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 »
- Authors:
-
- Univ. of York (United Kingdom). Department of Physics, York Plasma Institute
- Imperial College, London (United Kingdom). Plasma Physics Group, Blackett Laboratory
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Max-Planck-Institute for Plasma Physics (Germany)
- Chalmers University of Technology (Sweden). Department of Physics
- 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}
}
Web of Science
Works referenced in this record:
European roadmap to the realization of fusion energy: Mission for solution on heat-exhaust systems
journal, October 2015
- Turnyanskiy, M.; Neu, R.; Albanese, R.
- Fusion Engineering and Design, Vol. 96-97
Toroidal gyrofluid equations for simulations of tokamak turbulence
journal, November 1996
- Beer, M. A.; Hammett, G. W.
- Physics of Plasmas, Vol. 3, Issue 11
A cell-centered diffusion scheme on two-dimensional unstructured meshes
journal, June 2007
- Breil, Jérôme; Maire, Pierre-Henri
- Journal of Computational Physics, Vol. 224, Issue 2
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
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
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
Effect of electron collisions on ion‐acoustic waves and heat flow
journal, January 1994
- Epperlein, E. M.
- Physics of Plasmas, Vol. 1, Issue 1
Modification of the electron energy distribution function during lithium experiments on the National Spherical Torus Experiment
journal, October 2012
- Jaworski, M. A.; Bell, M. G.; Gray, T. K.
- Fusion Engineering and Design, Vol. 87, Issue 10
Parallel heat flux limits in the tokamak scrape-off layer
journal, October 2005
- Fundamenski, W.
- Plasma Physics and Controlled Fusion, Vol. 47, Issue 11
Nonlocal transport in hot plasma. Part I
journal, September 2013
- Brantov, A. V.; Bychenkov, V. Yu.
- Plasma Physics Reports, Vol. 39, Issue 9
Effect of Nonlocal Transport on Heat-Wave Propagation
journal, May 2004
- Gregori, G.; Glenzer, S. H.; Knight, J.
- Physical Review Letters, Vol. 92, Issue 20
Modeling of tokamak divertor plasma for weakly collisional parallel electron transport
journal, August 2015
- Umansky, M. V.; Dimits, A. M.; Joseph, I.
- Journal of Nuclear Materials, Vol. 463
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
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
Landau fluid models of collisionless magnetohydrodynamics
journal, November 1997
- Snyder, P. B.; Hammett, G. W.; Dorland, W.
- Physics of Plasmas, Vol. 4, Issue 11
Electron Heat Transport down Steep Temperature Gradients
journal, December 1982
- Matte, J. P.; Virmont, J.
- Physical Review Letters, Vol. 49, Issue 26
Nonlinear Inverse Bremsstrahlung and Heated-Electron Distributions
journal, March 1980
- Langdon, A. Bruce
- Physical Review Letters, Vol. 44, Issue 9
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
An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields
journal, February 2004
- Kingham, R. J.; Bell, A. R.
- Journal of Computational Physics, Vol. 194, Issue 1
Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models: Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models
journal, July 2016
- Joseph, I.; Dimits, A. M.
- Contributions to Plasma Physics, Vol. 56, Issue 6-8
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
Kinetic modelling of temperature equilibration rates in the plasma
journal, July 2013
- Meisl, G.; Chankin, A. V.; Coster, D. P.
- Journal of Nuclear Materials, Vol. 438
Anomalous heating by ion sound turbulence
journal, January 1978
- Dum, C. T.
- Physics of Fluids, Vol. 21, Issue 6
The role of a detailed configuration accounting (DCA) atomic physics package in explaining the energy balance in ignition-scale hohlraums
journal, September 2011
- Rosen, M. D.; Scott, H. A.; Hinkel, D. E.
- High Energy Density Physics, Vol. 7, Issue 3
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
Anomalous electron transport equations for ion sound and related turbulent spectra
journal, January 1978
- Dum, C. T.
- Physics of Fluids, Vol. 21, Issue 6
Electron parallel closures for arbitrary collisionality
journal, December 2014
- Ji, Jeong-Young; Held, Eric D.
