The solar atmosphere is a dynamic environment, constantly evolving to form a wide range of magnetically dominated structures (coronal loops, spicules, prominences, etc.) which cover a significant percentage of the surface at any one time. Oscillations and waves in many of these structures are now widely observed and have led to the new analytic technique of solar magneto-seismology, where inferences of the background conditions of the plasma can be deduced by studying magneto-hydrodynamic (MHD) waves. Here, we generalise a novel magneto-seismological method designed to infer the density distribution of a bounded plasma structure from the relationship of its fundamental and subsequent harmonics. Observations of the solar atmosphere have emphatically shown that stratification, leading to complex density profiles within plasma structures, is common thereby rendering this work instantly accessible to solar physics. We show, in a dynamic waveguide, how the period ratio differs from the idealised harmonic ratios prevalent in homogeneous structures. These ratios show strong agreement with recent observational work. Next, anti-node shifts are also analysed. Using typical scaling parameters for bulk flows within atmospheric waveguides, e.g., coronal loops, it is found that significant anti-node shifts can be predicted, even to the order of 10 Mm. It would be highly encouraged to design specific observations to confirm the predicted anti-node shifts and apply the developed theory of solar magneto-seismology to gain more accurate waveguide diagnostics of the solar atmosphere.
Oscillations, solar Waves, magnetohydrodynamic Waves, propagation
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We first thank M.S. Ruderman for many excellent discussions and thoughts which improved this manuscript. We thank the Science and Technology Facilities Council (UK) and the School of Mathematics and Statistics, University of Sheffield (UK) for the support received. RE is thankful to the NSF, Hungary (OTKA, Ref. No. K83133) and acknowledges M. Kéray for patient encouragement. Research at the Armagh Observatory is grant-aided by the N. Ireland Dept. of Culture, Arts and Leisure.
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