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Title: The importance of electrothermal terms in Ohm's law for magnetized spherical implosions

Abstract

The magnetohydrodynamics (MHD) of magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field 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 heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux 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 1-D, Lagrangian hydrocode LILAC and the Eulerian version of the 2-D 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 » 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 neutron-averaged 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.« less

Authors:
 [1];  [1];  [1];  [1]
  1. Univ. of Rochester, Rochester, NY (United States)
Publication Date:
Research Org.:
Univ. of Rochester, NY (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1228366
Alternate Identifier(s):
OSTI ID: 1225401
Grant/Contract Number:  
NA0001944; FC02-04ER54789; FG02-04ER54786
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 22; Journal Issue: 11; 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; 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. https://doi.org/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. https://doi.org/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 magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field 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 heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as a heat front moves into the gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux 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 1-D, Lagrangian hydrocode LILAC and the Eulerian version of the 2-D 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 neutron-averaged 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 = {Fri Nov 06 00:00:00 EST 2015},
month = {Fri Nov 06 00:00:00 EST 2015}
}

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Works referenced in this record:

Recent magneto-inertial fusion experiments on the field reversed configuration heating experiment
journal, August 2013


Seeding magnetic fields for laser-driven flux compression in high-energy-density plasmas
journal, April 2009

  • Gotchev, O. V.; Knauer, J. P.; Chang, P. Y.
  • Review of Scientific Instruments, Vol. 80, Issue 4
  • DOI: 10.1063/1.3115983

Ignition conditions for magnetized target fusion in cylindrical geometry
journal, January 2000


Note: Experimental platform for magnetized high-energy-density plasma studies at the omega laser facility
journal, January 2015

  • Fiksel, G.; Agliata, A.; Barnak, D.
  • Review of Scientific Instruments, Vol. 86, Issue 1
  • DOI: 10.1063/1.4905625

Compressing magnetic fields with high-energy lasers
journal, May 2010

  • Knauer, J. P.; Gotchev, O. V.; Chang, P. Y.
  • Physics of Plasmas, Vol. 17, Issue 5
  • DOI: 10.1063/1.3416557

An electron conductivity model for dense plasmas
journal, January 1984

  • Lee, Y. T.; More, R. M.
  • Physics of Fluids, Vol. 27, Issue 5
  • DOI: 10.1063/1.864744

Pulsed-power-driven 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
  • DOI: 10.1063/1.3333505

Parameter space for magnetized fuel targets in inertial confinement fusion
journal, March 1983


A Staggered Grid, Lagrangian–Eulerian Remap Code for 3-D MHD Simulations
journal, July 2001

  • Arber, T. D.; Longbottom, A. W.; Gerrard, C. L.
  • Journal of Computational Physics, Vol. 171, Issue 1
  • DOI: 10.1006/jcph.2001.6780

Magnetic-field generation in laser fusion and hot-electron transport
journal, August 1986

  • Haines, M. G.
  • Canadian Journal of Physics, Vol. 64, Issue 8
  • DOI: 10.1139/p86-160

High-gain, low-intensity ICF targets for a charged-particle beam fusion driver
journal, January 1981


Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
journal, July 1979


Modeling HEDLA magnetic field generation experiments on laser facilities
journal, March 2013


Compression of ultrahigh magnetic fields in a gas-puff Z pinch
journal, January 1988

  • Felber, F. S.; Malley, M. M.; Wessel, F. J.
  • Physics of Fluids, Vol. 31, Issue 7
  • DOI: 10.1063/1.866657

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
  • DOI: 10.1063/1.3696032

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

Efficient solution algorithms for the Riemann problem for real gases
journal, June 1985


Multidimensional analysis of direct-drive, plastic-shell implosions on OMEGA
journal, May 2005

  • Radha, P. B.; Collins, T. J. B.; Delettrez, J. A.
  • Physics of Plasmas, Vol. 12, Issue 5
  • DOI: 10.1063/1.1882333

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

The physics of burn in magnetized deuterium-tritium plasmas: spherical geometry
journal, February 1986


Heat flux effects in Ohm's law
journal, November 1986


Two-dimensional simulations of thermonuclear burn in ignition-scale 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
  • DOI: 10.1063/1.4816813

Topology of Megagauss Magnetic Fields and of Heat-Carrying Electrons Produced in a High-Power Laser-Solid Interaction
journal, December 2014


Magnetoimplosive Generators
journal, February 1966


Laser-Driven Magnetic-Flux Compression in High-Energy-Density Plasmas
journal, November 2009


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
  • DOI: 10.1109/TPS.2007.913814

Fusion Yield Enhancement in Magnetized Laser-Driven Implosions
journal, July 2011


Saturation Mechanisms for the Generated Magnetic Field in Nonuniform Laser-Matter Irradiation
journal, January 1997


Magnetoimplosive generators [Взрывомагнитные генераторы]
journal, January 1991


Magnetoimplosive generators
journal, May 1991


Works referencing / citing this record:

Simulation of self-generated 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
  • DOI: 10.1063/1.4983140

Perturbation modifications by pre-magnetisation of inertial confinement fusion implosions
journal, February 2019

  • Walsh, C. A.; McGlinchey, K.; Tong, J. K.
  • Physics of Plasmas, Vol. 26, Issue 2
  • DOI: 10.1063/1.5085498

Extended-magnetohydrodynamics in under-dense plasmas
journal, February 2020

  • Walsh, C. A.; Chittenden, J. P.; Hill, D. W.
  • Physics of Plasmas, Vol. 27, Issue 2
  • DOI: 10.1063/1.5124144

Inferring fuel areal density from secondary neutron yields in laser-driven magnetized liner inertial fusion
journal, February 2019

  • Davies, J. R.; Barnak, D. H.; Betti, R.
  • Physics of Plasmas, Vol. 26, Issue 2
  • DOI: 10.1063/1.5082960

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
  • DOI: 10.1063/1.4986640

Nernst thermomagnetic waves in magnetized high energy density plasmas
journal, November 2019

  • Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.
  • Physics of Plasmas, Vol. 26, Issue 11
  • DOI: 10.1063/1.5122178

Inertial-confinement fusion with lasers
journal, May 2016

  • Betti, R.; Hurricane, O. A.
  • Nature Physics, Vol. 12, Issue 5
  • DOI: 10.1038/nphys3736

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