- Physics of Plasmas, Vol. 21, Issue 12
Kinetic modeling of Nernst effect in magnetized hohlraums
journal, April 2016
- Joglekar, A. S.; Ridgers, C. P.; Kingham, R. J.
- Physical Review E, Vol. 93, Issue 4
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
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
Kinetic theory of ion acoustic waves in a plasma with collisional electrons
journal, December 1995
- Bychenkov, V. Yu.; Myatt, J.; Rozmus, W.
- Physical Review E, Vol. 52, Issue 6
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
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
Generalized fluid theory including non-Maxwellian kinetic effects
journal, March 2017
- Izacard, Olivier
- Journal of Plasma Physics, Vol. 83, Issue 2
Nonlocal Electron Heat Transport by Not Quite Maxwell-Boltzmann Distributions
journal, October 1986
- Albritton, J. R.; Williams, E. A.; Bernstein, I. B.
- Physical Review Letters, Vol. 57, Issue 15
Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas
journal, August 2016
- Izacard, Olivier
- Physics of Plasmas, Vol. 23, Issue 8
Towards a more universal understanding of radiation drive in gas-filled hohlraums
journal, May 2016
- Jones, O. S.; Thomas, C. A.; Amendt, P. A.
- Journal of Physics: Conference Series, Vol. 717
Predicted effects of parallel temperature gradients on the overestimation of TCV divertor target Langmuir probe Te measurements
journal, March 2003
- Horacek, J.; Pitts, R. A.; Stangeby, P. C.
- Journal of Nuclear Materials, Vol. 313-316
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
Progress in two-dimensional plasma edge modelling
journal, December 1992
- Reiter, D.
- Journal of Nuclear Materials, Vol. 196-198
Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer
journal, April 2013
- Omotani, J. T.; Dudson, B. D.
- Plasma Physics and Controlled Fusion, Vol. 55, Issue 5
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability
journal, June 1990
- Hammett, Gregory W.; Perkins, Francis W.
- Physical Review Letters, Vol. 64, Issue 25
Observation of non-Maxwellian electron distributions in the NSTX divertor
journal, July 2013
- Jaworski, M. A.; Bell, M. G.; Gray, T. K.
- Journal of Nuclear Materials, Vol. 438
BOUT++: A framework for parallel plasma fluid simulations
journal, September 2009
- Dudson, B. D.; Umansky, M. V.; Xu, X. Q.
- Computer Physics Communications, Vol. 180, Issue 9
Non-local Heat Conduction Along a Scrape-Off Layer with Strong Recycling
journal, January 1990
- Chodura, R.
- Contributions to Plasma Physics, Vol. 30, Issue 1
Non-local parallel transport in BOUT++
journal, August 2015
- Omotani, J. T.; Dudson, B. D.; Havlíčková, E.
- Journal of Nuclear Materials, Vol. 463
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
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
journal, August 2016
- Taitano, W. T.; Chacón, L.; Simakov, A. N.
- Journal of Computational Physics, Vol. 318
A variable projection method for solving separable nonlinear least squares problems
journal, March 1975
- Kaufman, Linda
- BIT, Vol. 15, Issue 1
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
Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators
journal, December 1997
- Brown, S. R.; Haines, M. G.
- Journal of Plasma Physics, Vol. 58, Issue 4
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
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
Non-Maxwellian electron distributions and continuum X-ray emission in inverse Bremsstrahlung heated plasmas
journal, November 1988
- Matte, J. P.; Lamoureux, M.; Moller, C.
- Plasma Physics and Controlled Fusion, Vol. 30, Issue 12
Implicit moment particle simulation of plasmas
journal, June 1981
- Mason, Rodney J.
- Journal of Computational Physics, Vol. 41, Issue 2
The EIRENE and B2-EIRENE Codes
journal, February 2005
- Reiter, D.; Baelmans, M.; Börner, P.
