Abstract
Some useful properties of a finite energy, constant-α, force-free magnetic field B α occupying a half-space D are presented. In particular:
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(a)
Fourier and Green representations of B α are obtained and used to derive conditions for the existence and uniqueness of a B α having a given normal component B z on the boundary ∂D.
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(b)
The asymptotic behaviour of B α at infinity as well as stability results against changes in the boundary condition on ∂D and in the value of α are established.
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(c)
The energy of B α is shown to be smaller than the energy of the open field having the same B z on ∂D, thus confirming an earlier conjecture (Aly, 1984).
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(d)
B α is proved to not be a Taylor-Heyvaerts-Priest state, in spite of the fact that its relative helicity H is finite and that it is the only solution of the Lagrange-Euler equation associated with the problem of minimizing the energy among all the fields having the same value of H and the same B z on ∂D.
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Aly, J.J. Some properties of finite energy constant-α force-free magnetic fields in a half-space. Sol Phys 138, 133–162 (1992). https://doi.org/10.1007/BF00146201
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DOI: https://doi.org/10.1007/BF00146201