The importance of electrothermal terms in Ohm's law for magnetized spherical implosions
Abstract
The magnetohydrodynamics (MHD) of magneticfield compression in laserdriven spherical targets is considered. Magneticfield evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heatflux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the crossfield velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The crossfield velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heatflux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of MHD routines to the 1D, Lagrangian hydrocode LILAC and the Eulerian version of the 2D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas ismore »
 Authors:

 Univ. of Rochester, Rochester, NY (United States)
 Publication Date:
 Research Org.:
 Univ. of Rochester, Rochester, NY (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1228366
 Alternate Identifier(s):
 OSTI ID: 1225401
 Grant/Contract Number:
 NA0001944; FC0204ER54789; FG0204ER54786
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 22; Journal Issue: 11; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; magnetic fields; limiters; electrical resistivity; shock waves; thermal conductivity
Citation Formats
Davies, J. R., Betti, R., Chang, P. Y., and Fiksel, G. The importance of electrothermal terms in Ohm's law for magnetized spherical implosions. United States: N. p., 2015.
Web. doi:10.1063/1.4935286.
Davies, J. R., Betti, R., Chang, P. Y., & Fiksel, G. The importance of electrothermal terms in Ohm's law for magnetized spherical implosions. United States. doi:10.1063/1.4935286.
Davies, J. R., Betti, R., Chang, P. Y., and Fiksel, G. Fri .
"The importance of electrothermal terms in Ohm's law for magnetized spherical implosions". United States. doi:10.1063/1.4935286. https://www.osti.gov/servlets/purl/1228366.
@article{osti_1228366,
title = {The importance of electrothermal terms in Ohm's law for magnetized spherical implosions},
author = {Davies, J. R. and Betti, R. and Chang, P. Y. and Fiksel, G.},
abstractNote = {The magnetohydrodynamics (MHD) of magneticfield compression in laserdriven spherical targets is considered. Magneticfield evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heatflux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the crossfield velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The crossfield velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heatflux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of MHD routines to the 1D, Lagrangian hydrocode LILAC and the Eulerian version of the 2D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas is removed. The Nernst term reduces the benefits of magnetization in inertial fusion. In addition, a Nernst flux limiter ≤ 0.12 is required in the gas in order to agree with measured neutron yield and increases in the neutronaveraged ion temperature caused by magnetization. This corresponds to maintaining the Nernst velocity below the shock velocity, which prevents significant decoupling of the magnetic field and gas compression.},
doi = {10.1063/1.4935286},
journal = {Physics of Plasmas},
number = 11,
volume = 22,
place = {United States},
year = {2015},
month = {11}
}
Web of Science
Works referenced in this record:
Recent magnetoinertial fusion experiments on the field reversed configuration heating experiment
journal, August 2013
 Degnan, J. H.; Amdahl, D. J.; Domonkos, M.
 Nuclear Fusion, Vol. 53, Issue 9
Seeding magnetic fields for laserdriven flux compression in highenergydensity plasmas
journal, April 2009
 Gotchev, O. V.; Knauer, J. P.; Chang, P. Y.
 Review of Scientific Instruments, Vol. 80, Issue 4
Ignition conditions for magnetized target fusion in cylindrical geometry
journal, January 2000
 Basko, M. M.; Kemp, A. J.; MeyerterVehn, J.
 Nuclear Fusion, Vol. 40, Issue 1
Note: Experimental platform for magnetized highenergydensity plasma studies at the omega laser facility
journal, January 2015
 Fiksel, G.; Agliata, A.; Barnak, D.
 Review of Scientific Instruments, Vol. 86, Issue 1
Fusion Yield Enhancement in Magnetized LaserDriven Implosions
journal, July 2011
 Chang, P. Y.; Fiksel, G.; Hohenberger, M.
 Physical Review Letters, Vol. 107, Issue 3
Compressing magnetic fields with highenergy lasers
journal, May 2010
 Knauer, J. P.; Gotchev, O. V.; Chang, P. Y.
 Physics of Plasmas, Vol. 17, Issue 5
An electron conductivity model for dense plasmas
journal, January 1984
 Lee, Y. T.; More, R. M.
 Physics of Fluids, Vol. 27, Issue 5
Pulsedpowerdriven cylindrical liner implosions of laser preheated fuel magnetized with an axial field
journal, May 2010
 Slutz, S. A.; Herrmann, M. C.; Vesey, R. A.
 Physics of Plasmas, Vol. 17, Issue 5
Experimental and Computational Progress on Liner Implosions for Compression of FRCs
journal, January 2008
 Degnan, James H.; Amdahl, David J.; Brown, Aaron
 IEEE Transactions on Plasma Science, Vol. 36, Issue 1
Parameter space for magnetized fuel targets in inertial confinement fusion
journal, March 1983
 Lindemuth, I. R.; Kirkpatrick, R. C.
 Nuclear Fusion, Vol. 23, Issue 3
A Staggered Grid, Lagrangian–Eulerian Remap Code for 3D MHD Simulations
journal, July 2001
 Arber, T. D.; Longbottom, A. W.; Gerrard, C. L.
 Journal of Computational Physics, Vol. 171, Issue 1
Magneticfield generation in laser fusion and hotelectron transport
journal, August 1986
 Haines, M. G.
 Canadian Journal of Physics, Vol. 64, Issue 8
Highgain, lowintensity ICF targets for a chargedparticle beam fusion driver
journal, January 1981
 Sweeney, M. A.; Farnsworth, A. V.
