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Title: Linear response of a Hall magnetic drift wave for verification of Hall MHD algorithms

Abstract

Numerical implementations of Hall magnetohydrodynamics (Hall MHD) can be challenging due to the nonlinear multidimensional nature of the Hall term. Here, a model problem is presented that couples the hydrodynamic motion of the plasma to Hall MHD evolution of the magnetic field. The Hall MHD equations are linearized about unperturbed solutions in both cylindrical and Cartesian coordinates in two dimensions. The magnetic field is assumed to lie in the ignorable direction, and the linear response about the unperturbed solution is considered. The resulting ordinary differential equation is used to numerically compute the eigenfunctions and eigenfrequencies of the mode. The resulting eigenfunctions do not make the local wave approximation but are instead global solutions that depend on the spatial dependence of the unperturbed Alfvén speed. Hall MHD simulations are then performed in the Ares multiphysics code and shown to agree with the predicted phase velocities of the wave, and the simulated solutions are shown to numerically converge to the semianalytic modes. By varying the background density of the plasma (and correspondingly, the ion inertial length), the importance of Hall physics can be varied. This allows the test problem to transition from the classical MHD limit to the extreme Hall MHD limit.more » Furthermore, this problem is a useful tool for the verification of Hall MHD routines implemented in various codes, and the robustness of a routine can be tested in regimes in which Hall physics is dominant.« less

Authors:
ORCiD logo [1];  [1];  [1]
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  1. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1561457
Alternate Identifier(s):
OSTI ID: 1567932
Report Number(s):
LLNL-JRNL-768218
Journal ID: ISSN 1070-664X; 958627; TRN: US2000618
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physics of Plasmas
Additional Journal Information:
Journal Volume: 26; Journal Issue: 7; 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

Farmer, W. A., Ellison, C. L., and Hammer, J. H. Linear response of a Hall magnetic drift wave for verification of Hall MHD algorithms. United States: N. p., 2019. Web. doi:10.1063/1.5094349.
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Farmer, W. A., Ellison, C. L., & Hammer, J. H. Linear response of a Hall magnetic drift wave for verification of Hall MHD algorithms. United States. https://doi.org/10.1063/1.5094349
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Farmer, W. A., Ellison, C. L., and Hammer, J. H. Tue . "Linear response of a Hall magnetic drift wave for verification of Hall MHD algorithms". United States. https://doi.org/10.1063/1.5094349. https://www.osti.gov/servlets/purl/1561457.
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@article{osti_1561457,
title = {Linear response of a Hall magnetic drift wave for verification of Hall MHD algorithms},
author = {Farmer, W. A. and Ellison, C. L. and Hammer, J. H.},
abstractNote = {Numerical implementations of Hall magnetohydrodynamics (Hall MHD) can be challenging due to the nonlinear multidimensional nature of the Hall term. Here, a model problem is presented that couples the hydrodynamic motion of the plasma to Hall MHD evolution of the magnetic field. The Hall MHD equations are linearized about unperturbed solutions in both cylindrical and Cartesian coordinates in two dimensions. The magnetic field is assumed to lie in the ignorable direction, and the linear response about the unperturbed solution is considered. The resulting ordinary differential equation is used to numerically compute the eigenfunctions and eigenfrequencies of the mode. The resulting eigenfunctions do not make the local wave approximation but are instead global solutions that depend on the spatial dependence of the unperturbed Alfvén speed. Hall MHD simulations are then performed in the Ares multiphysics code and shown to agree with the predicted phase velocities of the wave, and the simulated solutions are shown to numerically converge to the semianalytic modes. By varying the background density of the plasma (and correspondingly, the ion inertial length), the importance of Hall physics can be varied. This allows the test problem to transition from the classical MHD limit to the extreme Hall MHD limit. Furthermore, this problem is a useful tool for the verification of Hall MHD routines implemented in various codes, and the robustness of a routine can be tested in regimes in which Hall physics is dominant.},
doi = {10.1063/1.5094349},
journal = {Physics of Plasmas},
number = 7,
volume = 26,
place = {United States},
year = {Tue Jul 30 00:00:00 EDT 2019},
month = {Tue Jul 30 00:00:00 EDT 2019}
}
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https://doi.org/10.1063/1.5094349
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Figures / Tables:

FIG. 1 FIG. 1: Eigenfrequencies of the Cartesian problem for χ ∈ [1, 2] and κ = 1 as a function of h.
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Works referenced in this record:

Anomalous transport properties associated with the lower-hybrid-drift instability
journal, January 1975

