The Parker Problem and the Theory of Coronal Heating |
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Authors: | I J D Craig A D Sneyd |
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Institution: | (1) University of Waikato, Private Bag 3105, Hamilton, New Zealand |
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Abstract: | To illustrate his theory of coronal heating, Parker initially considers the problem of disturbing a homogeneous vertical magnetic
field that is line-tied across two infinite horizontal surfaces. It is argued that, in the absence of resistive effects, any
perturbed equilibrium must be independent of z. As a result random footpoint perturbations give rise to magnetic singularities, which generate strong Ohmic heating in the
case of resistive plasmas. More recently these ideas have been formalized in terms of a magneto-static theorem but no formal
proof has been provided. In this paper we investigate the Parker hypothesis by formulating the problem in terms of the fluid
displacement. We find that, contrary to Parker's assertion, well-defined solutions for arbitrary compressibility can be constructed
which possess non-trivial z-dependence. In particular, an analytic treatment shows that small-amplitude Fourier disturbances violate the symmetry ∂z = 0 for both compact and non-compact regions of the (x, y) plane. Magnetic relaxation experiments at various levels of gas pressure confirm the existence and stability of the Fourier
mode solutions. More general footpoint displacements that include appreciable shear and twist are also shown to relax to well-defined
non-singular equilibria. The implications for Parker's theory of coronal heating are discussed. |
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