Excess heating of corona and chromosphere above magnetic regions by non-linear Alfv�n waves

Excess heating of the active solar atmosphere is interpreted as the decay of MHD slow-mode waves produced in the corona through the non-linear coupling of Alfvén waves supplied from subphotospheric layers. It is stressed that the Alfvén-mode waves may be very efficiently generated directly in the convection layer under the photosphere in magnetic regions, and that such magnetic regions, at the same time, provide the ‘transparent windows’ for Alfvén waves in regard to the Joule and frictional dissipations in the photospheric and subphotospheric layers. Though the Alfvén waves suffer considerable reflection in the chromosphere and in the transition layer, a certain fraction is propagated out to the corona. A large velocity amplitude, exceeding the local Alfvén velocity, is attained during the propagation along the magnetic tubes of force into a region of lower density and weaker magnetic field. The otherwise divergence-free velocity field in Alfvén waves, in such a case, couples with a compressional component (slow-mode waves) which again is of considerable velocity amplitude relative to the local acoustic velocity when estimated by using the formula for non-linear coupling between MHD wave modes derived by Kaburaki and Uchida (1971). Therefore, the compressional waves thus produced through the non-linear coupling of Alfvén waves are eventually thermalized to provide a heat source. The introduction of this non-linear coupling process and the subsequent thermalization of the slow-mode waves may provide a means of converting the otherwise dissipation-free Alfvén mode energy into heat in the corona. The liberated heat will readily be redistributed by conduction along the magnetic lines of force, and thus the loop-like structure of the coronal condensations (or probably also the thread-like feature in the general corona) is explained in a natural fashion. Matter density in the arches is expected to be higher than the ambient density because of the higher temperature and, consequently, greater scale height in the arches.

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B. The Non-Linear Calculations for Pulsating Stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900019008 ◽

1967 ◽

Vol 28 ◽

pp. 105-176

Author(s):

Robert F. Christy

Keyword(s):

Major Part ◽

Afternoon Session ◽

Discussion Session ◽

Pulsating Stars ◽

Fourth Symposium ◽

Non Linear ◽

Considerable Discussion ◽

Informal Approach ◽

Preceding Session

(Ed. note: The custom in these Symposia has been to have a summary-introductory presentation which lasts about 1 to 1.5 hours, during which discussion from the floor is minor and usually directed at technical clarification. The remainder of the session is then devoted to discussion of the whole subject, oriented around the summary-introduction. The preceding session, I-A, at Nice, followed this pattern. Christy suggested that we might experiment in his presentation with a much more informal approach, allowing considerable discussion of the points raised in the summary-introduction during its presentation, with perhaps the entire morning spent in this way, reserving the afternoon session for discussion only. At Varenna, in the Fourth Symposium, several of the summaryintroductory papers presented from the astronomical viewpoint had been so full of concepts unfamiliar to a number of the aerodynamicists-physicists present, that a major part of the following discussion session had been devoted to simply clarifying concepts and then repeating a considerable amount of what had been summarized. So, always looking for alternatives which help to increase the understanding between the different disciplines by introducing clarification of concept as expeditiously as possible, we tried Christy's suggestion. Thus you will find the pattern of the following different from that in session I-A. I am much indebted to Christy for extensive collaboration in editing the resulting combined presentation and discussion. As always, however, I have taken upon myself the responsibility for the final editing, and so all shortcomings are on my head.)

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