- Fusion Science and Technology, Vol. 47, Issue 2
Self-consistent inclusion of classical large-angle Coulomb collisions in plasma Monte Carlo simulations
journal, October 2015
- Turrell, A. E.; Sherlock, M.; Rose, S. J.
- Journal of Computational Physics, Vol. 299
B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas
journal, December 1992
- Schneider, R.; Reiter, D.; Zehrfeld, H. P.
- Journal of Nuclear Materials, Vol. 196-198
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
Comparison for non-local hydrodynamic thermal conduction models
journal, February 2013
- Marocchino, A.; Tzoufras, M.; Atzeni, S.
- Physics of Plasmas, Vol. 20, Issue 2
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
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
Comparison of 2D models for the plasma edge with experimental measurements and assessment of deficiencies
journal, June 2009
- Chankin, A. V.; Coster, D. P.
- Journal of Nuclear Materials, Vol. 390-391
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
Benchmarks of KIPP: Vlasov-Fokker-Planck Code for Parallel Plasma Transport in the SOL and Divertor: Benchmarks of KIPP: Vlasov-Fokker-Planck Code for Parallel Plasma Transport in the SOL and Divertor
journal, June 2014
- Chankin, A. V.; Coster, D. P.
- Contributions to Plasma Physics, Vol. 54, Issue 4-6
Splitting schemes for the numerical solution of a two-dimensional Vlasov equation
journal, June 1978
- Shoucri, Magdi M.; Gagné, Real R. J.
- Journal of Computational Physics, Vol. 27, Issue 3
Assessment of the effect of parallel temperature gradients in the JET SOL on T measured by divertor target Langmuir probes
journal, August 2015
- Ďuran, I.; Ješko, K.; Fuchs, V.
- Journal of Nuclear Materials, Vol. 463
Extension of a reduced entropic model of electron transport to magnetized nonlocal regimes of high-energy-density plasmas
journal, June 2016
- Del Sorbo, D.; Feugeas, J. -L.; Nicolaï, Ph.
- Laser and Particle Beams, Vol. 34, Issue 3
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
Ion acoustic waves in plasmas with collisional electrons
journal, December 1994
- Bychenkov, V. Yu.; Myatt, J.; Rozmus, W.
- Physical Review E, Vol. 50, Issue 6
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
Nonlocal Heat Transport Due to Steep Temperature Gradients
journal, October 1983
- Luciani, J. F.; Mora, P.; Virmont, J.
- Physical Review Letters, Vol. 51, Issue 18
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
Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer
text, January 2013
- Omotani, John; Dudson, Ben
- arXiv
Non-local parallel transport in BOUT++
text, January 2014
- Omotani, J. T.; Dudson, B. D.; Havlickova, E.
- arXiv
Extension of a Reduced Entropic Model of Electron Transport to Magnetized Nonlocal Regimes of High-Energy-Density Plasmas
text, January 2017
- Del Sorbo, D.; Feugeas, J. -L.; Nicolaï, Ph.
- arXiv
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
journal, August 2016
- Taitano, W. T.; Chacón, L.; Simakov, A. N.
- Journal of Computational Physics, Vol. 318
Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas
journal, February 2008
- Ridgers, C. P.; Kingham, R. J.; Thomas, A. G. R.
- Physical Review Letters, Vol. 100, Issue 7
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
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
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
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
Physics of laser plasma interaction and particle transport in the context of inertial confinement fusion
journal, December 2018
- Tikhonchuk, V. T.
- Nuclear Fusion, Vol. 59, Issue 3
Suppression of the Biermann Battery and Stabilization of the Thermomagnetic Instability in Laser Fusion Conditions
journal, February 2020
- Sherlock, M.; Bissell, J. J.
- Physical Review Letters, Vol. 124, Issue 5
Physics of laser plasma interaction and particle transport in the context of inertial confinement fusion
journal, December 2018
- Tikhonchuk, V. T.
- Nuclear Fusion, Vol. 59, Issue 3
AWBS kinetic modeling of electrons with nonlocal Ohms law in plasmas relevant to inertial confinement fusion
preprint, January 2019
- Holec, M.; Loiseau, P.; Debayle, A.
- arXiv