Some properties of finite energy constant-alpha force-free magnetic fields in a half-space

Details Some properties of finite energy constant-alpha force-free magnetic fields in a half-space Some properties of finite energy constant-alpha force-free magnetic fields in a half-space

Mar 1992

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992soph..138..133a&link_type=abstract

Solar Physics (ISSN 0038-0938), vol. 138, March 1992, p. 133-162.

Physics

30

Force-Free Magnetic Fields, Solar Corona, Solar Magnetic Field, Euler-Lagrange Equation, Fourier Analysis, Green'S Functions, Half Spaces, Photosphere

Scientific paper

Some useful properties of a finite energy, constant-alpha force-free magnetic field B(alpha) occupying a half-space D are presented. In particular: (1) Fourier and Green representations of B(alpha) are obtained and used to derive conditions for the existence and uniqueness of a B(alpha) having a given normal component B(z) on the boundary delta-D. (2) The asymptotic behavior of B(alpha) at infinity as well as stability results against changes in the boundary condition on delta-D and in the value of alpha are established. (3) The energy of B(alpha) is shown to be smaller than the energy of the open field having the same B(z) on delta-D, thus confirming an earlier conjecture (Aly, 1984). and (4) B(alpha) 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 delta-D.

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