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 00:00:00 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), Vol. 5:1; ISSN 0899-8221
• Country of Publication: United States
• Language: English

Related Subjects

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