This work has been digitalized and published in 2013 by Verlag Zeitschrift für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namensnennung 4.0 Lizenz. Chromospheric and Coronal Heating Due to the Radiation and Collisional Damping of Fast Magnetosonic Surface Waves W. Sahyouni*, Zh. Kiss’ovski, and I. Zhelyazkov Faculty of Physics, Sofia University, BG-1126 Sofia, Bulgaria Z. Naturforsch. 42 a, 1443-1450 (1987); received July 24, 1986 We study the propagation of surface/pseudosurface modes in the structured solar atmosphere assuming that the surface waves may be able to heat the chromosphere and corona. The wave energy can be dissipated by radiation, ion viscosity, and electron heat conduction. For the solar corona, it is found that the pseudosurface waves, trapped in the coronal loops, dissipate efficiently only if their periods are longer than 200 seconds and only if the background magnetic field is smaller than 5 gauss. I. Introduction The mechanisms which convert the kinetic energy of the solar photosphere and convection zone into the thermal energy of the chromosphere and corona have been under study for a long time [1]. Coronal heating by MHD waves has been widely investigated. The MHD slow modes (Alfven and slow magnetosonic waves), however, can probably be ignored in this con text, since they propagate too slowly to carry the re quired energy flux into the corona, subject to the con straints imposed by the observed amplitudes of nonthermal motions in the corona and underlying chromosphere. The fast magnetosonic wave has a number of appealing features. Its group velocity is large, and it is therefore in principle capable of carry ing a large energy flux in the corona. It is intrinsically compressive and thus subject to dissipation by viscosi ty, heat conduction, and radiation [2], Recent studies of Leroy and Schwartz [3, 4] on propagation of bulk fast MHD waves (particularly magneto-acoustic grav ity oscillations) in a model of the solar atmosphere which includes the chromosphere, the transition re gion and the corona show that these fast modes can not supply the required energy flux into the corona. A remaining possibility takes advantage of observa tions that the corona is highly structured. The mag netic atmosphere of the solar corona can be viewed as made up of coronal loops (magnetic flux tubes), the transverse dimensions of which are much shorter than Reprint requests to Prof. Dr. 1. Zhelyazkov, Faculty of Phy sics, 5 Anton Ivanov Blvd., BG-1126 Sofia, Bulgaria. * Permanent address: Department of Physics, Faculty of Science, AL-BAATH University, Homs, Syria. longitudinal ones. The atmosphere is dominated by magnetic forces; the flow of heat is principally along the field lines. Density inhomogeneities also occur. As a result, a magnetic flux tube can become visible, standing out from its neighbours [5], even though the whole of the atmosphere is permeated by a magnetic field. Inhomogeneities in the magnetic field induction are probably not large, but even in a uniform field strong density variations will result in strong differences in Alfven speed, and it is the Alfven speed, rather than the field itself, that governs the wave propagation. In a structured atmosphere, where discontinuities of den sities, velocities etc. exist, new aspects immediately arise; in particular, the existence of discontinuities al lows the propagation of surface modes. These modes have properties which may make them capable of heating the chromosphere and corona. In this paper, we evaluate the extent to which fast magnetosonic surface waves can be collisionally dissi pated in the chromosphere and corona, i.e. we cal culate their dissipation by viscosity, heat conduction, and radiation. It is interesting to note that viscosity can contribute a much more important dissipative term than electrical resistivity [6]. Since we are consid ering collisional dissipation, we will confine our atten tion to dense chromospheric/coronal regions, where collisions are frequent; coronal holes will be ecxluded from our analysis. II. Basic Assumptions, Governing Equations, and Surface-Wave Dispersion Relation The dissipation of magnetoacoustic surface waves in a magnetic cylinder embedded in a magnetic envi- 0932-0784 / 87 / 1200-1443 $ 01.30/0. - Please order a reprint rather than making your own copy.