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

Brodrick, J. 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.

doi:10.1063/1.5001079

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

Journal Article · Wed Sep 06 00:00:00 EDT 2017 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.5001079· OSTI ID:2567580

; Kingham, R. J.; Marinak, M. M.; ; Chankin, A. V.; ; Umansky, M. V.; ; ; Parker, J. T.; Kerbel, G. D.; Sherlock, M.; Ridgers, C. P.

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%.

View Journal Article

Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 2567580

Alternate ID(s):: OSTI ID: 1378821
OSTI ID: 1393324

Report Number(s):: LLNL-JRNL--727659; 092309

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 9 Vol. 24; ISSN 1070-664X

Publisher:: American Institute of PhysicsCopyright Statement

Country of Publication:: United States

Language:: English

References (74)

Development and Benchmarking of a New Kinetic Code for Plasma Periphery (KIPP) Chankin, A. V.; Coster, D. P.; Meisl, G. Contributions to Plasma Physics, Vol. 52, Issue 5-6 https://doi.org/10.1002/ctpp.201210039	journal	June 2012
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 Chankin, A. V.; Coster, D. P. Contributions to Plasma Physics, Vol. 54, Issue 4-6 https://doi.org/10.1002/ctpp.201410047	journal	June 2014
Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models: Connecting Collisionless Landau Fluid Closures to Collisional Plasma Physics Models Joseph, I.; Dimits, A. M. Contributions to Plasma Physics, Vol. 56, Issue 6-8 https://doi.org/10.1002/ctpp.201610043	journal	July 2016
Non-local Heat Conduction Along a Scrape-Off Layer with Strong Recycling Chodura, R. Contributions to Plasma Physics, Vol. 30, Issue 1 https://doi.org/10.1002/ctpp.2150300125	journal	January 1990
2-D Fluid Transport Simulations of Gaseous/Radiative Divertors Rognlien, T. D.; Brown, P. N.; Campbell, R. B. Contributions to Plasma Physics, Vol. 34, Issue 2-3 https://doi.org/10.1002/ctpp.2150340241	journal	January 1994
A variable projection method for solving separable nonlinear least squares problems Kaufman, Linda BIT, Vol. 15, Issue 1 https://doi.org/10.1007/BF01932995	journal	March 1975
Splitting schemes for the numerical solution of a two-dimensional Vlasov equation Shoucri, Magdi M.; Gagné, Real R. J. Journal of Computational Physics, Vol. 27, Issue 3 https://doi.org/10.1016/0021-9991(78)90013-X	journal	June 1978
Implicit moment particle simulation of plasmas Mason, Rodney J. Journal of Computational Physics, Vol. 41, Issue 2 https://doi.org/10.1016/0021-9991(81)90094-2	journal	June 1981
Predicted effects of parallel temperature gradients on the overestimation of TCV divertor target Langmuir probe Te measurements Horacek, J.; Pitts, R. A.; Stangeby, P. C. Journal of Nuclear Materials, Vol. 313-316 https://doi.org/10.1016/S0022-3115(02)01479-4	journal	March 2003
Progress in two-dimensional plasma edge modelling Reiter, D. Journal of Nuclear Materials, Vol. 196-198 https://doi.org/10.1016/S0022-3115(06)80014-0	journal	December 1992
B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas Schneider, R.; Reiter, D.; Zehrfeld, H. P. Journal of Nuclear Materials, Vol. 196-198 https://doi.org/10.1016/S0022-3115(06)80147-9	journal	December 1992
BOUT++: A framework for parallel plasma fluid simulations Dudson, B. D.; Umansky, M. V.; Xu, X. Q. Computer Physics Communications, Vol. 180, Issue 9 https://doi.org/10.1016/j.cpc.2009.03.008	journal	September 2009
