TY - JOUR

T1 - A three-dimensional magnetohydrodynamic formalism for coronal helmet streamers

AU - Cuperman, S.

AU - Bruma, C.

AU - Detman, T.

AU - Dryer, M.

PY - 1993/2/10

Y1 - 1993/2/10

N2 - A three-dimensional magnetohydrodynamic (MHD) formulation of the steady state coronal helmet-streamer problem is presented. It includes the simple azimuthally symmetric (∂/∂φ = 0) and two-dimensional (∂/∂φ = 0, Bφ = 0) cases. The major mathematical difficulty - the correct, iterative calculation of the transverse electrical currents, which are the sources of the fields in Maxwell's equations - is eliminated. This is achieved by the elaboration of an algorithm connecting four different coordinate spaces: (1) spherical (r, φ, θ), in which the problem is defined and boundary conditions established; (2) computationally convenient (ν, μ, ξ), in which the entire space is represented by a rectangular box of sizes (1, 2, 1) (ν = ro/r, μ = cos θ, ξ = φ/2π), therefore allowing also the imposition of boundary conditions at infinity, ν = 0 (e.g., vanishing of the magnetic field components, etc.); (3) local Frenet's, (l, c, n), defined by the orthogonal unit vectors el = B/B, ec = R(∂el/∂l), and en = el x ec (tangent to the field line, pointing toward the center of curvature of the field line, and normal to the osculatory plane of the field, respectively; R is the curvature radius), required for the integration of the conductive, MHD equations along magnetic field lines; and (4) Cartesian (x, y, z), in which Frenet's unit vectors as well as the derivatives along their directions are defined. An analytical proof of the results for a particular two-dimensional model is presented.

AB - A three-dimensional magnetohydrodynamic (MHD) formulation of the steady state coronal helmet-streamer problem is presented. It includes the simple azimuthally symmetric (∂/∂φ = 0) and two-dimensional (∂/∂φ = 0, Bφ = 0) cases. The major mathematical difficulty - the correct, iterative calculation of the transverse electrical currents, which are the sources of the fields in Maxwell's equations - is eliminated. This is achieved by the elaboration of an algorithm connecting four different coordinate spaces: (1) spherical (r, φ, θ), in which the problem is defined and boundary conditions established; (2) computationally convenient (ν, μ, ξ), in which the entire space is represented by a rectangular box of sizes (1, 2, 1) (ν = ro/r, μ = cos θ, ξ = φ/2π), therefore allowing also the imposition of boundary conditions at infinity, ν = 0 (e.g., vanishing of the magnetic field components, etc.); (3) local Frenet's, (l, c, n), defined by the orthogonal unit vectors el = B/B, ec = R(∂el/∂l), and en = el x ec (tangent to the field line, pointing toward the center of curvature of the field line, and normal to the osculatory plane of the field, respectively; R is the curvature radius), required for the integration of the conductive, MHD equations along magnetic field lines; and (4) Cartesian (x, y, z), in which Frenet's unit vectors as well as the derivatives along their directions are defined. An analytical proof of the results for a particular two-dimensional model is presented.

KW - MHD

KW - Sun: corona

UR - http://www.scopus.com/inward/record.url?scp=12044255605&partnerID=8YFLogxK

U2 - 10.1086/172285

DO - 10.1086/172285

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AN - SCOPUS:12044255605

SN - 0004-637X

VL - 404

SP - 356

EP - 371

JO - Astrophysical Journal

JF - Astrophysical Journal

IS - 1

ER -