Physics
Scientific paper
Jan 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003phpl...10..241a&link_type=abstract
Physics of Plasmas, Volume 10, Issue 1, pp. 241-248 (2003).
Physics
Magnetohydrodynamic Waves, Magnetohydrodynamics And Plasmas
Scientific paper
One of the outstanding challenges of solar physics is understanding the mechanism for heating the solar corona, a low-β, low-resistivity plasma driven slowly by the shuffling of ``footpoints'' (ends of flux tubes) anchored in the photosphere. The corona's low resistivity means that enormous current densities must be present for Ohmic dissipation to be effective. Two ways that this can occur in a slowly evolving, ``quasiequilibrium'' medium are by the formation of current sheets or by the excitation of very low-frequency Alfvén resonances. Both processes lead to singular current densities in the ideal limit, and both may result from the excitation of very low- (or zero-) frequency shear Alfvén resonances. Thus, understanding the conditions under which zero-frequency Alfvén resonances can occur may ultimately be important in understanding coronal heating. This paper examines shear Alfvén resonances in line-tied magnetic geometries, with special attention being paid to geometries with discontinuities in the field line mapping as candidates for having zero-frequency Alfvén resonances. Two such geometries have been examined in detail: a two-dimensional X-point and a three-dimensional magnetic null. Qualitative differences in the two spectra are observed. The X-point geometry has Alfvén resonances of vanishing frequency, whereas the magnetic null geometry has a finite cutoff in resonant frequency for all field lines in the system. The Alfvén continuum for a null depends on its geometry, however, and much lower (though still nonzero) resonant frequencies are found when the flux surfaces are moderately eccentric. Consequently, a subset of magnetic nulls in complex, line tied geometries may have flux surfaces that can be driven resonantly by a driver of much lower frequency than for similar media without nulls. To the extent that nulls are generic features of complex magnetic geometries {and there is some reason to suspect that they are [Albright, Phys. Plasmas 6, 4222 (1999)]} this result may resolve one of the unsettled difficulties with Alfvén heating models of the solar corona.
Albright Brian James
Cowley Steve C.
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