, M. M., Patel, M. V., Chankin, A. V., Omotani, J. T., Umansky, M. V., Del Sorbo, D., Dudson, B., Parker, J. T., Kerbel, G. D., Sherlock, M., and Ridgers, C. P. Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications. United States: N. p., 2017. Web. doi:10.1063/1.5001079.
Brodrick, Jonathan P., Kingham, R. J., Marinak, M. M., Patel, M. V., Chankin, A. V., Omotani, J. T., Umansky, M. V., Del Sorbo, D., Dudson, B., Parker, J. T., Kerbel, G. D., Sherlock, M., & Ridgers, C. P. Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications. United States. https://doi.org/10.1063/1.5001079
Brodrick, Jonathan P., Kingham, R. J., Marinak, M. M., Patel, M. V., Chankin, A. V., Omotani, J. T., Umansky, M. V., Del Sorbo, D., Dudson, B., Parker, J. T., Kerbel, G. D., Sherlock, M., and Ridgers, C. P. Wed . "Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications". United States. https://doi.org/10.1063/1.5001079. https://www.osti.gov/servlets/purl/1393324.
@article{osti_1393324,
title = {Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications},
author = {Brodrick, Jonathan P. and Kingham, R. J. and Marinak, M. M. and Patel, M. V. and Chankin, A. V. and Omotani, J. T. and Umansky, M. V. and Del Sorbo, D. and Dudson, B. and Parker, J. T. and Kerbel, G. D. and Sherlock, M. and Ridgers, C. P.},
abstractNote = {Three models for nonlocal electron thermal transport are here compared against Vlasov-Fokker-Planck (VFP) codes to assess their accuracy in situations relevant to both inertial fusion hohlraums and tokamak scrape-off layers. The models tested are (i) a moment-based approach using an eigenvector integral closure (EIC) originally developed by Ji, Held, and Sovinec [Phys. Plasmas 16, 022312 (2009)]; (ii) the non-Fourier Landau-fluid (NFLF) model of Dimits, Joseph, and Umansky [Phys. Plasmas 21, 055907 (2014)]; and (iii) Schurtz, Nicolaï, and Busquet’s [Phys. Plasmas 7, 4238 (2000)] multigroup diffusion model (SNB). We find that while the EIC and NFLF models accurately predict the damping rate of a small-amplitude temperature perturbation (within 10% at moderate collisionalities), they overestimate the peak heat flow by as much as 35% and do not predict preheat in the more relevant case where there is a large temperature difference. The SNB model, however, agrees better with VFP results for the latter problem if care is taken with the definition of the mean free path. Additionally, we present for the first time a comparison of the SNB model against a VFP code for a hohlraum-relevant problem with inhomogeneous ionisation and show that the model overestimates the heat flow in the helium gas-fill by a factor of ~2 despite predicting the peak heat flux to within 16%.},
doi = {10.1063/1.5001079},
journal = {Physics of Plasmas},
number = 9,
volume = 24,
place = {United States},
year = {Wed Sep 06 00:00:00 EDT 2017},
month = {Wed Sep 06 00:00:00 EDT 2017}
}

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Works referenced in this record:

European roadmap to the realization of fusion energy: Mission for solution on heat-exhaust systems
journal, October 2015


Toroidal gyrofluid equations for simulations of tokamak turbulence
journal, November 1996

  • Beer, M. A.; Hammett, G. W.
  • Physics of Plasmas, Vol. 3, Issue 11
  • DOI: 10.1063/1.871538

A cell-centered diffusion scheme on two-dimensional unstructured meshes
journal, June 2007


Self‐consistent, nonlocal electron heat flux at arbitrary ion charge number
journal, November 1992

  • Sanmartín, Juan R.; Ramírez, J.; Fernández‐Feria, R.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 11
  • DOI: 10.1063/1.860366

Imposed magnetic field and hot electron propagation in inertial fusion hohlraums
journal, December 2015

  • Strozzi, David J.; Perkins, L. J.; Marinak, M. M.
  • Journal of Plasma Physics, Vol. 81, Issue 6
  • DOI: 10.1017/S0022377815001348

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

  • Chang, Zuoyang; Callen, J. D.
  • Physics of Fluids B: Plasma Physics, Vol. 4, Issue 5
  • DOI: 10.1063/1.860125

Effect of electron collisions on ion‐acoustic waves and heat flow
journal, January 1994


Modification of the electron energy distribution function during lithium experiments on the National Spherical Torus Experiment
journal, October 2012


Parallel heat flux limits in the tokamak scrape-off layer
journal, October 2005


Nonlocal transport in hot plasma. Part I
journal, September 2013


Effect of Nonlocal Transport on Heat-Wave Propagation
journal, May 2004


Modeling of tokamak divertor plasma for weakly collisional parallel electron transport
journal, August 2015


Moment approach to deriving parallel heat flow for general collisionality
journal, February 2009

  • Ji, Jeong-Young; Held, Eric D.; Sovinec, Carl R.
  • Physics of Plasmas, Vol. 16, Issue 2
  • DOI: 10.1063/1.3079072

