Modeling of a linear force-free magnetic field in a bounded domain
V. I. Abramenko, V. B. Yurchishin
Center For Solar Terrestrial Research - Big Bear Solar Observatory
A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, Ω) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the Bz component specified at the Ω boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ∇2u + α2u. Specifying two scalar functions, Bx and By on the intersection of the lateral part of the Ω boundary with one selected plane z = constant, and using Bz inside the Ω, we have found Bx and By throughout Ω. The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B′ does not exceed 1.0%. Boundary conditions for the B′ calculation were taken as given by the analytic LFFF solution B. Comparison of B′ with B″, which was calculated by the potential non-pholospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume. The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.
Dive into the research topics of 'Modeling of a linear force-free magnetic field in a bounded domain'. Together they form a unique fingerprint.
force-free magnetic fields Physics & Astronomy 100%
magnetic field Earth & Environmental Sciences 56%
boundary condition Earth & Environmental Sciences 38%
boundary conditions Physics & Astronomy 34%
iteration Physics & Astronomy 30%
modeling Earth & Environmental Sciences 26%
Helmholtz equation Earth & Environmental Sciences 22%
differential operators Physics & Astronomy 20%
Abramenko, V. I., & Yurchishin, V. B. (1996). Modeling of a linear force-free magnetic field in a bounded domain. Solar Physics, 168(1), 47-63. https://doi.org/10.1007/BF00145824
Abramenko, V. I. ; Yurchishin, V. B. / Modeling of a linear force-free magnetic field in a bounded domain. In: Solar Physics. 1996 ; Vol. 168, No. 1. pp. 47-63.
@article{3e89e7f195674c26a28ec23567ff1c38,
title = "Modeling of a linear force-free magnetic field in a bounded domain",
abstract = "A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, Ω) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the Bz component specified at the Ω boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ∇2u + α2u. Specifying two scalar functions, Bx and By on the intersection of the lateral part of the Ω boundary with one selected plane z = constant, and using Bz inside the Ω, we have found Bx and By throughout Ω. The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B′ does not exceed 1.0%. Boundary conditions for the B′ calculation were taken as given by the analytic LFFF solution B. Comparison of B′ with B″, which was calculated by the potential non-pholospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume. The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.",
author = "Abramenko, {V. I.} and Yurchishin, {V. B.}",
doi = "10.1007/BF00145824",
journal = "Solar Physics",
Abramenko, VI & Yurchishin, VB 1996, 'Modeling of a linear force-free magnetic field in a bounded domain', Solar Physics, vol. 168, no. 1, pp. 47-63. https://doi.org/10.1007/BF00145824
Modeling of a linear force-free magnetic field in a bounded domain. / Abramenko, V. I.; Yurchishin, V. B.
In: Solar Physics, Vol. 168, No. 1, 01.01.1996, p. 47-63.
T1 - Modeling of a linear force-free magnetic field in a bounded domain
AU - Abramenko, V. I.
AU - Yurchishin, V. B.
N2 - A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, Ω) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the Bz component specified at the Ω boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ∇2u + α2u. Specifying two scalar functions, Bx and By on the intersection of the lateral part of the Ω boundary with one selected plane z = constant, and using Bz inside the Ω, we have found Bx and By throughout Ω. The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B′ does not exceed 1.0%. Boundary conditions for the B′ calculation were taken as given by the analytic LFFF solution B. Comparison of B′ with B″, which was calculated by the potential non-pholospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume. The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.
AB - A method for the reconstruction of the linear force-free magnetic field in a bounded domain (as a rectangular box, Ω) is presented here. The Dirichlet boundary-value problem for the Helmholtz equation is solved for the Bz component specified at the Ω boundary. Chebyshev's iteration method with the optimal rearrangement of the iteration parameters sequence was used. The solution is obtained as for the positive-definite, and for the non-sign-definite difference analogue of the differential operator ∇2u + α2u. Specifying two scalar functions, Bx and By on the intersection of the lateral part of the Ω boundary with one selected plane z = constant, and using Bz inside the Ω, we have found Bx and By throughout Ω. The algorithm was tested with the numerical procedure which gives the analytic solution B of the linear force-free field (LFFF) equations for the dipole in a half-space. The root-mean-square deviation of the analytic solution B from the calculated B′ does not exceed 1.0%. Boundary conditions for the B′ calculation were taken as given by the analytic LFFF solution B. Comparison of B′ with B″, which was calculated by the potential non-pholospheric boundary conditions, show that they differ significantly. Thus, the specification of boundary conditions at non-photospheric boundaries of the volume under consideration is of particular importance when modeling the LFFF in a bounded volume. The algorithm proposed here allows one to use the information about magnetic fields in the corona for the modeling of LFFF in a limited domain above an active region on the Sun.
U2 - 10.1007/BF00145824
DO - 10.1007/BF00145824
JO - Solar Physics
JF - Solar Physics
Abramenko VI, Yurchishin VB. Modeling of a linear force-free magnetic field in a bounded domain. Solar Physics. 1996 Jan 1;168(1):47-63. doi: 10.1007/BF00145824