  • Davidson, R. C.; Gladd, N. T.
  • Physics of Fluids, Vol. 18, Issue 10
  • DOI: 10.1063/1.861021

Development and modeling of a polar-direct-drive exploding pusher platform at the National Ignition Facility
journal, July 2018

  • Ellison, C. Leland; Whitley, Heather D.; Brown, Colin R. D.
  • Physics of Plasmas, Vol. 25, Issue 7
  • DOI: 10.1063/1.5025724

Physical constraints in numerical calculations of diffusion
journal, July 1981

Measurement of Lower-Hybrid Drift Turbulence in a Reconnecting Current Sheet
journal, December 2001

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

Accurate semi-implicit treatment of the Hall effect in magnetohydrodynamic computations
journal, July 1989

Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder
journal, April 2015

Theory and simulation of a high‐frequency magnetic drift wave
journal, December 1991

  • Huba, J. D.
  • Physics of Fluids B: Plasma Physics, Vol. 3, Issue 12
  • DOI: 10.1063/1.859752

Relaxation model for extended magnetohydrodynamics: Comparison to magnetohydrodynamics for dense Z-pinches
journal, January 2011

  • Seyler, C. E.; Martin, M. R.
  • Physics of Plasmas, Vol. 18, Issue 1
  • DOI: 10.1063/1.3543799

Effects of finite plasma beta on the lower-hybrid-drift instability
journal, January 1977

  • Davidson, R. C.; Gladd, N. T.; Wu, C. S.
  • Physics of Fluids, Vol. 20, Issue 2
  • DOI: 10.1063/1.861867

The lower-hybrid-drift instability as a source of anomalous resistivity for magnetic field line reconnection
journal, March 1977

  • Huba, J. D.; Gladd, N. T.; Papadopoulos, K.
  • Geophysical Research Letters, Vol. 4, Issue 3
  • DOI: 10.1029/GL004i003p00125

The influence of Hall physics on power-flow along a coaxial transmission line
journal, October 2018

  • Hamlin, N. D.; Seyler, C. E.
  • Physics of Plasmas, Vol. 25, Issue 10
  • DOI: 10.1063/1.5042441

Helical instability in MagLIF due to axial flux compression by low-density plasma
journal, June 2018

  • Seyler, C. E.; Martin, M. R.; Hamlin, N. D.
  • Physics of Plasmas, Vol. 25, Issue 6
  • DOI: 10.1063/1.5028365

Simulations on lower hybrid drift instability and anomalous resistivity in the magnetic neutral sheet
journal, January 1981

Scaling of forced magnetic reconnection in the Hall-magnetohydrodynamic Taylor problem
journal, March 2004

A new 3D MHD algorithm: the distribution function method
journal, April 1999

Experimental study of current loss and plasma formation in the Z machine post-hole convolute
journal, January 2017

A 2D high-β Hall MHD implicit nonlinear solver
journal, July 2003

Hall magnetohydrodynamic reconnection: The Geospace Environment Modeling challenge
journal, March 2001

  • Ma, Z. W.; Bhattacharjee, A.
  • Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3
  • DOI: 10.1029/1999JA001004

Target design for high fusion yield with the double Z-pinch-driven hohlraum
journal, May 2007

  • Vesey, R. A.; Herrmann, M. C.; Lemke, R. W.
  • Physics of Plasmas, Vol. 14, Issue 5
  • DOI: 10.1063/1.2472364

A study of ALE simulations of Rayleigh–Taylor instability
journal, March 2001

  • Darlington, Rebecca M.; McAbee, Thomas L.; Rodrigue, Garry
  • Computer Physics Communications, Vol. 135, Issue 1
  • DOI: 10.1016/S0010-4655(00)00216-2

Geospace Environmental Modeling (GEM) Magnetic Reconnection Challenge
journal, March 2001

  • Birn, J.; Drake, J. F.; Shay, M. A.
  • Journal of Geophysical Research: Space Physics, Vol. 106, Issue A3
  • DOI: 10.1029/1999JA900449

Rayleigh–Taylor instability: Comparison of hybrid and nonideal magnetohydrodynamic simulations
journal, June 1998

  • Huba, J. D.; Winske, D.
  • Physics of Plasmas, Vol. 5, Issue 6
  • DOI: 10.1063/1.872904
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    Figures / Tables found in this record:

    FIG. 1 (p. 13)figure
    FIG. 2 (p. 14)figure
    FIG. 3 (p. 15)figure
    TABLE I (p. 17)table
    FIG. 4 (p. 18)figure
    FIG. 5 (p. 19)figure
    FIG. 6 (p. 19)figure
    FIG. 7 (p. 20)figure
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