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

  • Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L.
  • Physical Review, Vol. 107, Issue 1
  • DOI: 10.1103/PhysRev.107.1

Landau fluid models of collisionless magnetohydrodynamics
journal, November 1997

  • Snyder, P. B.; Hammett, G. W.; Dorland, W.
  • Physics of Plasmas, Vol. 4, Issue 11
  • DOI: 10.1063/1.872517

Electron Heat Transport down Steep Temperature Gradients
journal, December 1982


Nonlinear Inverse Bremsstrahlung and Heated-Electron Distributions
journal, March 1980


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

  • Dimits, A. M.; Joseph, I.; Umansky, M. V.
  • Physics of Plasmas, Vol. 21, Issue 5
  • DOI: 10.1063/1.4876617

An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields
journal, February 2004


Development and Benchmarking of a New Kinetic Code for Plasma Periphery (KIPP)
journal, June 2012

  • Chankin, A. V.; Coster, D. P.; Meisl, G.
  • Contributions to Plasma Physics, Vol. 52, Issue 5-6
  • DOI: 10.1002/ctpp.201210039

Kinetic modelling of temperature equilibration rates in the plasma
journal, July 2013


Anomalous heating by ion sound turbulence
journal, January 1978


The role of a detailed configuration accounting (DCA) atomic physics package in explaining the energy balance in ignition-scale hohlraums
journal, September 2011


Kinetic effects in tokamak scrape-off layer plasmas
journal, May 1997

  • Batishchev, O. V.; Krasheninnikov, S. I.; Catto, Peter J.
  • Physics of Plasmas, Vol. 4, Issue 5
  • DOI: 10.1063/1.872280

Anomalous electron transport equations for ion sound and related turbulent spectra
journal, January 1978


Electron parallel closures for arbitrary collisionality
journal, December 2014

  • Ji, Jeong-Young; Held, Eric D.
  • Physics of Plasmas, Vol. 21, Issue 12
  • DOI: 10.1063/1.4904906

Kinetic modeling of Nernst effect in magnetized hohlraums
journal, April 2016


Use of external magnetic fields in hohlraum plasmas to improve laser-coupling
journal, January 2015

  • Montgomery, D. S.; Albright, B. J.; Barnak, D. H.
  • Physics of Plasmas, Vol. 22, Issue 1
  • DOI: 10.1063/1.4906055

2-D Fluid Transport Simulations of Gaseous/Radiative Divertors
journal, January 1994

  • Rognlien, T. D.; Brown, P. N.; Campbell, R. B.
  • Contributions to Plasma Physics, Vol. 34, Issue 2-3
  • DOI: 10.1002/ctpp.2150340241

Kinetic theory of ion acoustic waves in a plasma with collisional electrons
journal, December 1995


Dynamics of ion temperature gradient turbulence and transport with a static magnetic island
journal, February 2016

  • Izacard, Olivier; Holland, Christopher; James, Spencer D.
  • Physics of Plasmas, Vol. 23, Issue 2
  • DOI: 10.1063/1.4941704

Heat transport and electron distribution function in laser produced plasmas with hot spots
journal, May 2002

  • Batishchev, O. V.; Bychenkov, V. Yu.; Detering, F.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1461385

Generalized fluid theory including non-Maxwellian kinetic effects
journal, March 2017


Nonlocal Electron Heat Transport by Not Quite Maxwell-Boltzmann Distributions
journal, October 1986


Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas
journal, August 2016


Towards a more universal understanding of radiation drive in gas-filled hohlraums
journal, May 2016


Predicted effects of parallel temperature gradients on the overestimation of TCV divertor target Langmuir probe Te measurements
journal, March 2003


Reduced entropic model for studies of multidimensional nonlocal transport in high-energy-density plasmas
journal, August 2015

  • Del Sorbo, D.; Feugeas, J. -L.; Nicolaï, Ph.
  • Physics of Plasmas, Vol. 22, Issue 8
  • DOI: 10.1063/1.4926824

Progress in two-dimensional plasma edge modelling
journal, December 1992


Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer
journal, April 2013


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


Observation of non-Maxwellian electron distributions in the NSTX divertor
journal, July 2013


BOUT++: A framework for parallel plasma fluid simulations
journal, September 2009


Non-local Heat Conduction Along a Scrape-Off Layer with Strong Recycling
journal, January 1990


Non-local parallel transport in BOUT++
journal, August 2015


A comparison of non-local electron transport models for laser-plasmas relevant to inertial confinement fusion
journal, August 2017

  • Sherlock, M.; Brodrick, J. P.; Ridgers, C. P.
  • Physics of Plasmas, Vol. 24, Issue 8
  • DOI: 10.1063/1.4986095

An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
journal, August 2016


Simulation of electron kinetics in gas discharges
journal, June 2006

  • Kolobov, V. I.; Arslanbekov, R. R.
  • IEEE Transactions on Plasma Science, Vol. 34, Issue 3
  • DOI: 10.1109/TPS.2006.875850

Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators
journal, December 1997


The development of a Krook model for nonlocal transport in laser produced plasmas. I. Basic theory
journal, August 2008

