Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations

In this work we numerically test a model of Hall magnetohydrodynamics in the presence of a strong mean magnetic field: the reduced Hall magnetohydrodynamic model (RHMHD) derived by [Gomez, Phys. Plasmas 15, 102303 (2008)] with the addition of weak compressible effects. The main advantage of this mod...

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Autores principales: Martin, L.N., Dmitruk, P., Gomez, D.O.
Formato: JOUR
Materias:
Computational costs
Hall magnetohydrodynamics
Hall MHD
Initial conditions
Mean magnetic field
Strong magnetic fields
Hall effect
Magnetic fields
Magnetohydrodynamics
Magnetoplasma
Three dimensional computer graphics
Turbulence
Three dimensional
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_1070664X_v17_n11_p_Martin
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_1070664X_v17_n11_p_Martin2023-10-03T16:02:31Z Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations Martin, L.N. Dmitruk, P. Gomez, D.O. Computational costs Hall magnetohydrodynamics Hall MHD Initial conditions Mean magnetic field Strong magnetic fields Hall effect Magnetic fields Magnetohydrodynamics Magnetoplasma Three dimensional computer graphics Turbulence Three dimensional In this work we numerically test a model of Hall magnetohydrodynamics in the presence of a strong mean magnetic field: the reduced Hall magnetohydrodynamic model (RHMHD) derived by [Gomez, Phys. Plasmas 15, 102303 (2008)] with the addition of weak compressible effects. The main advantage of this model lies in the reduction of computational cost. Nevertheless, up until now the degree of agreement with the original Hall MHD system and the range of validity in a regime of turbulence were not established. In this work direct numerical simulations of three-dimensional Hall MHD turbulence in the presence of a strong mean magnetic field are compared with simulations of the weak compressible RHMHD model. The results show that the degree of agreement is very high (when the different assumptions of RHMHD, such as spectral anisotropy, are satisfied). Nevertheless, when the initial conditions are isotropic but the mean magnetic field is maintained strong, the results differ at the beginning but asymptotically reach a good agreement at relatively short times. We also found evidence that the compressibility still plays a role in the dynamics of these systems, and the weak compressible RHMHD model is able to capture these effects. In conclusion the weak compressible RHMHD model is a valid approximation of the Hall MHD turbulence in the relevant physical context. © 2010 American Institute of Physics. Fil:Dmitruk, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Gomez, D.O. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_1070664X_v17_n11_p_Martin
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Computational costs
Hall magnetohydrodynamics
Hall MHD
Initial conditions
Mean magnetic field
Strong magnetic fields
Hall effect
Magnetic fields
Magnetohydrodynamics
Magnetoplasma
Three dimensional computer graphics
Turbulence
Three dimensional
spellingShingle Computational costs
Hall magnetohydrodynamics
Hall MHD
Initial conditions
Mean magnetic field
Strong magnetic fields
Hall effect
Magnetic fields
Magnetohydrodynamics
Magnetoplasma
Three dimensional computer graphics
Turbulence
Three dimensional
Martin, L.N.
Dmitruk, P.
Gomez, D.O.
Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
topic_facet Computational costs
Hall magnetohydrodynamics
Hall MHD
Initial conditions
Mean magnetic field
Strong magnetic fields
Hall effect
Magnetic fields
Magnetohydrodynamics
Magnetoplasma
Three dimensional computer graphics
Turbulence
Three dimensional
description In this work we numerically test a model of Hall magnetohydrodynamics in the presence of a strong mean magnetic field: the reduced Hall magnetohydrodynamic model (RHMHD) derived by [Gomez, Phys. Plasmas 15, 102303 (2008)] with the addition of weak compressible effects. The main advantage of this model lies in the reduction of computational cost. Nevertheless, up until now the degree of agreement with the original Hall MHD system and the range of validity in a regime of turbulence were not established. In this work direct numerical simulations of three-dimensional Hall MHD turbulence in the presence of a strong mean magnetic field are compared with simulations of the weak compressible RHMHD model. The results show that the degree of agreement is very high (when the different assumptions of RHMHD, such as spectral anisotropy, are satisfied). Nevertheless, when the initial conditions are isotropic but the mean magnetic field is maintained strong, the results differ at the beginning but asymptotically reach a good agreement at relatively short times. We also found evidence that the compressibility still plays a role in the dynamics of these systems, and the weak compressible RHMHD model is able to capture these effects. In conclusion the weak compressible RHMHD model is a valid approximation of the Hall MHD turbulence in the relevant physical context. © 2010 American Institute of Physics.
format JOUR
author Martin, L.N.
Dmitruk, P.
Gomez, D.O.
author_facet Martin, L.N.
Dmitruk, P.
Gomez, D.O.
author_sort Martin, L.N.
title Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
title_short Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
title_full Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
title_fullStr Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
title_full_unstemmed Hall effect in a strong magnetic field: Direct comparisons of compressible magnetohydrodynamics and the reduced Hall magnetohydrodynamic equations
title_sort hall effect in a strong magnetic field: direct comparisons of compressible magnetohydrodynamics and the reduced hall magnetohydrodynamic equations
url http://hdl.handle.net/20.500.12110/paper_1070664X_v17_n11_p_Martin
work_keys_str_mv AT martinln halleffectinastrongmagneticfielddirectcomparisonsofcompressiblemagnetohydrodynamicsandthereducedhallmagnetohydrodynamicequations
AT dmitrukp halleffectinastrongmagneticfielddirectcomparisonsofcompressiblemagnetohydrodynamicsandthereducedhallmagnetohydrodynamicequations
AT gomezdo halleffectinastrongmagneticfielddirectcomparisonsofcompressiblemagnetohydrodynamicsandthereducedhallmagnetohydrodynamicequations
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