The influence of classical (Spitzer) thermal conduction on longitudinal acoustic waves in a coronal loop is determined through an idealized but exactly solvable model. The model consists of an isothermal, stratified (constant gravity) atmosphere in which a monochromatic acoustic wave, traveling in the direction of decreasing density, is imposed throughout the lower half of the atmosphere. Based on the linearized equations of motion, the complete steady state (t → ∞) solution is obtained. In addition to the imposed driving wave, the solution also contains reflected and transmitted acoustic and thermal conduction waves. The mode transformation and mixing occurs in the vicinity of the atmospheric layer where the gas pressure passes through a critical value set by the magnitude of the thermal conduction and other model parameters. For 5 minute waves in a million degree loop, this critical pressure is on the order of 8 × 10-4 in cgs units. Since the apex gas pressure of many coronal loops of current interest is thought to be comfortably in excess of this value, mode mixing and transformation is not likely to be a relevant factor for understanding acoustic waves in these structures. On the other hand, enhanced thermal conductivity as a result of plasma instabilities, for example, could revive the importance of this mechanism for coronal loops. If this mixing layer is present, the calculations show that the pair of thermal conduction waves invariably gains the overwhelming majority of the energy flux of the incoming acoustic wave. This energy is rapidly dissipated in the neighborhood of the mixing layer.
展开▼
