Symmetries of resistive two-fluid magnetohydrodynamics under reversals of toroidal field, current, and rotation

TY - JOUR

T1 - Symmetries of resistive two-fluid magnetohydrodynamics under reversals of toroidal field, current, and rotation

AU - Ferraro, N. M.

PY - 2012/1

Y1 - 2012/1

N2 - The discrete symmetries of time-dependent, non-axisymmetric, two-fluid magnetohydrodynamics (MHD) equations are considered. Solutions of the time-independent, axisymmetric, ideal-MHD equations remain solutions under reversals of the toroidal field, current density, or rotation. Introducing non-axisymmetry, resistivity, and two-fluid effects into the equations each break different symmetries. Symmetry groups for solutions possessing up-down spatial symmetry, and the effect of flipping the magnetic geometry across the horizontal midplane, are also considered. It is shown that poloidal velocity may or may not be reversed under a simultaneous reversal of the toroidal field and a vertical reflection of the magnetic geometry, depending on the symmetry of the velocity. Because the symmetry groups of ideal, resistive, and two-fluid MHD are distinct, it may be possible to ascertain the dominant physical mechanism of various phenomena through empirical observations of symmetry-breaking. These results, which hold for nonlinear solutions in arbitrary geometry, should also be of use in testing numerical codes.

AB - The discrete symmetries of time-dependent, non-axisymmetric, two-fluid magnetohydrodynamics (MHD) equations are considered. Solutions of the time-independent, axisymmetric, ideal-MHD equations remain solutions under reversals of the toroidal field, current density, or rotation. Introducing non-axisymmetry, resistivity, and two-fluid effects into the equations each break different symmetries. Symmetry groups for solutions possessing up-down spatial symmetry, and the effect of flipping the magnetic geometry across the horizontal midplane, are also considered. It is shown that poloidal velocity may or may not be reversed under a simultaneous reversal of the toroidal field and a vertical reflection of the magnetic geometry, depending on the symmetry of the velocity. Because the symmetry groups of ideal, resistive, and two-fluid MHD are distinct, it may be possible to ascertain the dominant physical mechanism of various phenomena through empirical observations of symmetry-breaking. These results, which hold for nonlinear solutions in arbitrary geometry, should also be of use in testing numerical codes.

UR - https://www.scopus.com/pages/publications/84859169212

UR - https://www.scopus.com/pages/publications/84859169212#tab=citedBy

U2 - 10.1063/1.3677258

DO - 10.1063/1.3677258

M3 - Article

SN - 1070-664X

VL - 19

JO - Physics of Plasmas

JF - Physics of Plasmas

IS - 1

M1 - 014505

ER -