Modification of the electron energy distribution function during lithium experiments on the National Spherical Torus Experiment Jaworski, M. A.; Bell, M. G.; Gray, T. K. Fusion Engineering and Design, Vol. 87, Issue 10 https://doi.org/10.1016/j.fusengdes.2011.07.013	journal	October 2012
European roadmap to the realization of fusion energy: Mission for solution on heat-exhaust systems Turnyanskiy, M.; Neu, R.; Albanese, R. Fusion Engineering and Design, Vol. 96-97 https://doi.org/10.1016/j.fusengdes.2015.04.041	journal	October 2015
The role of a detailed configuration accounting (DCA) atomic physics package in explaining the energy balance in ignition-scale hohlraums Rosen, M. D.; Scott, H. A.; Hinkel, D. E. High Energy Density Physics, Vol. 7, Issue 3 https://doi.org/10.1016/j.hedp.2011.03.008	journal	September 2011
An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields Kingham, R. J.; Bell, A. R. Journal of Computational Physics, Vol. 194, Issue 1 https://doi.org/10.1016/j.jcp.2003.08.017	journal	February 2004
A cell-centered diffusion scheme on two-dimensional unstructured meshes Breil, Jérôme; Maire, Pierre-Henri Journal of Computational Physics, Vol. 224, Issue 2 https://doi.org/10.1016/j.jcp.2006.10.025	journal	June 2007
A high-order finite-volume algorithm for Fokker–Planck collisions in magnetized plasmas Xiong, Z.; Cohen, R. H.; Rognlien, T. D. Journal of Computational Physics, Vol. 227, Issue 15 https://doi.org/10.1016/j.jcp.2008.04.004	journal	July 2008
A review of Vlasov–Fokker–Planck numerical modeling of inertial confinement fusion plasma Thomas, A. G. R.; Tzoufras, M.; Robinson, A. P. L. Journal of Computational Physics, Vol. 231, Issue 3 https://doi.org/10.1016/j.jcp.2011.09.028	journal	February 2012
Self-consistent inclusion of classical large-angle Coulomb collisions in plasma Monte Carlo simulations Turrell, A. E.; Sherlock, M.; Rose, S. J. Journal of Computational Physics, Vol. 299 https://doi.org/10.1016/j.jcp.2015.06.034	journal	October 2015
An adaptive, conservative 0D-2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes Taitano, W. T.; Chacón, L.; Simakov, A. N. Journal of Computational Physics, Vol. 318 https://doi.org/10.1016/j.jcp.2016.03.071	journal	August 2016
Comparison of 2D models for the plasma edge with experimental measurements and assessment of deficiencies Chankin, A. V.; Coster, D. P. Journal of Nuclear Materials, Vol. 390-391 https://doi.org/10.1016/j.jnucmat.2009.01.307	journal	June 2009
Kinetic modelling of temperature equilibration rates in the plasma Meisl, G.; Chankin, A. V.; Coster, D. P. Journal of Nuclear Materials, Vol. 438 https://doi.org/10.1016/j.jnucmat.2013.01.064	journal	July 2013
Observation of non-Maxwellian electron distributions in the NSTX divertor Jaworski, M. A.; Bell, M. G.; Gray, T. K. Journal of Nuclear Materials, Vol. 438 https://doi.org/10.1016/j.jnucmat.2013.01.076	journal	July 2013
Modeling of tokamak divertor plasma for weakly collisional parallel electron transport Umansky, M. V.; Dimits, A. M.; Joseph, I. Journal of Nuclear Materials, Vol. 463 https://doi.org/10.1016/j.jnucmat.2014.10.015	journal	August 2015
Non-local parallel transport in BOUT++ Omotani, J. T.; Dudson, B. D.; Havlíčková, E. Journal of Nuclear Materials, Vol. 463 https://doi.org/10.1016/j.jnucmat.2014.10.040	journal	August 2015
Assessment of the effect of parallel temperature gradients in the JET SOL on T measured by divertor target Langmuir probes Ďuran, I.; Ješko, K.; Fuchs, V. Journal of Nuclear Materials, Vol. 463 https://doi.org/10.1016/j.jnucmat.2015.01.051	journal	August 2015
