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8 - Connection Formulas

Published online by Cambridge University Press:  15 July 2019

Bernard Roberts
Affiliation:
University of St Andrews, Scotland
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Summary

Connection formulas for a magnetic flux tube that describe the approximate behaviour of the perturbations across thin layers where dissipative processes (here electrical conductivity) act are derived for the Alfven singularity. The tube may be twisted or untwisted. In an appropriate limit these formulas reduce to jumps across a narrow region. Such jumps are described in terms of introduced functions $F$ and $G$ and their related functions. Jump relations are used to derive approximate dispersion relations, leading to the determination of resonant absorption decay rates. Decay rates are determined for two specific density profiles, the linear one and the sinusoidal profile. Jump conditions pertaining to the slow mode are also discussed. The equivalent jump relations holding for Cartesian geometry are obtained and illustrated for a single magnetic interface, obtaining decay rates.

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Publisher: Cambridge University Press
Print publication year: 2019

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  • Connection Formulas
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.009
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  • Connection Formulas
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.009
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Connection Formulas
  • Bernard Roberts, University of St Andrews, Scotland
  • Book: MHD Waves in the Solar Atmosphere
  • Online publication: 15 July 2019
  • Chapter DOI: https://doi.org/10.1017/9781108613774.009
Available formats
×