  • Manheimer, Wallace; Colombant, Denis; Goncharov, Valeri
  • Physics of Plasmas, Vol. 15, Issue 8
  • DOI: 10.1063/1.2963078

A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes
journal, January 2000

  • Schurtz, G. P.; Nicolaï, Ph. D.; Busquet, M.
  • Physics of Plasmas, Vol. 7, Issue 10
  • DOI: 10.1063/1.1289512

Non-Maxwellian electron distributions and continuum X-ray emission in inverse Bremsstrahlung heated plasmas
journal, November 1988


Implicit moment particle simulation of plasmas
journal, June 1981


The EIRENE and B2-EIRENE Codes
journal, February 2005

  • Reiter, D.; Baelmans, M.; Börner, P.
  • Fusion Science and Technology, Vol. 47, Issue 2
  • DOI: 10.13182/FST47-172

Self-consistent inclusion of classical large-angle Coulomb collisions in plasma Monte Carlo simulations
journal, October 2015


B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas
journal, December 1992


Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation
journal, January 1986

  • Epperlein, E. M.; Haines, M. G.
  • Physics of Fluids, Vol. 29, Issue 4
  • DOI: 10.1063/1.865901

Comparison for non-local hydrodynamic thermal conduction models
journal, February 2013

  • Marocchino, A.; Tzoufras, M.; Atzeni, S.
  • Physics of Plasmas, Vol. 20, Issue 2
  • DOI: 10.1063/1.4789878

A practical nonlocal model for heat transport in magnetized laser plasmas
journal, March 2006

  • Nicolaï, Ph. D.; Feugeas, J. -L. A.; Schurtz, G. P.
  • Physics of Plasmas, Vol. 13, Issue 3
  • DOI: 10.1063/1.2179392

A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma
journal, February 2012

  • Thomas, A. G. R.; Tzoufras, M.; Robinson, A. P. L.
  • Journal of Computational Physics, Vol. 231, Issue 3
  • DOI: 10.1016/j.jcp.2011.09.028

Comparison of 2D models for the plasma edge with experimental measurements and assessment of deficiencies
journal, June 2009


Transport in the presence of inverse bremsstrahlung heating and magnetic fields
journal, September 2008

  • Ridgers, C. P.; Thomas, A. G. R.; Kingham, R. J.
  • Physics of Plasmas, Vol. 15, Issue 9
  • DOI: 10.1063/1.2978092

Splitting schemes for the numerical solution of a two-dimensional Vlasov equation
journal, June 1978


Assessment of the effect of parallel temperature gradients in the JET SOL on T measured by divertor target Langmuir probes
journal, August 2015


Extension of a reduced entropic model of electron transport to magnetized nonlocal regimes of high-energy-density plasmas
journal, June 2016


A practical nonlocal model for electron heat transport in laser plasmas
journal, November 1991

  • Epperlein, E. M.; Short, R. W.
  • Physics of Fluids B: Plasma Physics, Vol. 3, Issue 11
  • DOI: 10.1063/1.859789

Ion acoustic waves in plasmas with collisional electrons
journal, December 1994


A high-order finite-volume algorithm for Fokker–Planck collisions in magnetized plasmas
journal, July 2008

  • Xiong, Z.; Cohen, R. H.; Rognlien, T. D.
  • Journal of Computational Physics, Vol. 227, Issue 15
  • DOI: 10.1016/j.jcp.2008.04.004

Nonlocal Heat Transport Due to Steep Temperature Gradients
journal, October 1983


Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations
journal, August 2015

  • Cao, Duc; Moses, Gregory; Delettrez, Jacques
  • Physics of Plasmas, Vol. 22, Issue 8
  • DOI: 10.1063/1.4928445

Non-local parallel transport in BOUT++
text, January 2014


An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
journal, August 2016


Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas
journal, February 2008


Works referencing / citing this record:

Magnetised thermal self-focusing and filamentation of long-pulse lasers in plasmas relevant to magnetised ICF experiments
journal, September 2018

  • Watkins, H. C.; Kingham, R. J.
  • Physics of Plasmas, Vol. 25, Issue 9
  • DOI: 10.1063/1.5049229

Heat transport modeling of the dot spectroscopy platform on NIF
journal, February 2018

  • Farmer, W. A.; Jones, O. S.; Barrios, M. A.
  • Plasma Physics and Controlled Fusion, Vol. 60, Issue 4
  • DOI: 10.1088/1361-6587/aaaefd

Validation of OSHUN against collisionless and collisional plasma physics
journal, May 2018

  • Joglekar, Archis S.; Winjum, Benjamin J.; Tableman, Adam
  • Plasma Physics and Controlled Fusion, Vol. 60, Issue 6
  • DOI: 10.1088/1361-6587/aab978

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

  • Brodrick, J. P.; Sherlock, M.; Farmer, W. A.
  • Plasma Physics and Controlled Fusion, Vol. 60, Issue 8
  • DOI: 10.1088/1361-6587/aaca0b

Suppression of the Biermann Battery and Stabilization of the Thermomagnetic Instability in Laser Fusion Conditions
journal, February 2020