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A Unified Theory of Coronal Heating

Published online by Cambridge University Press:  04 August 2017

James A. Ionson*
Affiliation:
Laboratory for Astronomy and Solar Physics, NASA-Goddard Space Flight Center, Greenbelt, MD 20771

Extract

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This presentation focuses upon the coronal heating problem and reports the results of Ionson's (1984) unified theory of electrodynamic heating. This generalized theory, which is based upon Ionson's (1982) LRC approach, unveils a variety of new heating mechanisms and links together previously proposed processes. Specifically, Ionson (1984) has derived a standing wave equation for the global current, I, driven by emfs that are generated by the β≳1 convection. This global electrodynamics equation has the same form as a driven LRC equation where the equivalent inductance, L=4ℓ/πc2, scales with the coronal loop length and where the equivalent capacitance, C=c2 ℓ/4πv2 A, is essentially the product of the free space capacitance, ℓ/4π, and the low frequency dielectric constant, c2/v2 A. The driving emf, ∊=vBa/c, is a formal integration constant associated with the convective stressing of β≳1 magnetic fields. Since the transition from the β≳1 driver to the β<1 coronal loop is typically small compared to the “wavelength” of the associated magnetic fluctuation, this integration constant is not sensitive to details of the transition zone. The total resistance, Rtot = L(1/tdiss+1/tphase+1/tleak), represents electrodynamic energy “loss” from dissipation, magnetic stress leakage out of the loop and phase-mixing. These three processes have been parameterized by appropriate timescales. Note that Rleak=L/tleak and Rphase=L/tphase do not result in resistive heating but do participate in limiting the amplitude of the global current, I. This is fairly obvious with regard to magnetic stress leakage but not for phase-mixing. The phase-mixing resistance, Rphase, represents coupling between the global current and the local current density. Since the global current is essentially an integration of the local currents, the degree of coherency between the local currents can play an important role in determining the ultimate amplitude of I. The rate at which coherency between the local currents is lost is given by the phase-mixing time, tphase. A loss of coherency implies a corresponding reduction in the amplitude of I. In this sense, Rphase measures the phase-mixing contribution to the global current limitation process.

Type
Session II
Copyright
Copyright © Reidel 1985 

References

Ionson, J. A., 1982, Ap. J., 254, 318.Google Scholar
Ionson, J. A., 1984, Ap. J., Jan. 1.Google Scholar