## Abstract

A simple umbral model incorporating spreading magnetic field lines is introduced, and the equations governing Magneto-Acoustic-Gravity (MAG) and Alfvén modes are derived. In the absence of stratification analytic solutions may be found. For the MAG modes, under coronal conditions, these consist of a travelling (slow) wave and an evanescent (fast) mode, whilst the Alfvén solution may be expressed in terms of a Hankel function. These are matched onto numerical solutions in a stratified model photosphere-chromosphere, and the vertical energy fluxes are calculated. Resonant frequencies are generally found to be shifted downwards compared with the vertical field case, though the MAG flux is virtually unaltered otherwise; however, the Alfvén flux is increased by up to two orders of magnitude. In an unstratified medium, the usual formula for the Alfvén flux, F = ρ{variant}a 〈δv^{2}〉, is shown to be generally incorrect in the presence of field spread, and must be replaced by F = N^{-2/3}(4π)^{-1}ρ{variant}a 〈δv^{2}〉, where N is a spread parameter which usually satisfies N ≪ 1.

Original language | English |
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Pages (from-to) | 77-102 |

Number of pages | 26 |

Journal | Solar Physics |

Volume | 88 |

Issue number | 1-2 |

DOIs | |

Publication status | Published - 1 Oct 1983 |