Imposed magnetic field and hot electron propagation in inertial fusion hohlraums Strozzi, David J.; Perkins, L. J.; Marinak, M. M. Journal of Plasma Physics, Vol. 81, Issue 6 https://doi.org/10.1017/S0022377815001348	journal	December 2015
Generalized fluid theory including non-Maxwellian kinetic effects Izacard, Olivier Journal of Plasma Physics, Vol. 83, Issue 2 https://doi.org/10.1017/S0022377817000150	journal	March 2017
Transport in partially degenerate, magnetized plasmas. Part 1. Collision operators Brown, S. R.; Haines, M. G. Journal of Plasma Physics, Vol. 58, Issue 4 https://doi.org/10.1017/S0022377897006041	journal	December 1997
Extension of a reduced entropic model of electron transport to magnetized nonlocal regimes of high-energy-density plasmas Del Sorbo, D.; Feugeas, J. -L.; Nicolaï, Ph. Laser and Particle Beams, Vol. 34, Issue 3 https://doi.org/10.1017/S0263034616000252	journal	June 2016
A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes Schurtz, G. P.; Nicolaï, Ph. D.; Busquet, M. Physics of Plasmas, Vol. 7, Issue 10 https://doi.org/10.1063/1.1289512	journal	January 2000
Heat transport and electron distribution function in laser produced plasmas with hot spots Batishchev, O. V.; Bychenkov, V. Yu.; Detering, F. Physics of Plasmas, Vol. 9, Issue 5 https://doi.org/10.1063/1.1461385	journal	May 2002
A practical nonlocal model for heat transport in magnetized laser plasmas Nicolaï, Ph. D.; Feugeas, J. -L. A.; Schurtz, G. P. Physics of Plasmas, Vol. 13, Issue 3 https://doi.org/10.1063/1.2179392	journal	March 2006
The development of a Krook model for nonlocal transport in laser produced plasmas. I. Basic theory Manheimer, Wallace; Colombant, Denis; Goncharov, Valeri Physics of Plasmas, Vol. 15, Issue 8 https://doi.org/10.1063/1.2963078	journal	August 2008
Transport in the presence of inverse bremsstrahlung heating and magnetic fields Ridgers, C. P.; Thomas, A. G. R.; Kingham, R. J. Physics of Plasmas, Vol. 15, Issue 9 https://doi.org/10.1063/1.2978092	journal	September 2008
Moment approach to deriving parallel heat flow for general collisionality Ji, Jeong-Young; Held, Eric D.; Sovinec, Carl R. Physics of Plasmas, Vol. 16, Issue 2 https://doi.org/10.1063/1.3079072	journal	February 2009
Comparison for non-local hydrodynamic thermal conduction models Marocchino, A.; Tzoufras, M.; Atzeni, S. Physics of Plasmas, Vol. 20, Issue 2 https://doi.org/10.1063/1.4789878	journal	February 2013
A fast non-Fourier method for Landau-fluid operators Dimits, A. M.; Joseph, I.; Umansky, M. V. Physics of Plasmas, Vol. 21, Issue 5 https://doi.org/10.1063/1.4876617	journal	May 2014
Electron parallel closures for arbitrary collisionality Ji, Jeong-Young; Held, Eric D. Physics of Plasmas, Vol. 21, Issue 12 https://doi.org/10.1063/1.4904906	journal	December 2014
Use of external magnetic fields in hohlraum plasmas to improve laser-coupling Montgomery, D. S.; Albright, B. J.; Barnak, D. H. Physics of Plasmas, Vol. 22, Issue 1 https://doi.org/10.1063/1.4906055	journal	January 2015
Reduced entropic model for studies of multidimensional nonlocal transport in high-energy-density plasmas Del Sorbo, D.; Feugeas, J. -L.; Nicolaï, Ph. Physics of Plasmas, Vol. 22, Issue 8 https://doi.org/10.1063/1.4926824	journal	August 2015
Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations Cao, Duc; Moses, Gregory; Delettrez, Jacques Physics of Plasmas, Vol. 22, Issue 8 https://doi.org/10.1063/1.4928445	journal	August 2015
