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

Farmer, W. A.; Ellison, C. L.; Hammer, J. H.

doi:10.1063/1.5094349

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

Journal Article · 30 July 2019 · Physics of Plasmas

DOI: https://doi.org/10.1063/1.5094349 · OSTI ID:1561457

^[1]; Ellison, C. L. ^[1]; Hammer, J. H. ^[1]

Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

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.

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1561457

Alternate ID(s):: OSTI ID: 1567932

Report Number(s):: LLNL-JRNL-768218; 958627; TRN: US2000618

Journal Information:: Physics of Plasmas, Vol. 26, Issue 7; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 5 works

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