 Nuclear Fusion, Vol. 21, Issue 1
Towards the ultimate conservative difference scheme. V. A secondorder sequel to Godunov's method
journal, July 1979
 van Leer, Bram
 Journal of Computational Physics, Vol. 32, Issue 1
Modeling HEDLA magnetic field generation experiments on laser facilities
journal, March 2013
 Fatenejad, M.; Bell, A. R.; BenuzziMounaix, A.
 High Energy Density Physics, Vol. 9, Issue 1
LaserDriven MagneticFlux Compression in HighEnergyDensity Plasmas
journal, November 2009
 Gotchev, O. V.; Chang, P. Y.; Knauer, J. P.
 Physical Review Letters, Vol. 103, Issue 21
Compression of ultrahigh magnetic fields in a gaspuff Z pinch
journal, January 1988
 Felber, F. S.; Malley, M. M.; Wessel, F. J.
 Physics of Fluids, Vol. 31, Issue 7
Inertial confinement fusion implosions with imposed magnetic field compression using the OMEGA Laser
journal, May 2012
 Hohenberger, M.; Chang, P. Y.; Fiksel, G.
 Physics of Plasmas, Vol. 19, Issue 5
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
Efficient solution algorithms for the Riemann problem for real gases
journal, June 1985
 Colella, Phillip; Glaz, Harland M.
 Journal of Computational Physics, Vol. 59, Issue 2
Multidimensional analysis of directdrive, plasticshell implosions on OMEGA
journal, May 2005
 Radha, P. B.; Collins, T. J. B.; Delettrez, J. A.
 Physics of Plasmas, Vol. 12, Issue 5
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
Magnetoimplosive Generators
journal, February 1966
 Sakharov, Andrei D.
 Soviet Physics Uspekhi, Vol. 9, Issue 2
Divergencefreepreserving highorder schemes for magnetohydrodynamics: An artificial magnetic resistivity method
journal, October 2013
 Kawai, Soshi
 Journal of Computational Physics, Vol. 251
The physics of burn in magnetized deuteriumtritium plasmas: spherical geometry
journal, February 1986
 Jones, R. D.; Mead, W. C.
 Nuclear Fusion, Vol. 26, Issue 2
Saturation Mechanisms for the Generated Magnetic Field in Nonuniform LaserMatter Irradiation
journal, January 1997
 Haines, M. G.
 Physical Review Letters, Vol. 78, Issue 2
Heat flux effects in Ohm's law
journal, November 1986
 Haines, M. G.
 Plasma Physics and Controlled Fusion, Vol. 28, Issue 11
Twodimensional simulations of thermonuclear burn in ignitionscale inertial confinement fusion targets under compressed axial magnetic fields
journal, July 2013
 Perkins, L. J.; Logan, B. G.; Zimmerman, G. B.
 Physics of Plasmas, Vol. 20, Issue 7
Topology of Megagauss Magnetic Fields and of HeatCarrying Electrons Produced in a HighPower LaserSolid Interaction
journal, December 2014
 Lancia, L.; Albertazzi, B.; Boniface, C.
 Physical Review Letters, Vol. 113, Issue 23
Magnetoimplosive Generators
journal, February 1966
 Sakharov, Andrei D.
 Soviet Physics Uspekhi, Vol. 9, Issue 2
LaserDriven MagneticFlux Compression in HighEnergyDensity Plasmas
journal, November 2009
 Gotchev, O. V.; Chang, P. Y.; Knauer, J. P.
 Physical Review Letters, Vol. 103, Issue 21
Experimental and Computational Progress on Liner Implosions for Compression of FRCs
journal, January 2008
 Degnan, James H.; Amdahl, David J.; Brown, Aaron
 IEEE Transactions on Plasma Science, Vol. 36, Issue 1
Fusion Yield Enhancement in Magnetized LaserDriven Implosions
journal, July 2011
 Chang, P. Y.; Fiksel, G.; Hohenberger, M.
 Physical Review Letters, Vol. 107, Issue 3
Saturation Mechanisms for the Generated Magnetic Field in Nonuniform LaserMatter Irradiation
journal, January 1997
 Haines, M. G.
 Physical Review Letters, Vol. 78, Issue 2
Topology of Megagauss Magnetic Fields and of HeatCarrying Electrons Produced in a HighPower LaserSolid Interaction
journal, December 2014
 Lancia, L.; Albertazzi, B.; Boniface, C.
 Physical Review Letters, Vol. 113, Issue 23
Works referencing / citing this record:
Simulation of selfgenerated magnetic fields in an inertial fusion hohlraum environment
journal, May 2017
 Farmer, W. A.; Koning, J. M.; Strozzi, D. J.
 Physics of Plasmas, Vol. 24, Issue 5
Perturbation modifications by premagnetisation of inertial confinement fusion implosions
journal, February 2019
 Walsh, C. A.; McGlinchey, K.; Tong, J. K.
 Physics of Plasmas, Vol. 26, Issue 2
Extendedmagnetohydrodynamics in underdense plasmas
journal, February 2020
 Walsh, C. A.; Chittenden, J. P.; Hill, D. W.
 Physics of Plasmas, Vol. 27, Issue 2
Inferring fuel areal density from secondary neutron yields in laserdriven magnetized liner inertial fusion
journal, February 2019
 Davies, J. R.; Barnak, D. H.; Betti, R.
 Physics of Plasmas, Vol. 26, Issue 2
Axial magnetic field injection in magnetized liner inertial fusion
journal, October 2017
 Gourdain, P. A.; Adams, M. B.; Davies, J. R.
 Physics of Plasmas, Vol. 24, Issue 10
Inertialconfinement fusion with lasers
journal, May 2016
 Betti, R.; Hurricane, O. A.
 Nature Physics, Vol. 12, Issue 5
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