Dynamics of ion temperature gradient turbulence and transport with a static magnetic island Izacard, Olivier; Holland, Christopher; James, Spencer D. Physics of Plasmas, Vol. 23, Issue 2 https://doi.org/10.1063/1.4941704	journal	February 2016
Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas Izacard, Olivier Physics of Plasmas, Vol. 23, Issue 8 https://doi.org/10.1063/1.4960123	journal	August 2016
A comparison of non-local electron transport models for laser-plasmas relevant to inertial confinement fusion Sherlock, M.; Brodrick, J. P.; Ridgers, C. P. Physics of Plasmas, Vol. 24, Issue 8 https://doi.org/10.1063/1.4986095	journal	August 2017
A practical nonlocal model for electron heat transport in laser plasmas Epperlein, E. M.; Short, R. W. Physics of Fluids B: Plasma Physics, Vol. 3, Issue 11 https://doi.org/10.1063/1.859789	journal	November 1991
Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry Chang, Zuoyang; Callen, J. D. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 5 https://doi.org/10.1063/1.860125	journal	May 1992
Self‐consistent, nonlocal electron heat flux at arbitrary ion charge number Sanmartín, Juan R.; Ramírez, J.; Fernández‐Feria, R. Physics of Fluids B: Plasma Physics, Vol. 4, Issue 11 https://doi.org/10.1063/1.860366	journal	November 1992
Anomalous heating by ion sound turbulence Dum, C. T. Physics of Fluids, Vol. 21, Issue 6 https://doi.org/10.1063/1.862338	journal	January 1978
Anomalous electron transport equations for ion sound and related turbulent spectra Dum, C. T. Physics of Fluids, Vol. 21, Issue 6 https://doi.org/10.1063/1.862339	journal	January 1978
Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker–Planck equation Epperlein, E. M.; Haines, M. G. Physics of Fluids, Vol. 29, Issue 4 https://doi.org/10.1063/1.865901	journal	January 1986
Effect of electron collisions on ion‐acoustic waves and heat flow Epperlein, E. M. Physics of Plasmas, Vol. 1, Issue 1 https://doi.org/10.1063/1.870563	journal	January 1994
Toroidal gyrofluid equations for simulations of tokamak turbulence Beer, M. A.; Hammett, G. W. Physics of Plasmas, Vol. 3, Issue 11 https://doi.org/10.1063/1.871538	journal	November 1996
Kinetic effects in tokamak scrape-off layer plasmas Batishchev, O. V.; Krasheninnikov, S. I.; Catto, Peter J. Physics of Plasmas, Vol. 4, Issue 5 https://doi.org/10.1063/1.872280	journal	May 1997
Landau fluid models of collisionless magnetohydrodynamics Snyder, P. B.; Hammett, G. W.; Dorland, W. Physics of Plasmas, Vol. 4, Issue 11 https://doi.org/10.1063/1.872517	journal	November 1997
Non-Maxwellian electron distributions and continuum X-ray emission in inverse Bremsstrahlung heated plasmas Matte, J. P.; Lamoureux, M.; Moller, C. Plasma Physics and Controlled Fusion, Vol. 30, Issue 12 https://doi.org/10.1088/0741-3335/30/12/004	journal	November 1988
Parallel heat flux limits in the tokamak scrape-off layer Fundamenski, W. Plasma Physics and Controlled Fusion, Vol. 47, Issue 11 https://doi.org/10.1088/0741-3335/47/11/R01	journal	October 2005
Non-local approach to kinetic effects on parallel transport in fluid models of the scrape-off layer Omotani, J. T.; Dudson, B. D. Plasma Physics and Controlled Fusion, Vol. 55, Issue 5 https://doi.org/10.1088/0741-3335/55/5/055009	journal	April 2013
Towards a more universal understanding of radiation drive in gas-filled hohlraums Jones, O. S.; Thomas, C. A.; Amendt, P. A. Journal of Physics: Conference Series, Vol. 717 https://doi.org/10.1088/1742-6596/717/1/012026	journal	May 2016
