A model for magnetic energy storage and Taylor's relaxation in the solar corona. I: Helicity-constrained minimum energy state in a half-cylinder

Journal Article · Fri Jan 01 04:00:00 EST 1993 · Physics of Fluids B; (United States)

DOI:https://doi.org/10.1063/1.860862· OSTI ID:6941023

Aly, J J ^[1]

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1. Service d'Astrophysique, CEN Saclay, F-91191 Gif sur Yvette Cedex (France)

The problem of the existence of a minimum energy state is studied in the set H of all the magnetic fields [bold B]: (i) occupying the half-cylinder [ital D]=[l brace][ital r][lt][ital R],[ital z][gt]0[r brace]; (ii) having a normal component vanishing on the vertical part [l brace][ital r]=[ital R][r brace] of the boundary of [ital D] and taking given values [ital Q]([ital r]) on its horizontal part [l brace][ital z]=0[r brace]; (iii) having a relative helicity equal to a prescribed value [ital H]. It is first shown that the only field that may possibly be an energy minimizer in H is the unique (and therefore axisymmetric) constant-[alpha] force-free field [bold B][sub [alpha]] contained in that set. Thus it is proved that [bold B][sub [alpha]] minimizes the energy indeed if and only if 0[le][vert bar][ital H][vert bar][le][ital H][sub [ital c]][le][infinity], where [ital H][sub [ital c]] is an estimated critical value. For [ital H][sub [ital c]][le][vert bar][ital H][vert bar][le][infinity], on the contrary, it is possible to construct in H nonaxisymmetric fields with an energy smaller than that of [bold B][sub [alpha]] and no minimum energy state does exist. However, [bold B][sub [alpha]] still minimizes the energy for [ital H][sub [ital c]] [le][vert bar] [ital H][vert bar] [le] [ital H][sup ax][sub [ital c]] (with possibly [ital H][sup ax][sub [ital c]] = [infinity]) if attention is restricted to the axisymmetric fields of H. These results are used to put a limit on the validity of a popular model of the heating of the solar corona, in which the field of a coronal structure is supposed to release sporadically, by Taylor's relaxation, a part of the energy it continuously extracts from the kinetic energy of the photospheric motions. It is argued that, as a consequence of the results above, one of the basic assumptions of the model breaks down when the field becomes highly sheared.

• OSTI ID: 6941023
• Journal Information: Physics of Fluids B; (United States), Journal Name: Physics of Fluids B; (United States) Vol. 5:1; ISSN 0899-8221; ISSN PFBPEI
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700370* -- Plasma Fluid & MHD Properties-- (1992-)
ATMOSPHERES
ENERGY
ENERGY STORAGE
EQUILIBRIUM
FLUID MECHANICS
HELICITY
HYDRODYNAMICS
MAGNETIC ENERGY STORAGE
MAGNETOHYDRODYNAMICS
MECHANICS
MHD EQUILIBRIUM
MINIMIZATION
PARTICLE PROPERTIES
RELAXATION
SOLAR ATMOSPHERE
SOLAR CORONA
STELLAR ATMOSPHERES
STELLAR CORONAE
STORAGE