Fokker-Planck Equation for an Inverse-Square Force Rosenbluth, Marshall N.; MacDonald, William M.; Judd, David L. Physical Review, Vol. 107, Issue 1 https://doi.org/10.1103/PhysRev.107.1	journal	July 1957
Ion acoustic waves in plasmas with collisional electrons Bychenkov, V. Yu.; Myatt, J.; Rozmus, W. Physical Review E, Vol. 50, Issue 6 https://doi.org/10.1103/PhysRevE.50.5134	journal	December 1994
Kinetic theory of ion acoustic waves in a plasma with collisional electrons Bychenkov, V. Yu.; Myatt, J.; Rozmus, W. Physical Review E, Vol. 52, Issue 6 https://doi.org/10.1103/PhysRevE.52.6759	journal	December 1995
Kinetic modeling of Nernst effect in magnetized hohlraums Joglekar, A. S.; Ridgers, C. P.; Kingham, R. J. Physical Review E, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevE.93.043206	journal	April 2016
Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas Ridgers, C. P.; Kingham, R. J.; Thomas, A. G. R. Physical Review Letters, Vol. 100, Issue 7 https://doi.org/10.1103/PhysRevLett.100.075003	journal	February 2008
Nonlinear Inverse Bremsstrahlung and Heated-Electron Distributions Langdon, A. Bruce Physical Review Letters, Vol. 44, Issue 9 https://doi.org/10.1103/PhysRevLett.44.575	journal	March 1980
Electron Heat Transport down Steep Temperature Gradients Matte, J. P.; Virmont, J. Physical Review Letters, Vol. 49, Issue 26 https://doi.org/10.1103/PhysRevLett.49.1936	journal	December 1982
Nonlocal Heat Transport Due to Steep Temperature Gradients Luciani, J. F.; Mora, P.; Virmont, J. Physical Review Letters, Vol. 51, Issue 18 https://doi.org/10.1103/PhysRevLett.51.1664	journal	October 1983
Nonlocal Electron Heat Transport by Not Quite Maxwell-Boltzmann Distributions Albritton, J. R.; Williams, E. A.; Bernstein, I. B. Physical Review Letters, Vol. 57, Issue 15 https://doi.org/10.1103/PhysRevLett.57.1887	journal	October 1986
Fluid moment models for Landau damping with application to the ion-temperature-gradient instability Hammett, Gregory W.; Perkins, Francis W. Physical Review Letters, Vol. 64, Issue 25 https://doi.org/10.1103/PhysRevLett.64.3019	journal	June 1990
Effect of Nonlocal Transport on Heat-Wave Propagation Gregori, G.; Glenzer, S. H.; Knight, J. Physical Review Letters, Vol. 92, Issue 20 https://doi.org/10.1103/PhysRevLett.92.205006	journal	May 2004
Simulation of electron kinetics in gas discharges Kolobov, V. I.; Arslanbekov, R. R. IEEE Transactions on Plasma Science, Vol. 34, Issue 3 https://doi.org/10.1109/TPS.2006.875850	journal	June 2006
Nonlocal transport in hot plasma. Part I Brantov, A. V.; Bychenkov, V. Yu. Plasma Physics Reports, Vol. 39, Issue 9 https://doi.org/10.1134/S1063780X13090018	journal	September 2013
The EIRENE and B2-EIRENE Codes Reiter, D.; Baelmans, M.; Börner, P. Fusion Science and Technology, Vol. 47, Issue 2 https://doi.org/10.13182/FST47-172	journal	February 2005

Similar Records

Improved non-local electron thermal transport model for two-dimensional radiation hydrodynamics simulations

Journal Article · Sat Aug 15 00:00:00 EDT 2015 · Physics of Plasmas · OSTI ID:22490048

A practical nonlocal model for heat transport in magnetized laser plasmas

Journal Article · Tue Mar 14 23:00:00 EST 2006 · Physics of Plasmas · OSTI ID:20782561

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

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

Citation Formats

References (74)

Similar Records

Related Subjects