5 Theoretical Aspects of Small Amplitude Oscillations:
Damping Mechanisms

Temporal and spatial damping is a recurrently observed characteristic of prominence oscillations (see Section 3.5). Several theoretical mechanisms have been proposed in order to explain the observed damping. Direct dissipation mechanisms seem to be inefficient, as shown by Ballai (2003), who estimated, through order of magnitude calculations, that several isotropic and anisotropic dissipative mechanisms, such as viscosity, magnetic diffusivity, radiative losses, and thermal conduction cannot in general explain the observed wave damping. The time and spatial damping of linear non-adiabatic MHD waves has been considered by Carbonell et al. (2004, 2009Jump To The Next Citation Point), Terradas et al. (2001Jump To The Next Citation Point), Terradas et al. (2005), Carbonell et al. (2006Jump To The Next Citation Point), and Soler et al. (2007Jump To The Next Citation Point, 2008Jump To The Next Citation Point). The overall conclusion from these studies is that thermal mechanisms can only account for the damping of slow waves in an efficient manner, while fast waves remain almost undamped. Since prominences can be considered as partially ionized plasmas, a possible mechanism to damp fast and Alfvén waves could be ion-neutral collisions (Forteza et al., 2007Jump To The Next Citation Point, 2008Jump To The Next Citation Point), although the ratio of the damping time to the period does not completely match the observations. Besides non-ideal mechanisms, another possibility to attenuate fast waves in thin filament threads comes from resonant wave damping (see, e.g., Goossens et al., 2010Jump To The Next Citation Point), which needs the presence of a smooth radial profile of the Alfvén speed. This phenomenon is well studied for transverse kink waves in coronal loops (Goossens et al., 2006Jump To The Next Citation Point; Goossens, 2008Jump To The Next Citation Point) and provides a plausible explanation for quickly damped transverse loop oscillations first observed by TRACE (Aschwanden et al., 1999; Nakariakov et al., 1999).

The time scales of damping produced by these different mechanisms should be compared with those obtained from observations, that indicate that the ratio of the damping time to the period, τd∕P, is of the order of 1 to 4. The theoretical approach of many works about the damping of prominence oscillations has been to first study a given damping mechanism in a uniform and unbounded medium and, thereafter, to introduce structuring and non-uniformity. This has led to an increasing complexity of theoretical models in such a way that some of them now combine different damping mechanisms. Detailed reports on theoretical studies of small amplitude oscillations in prominences and their damping can be found in Oliver (2009), Ballester (2010), and Arregui and Ballester (2011). Here, we collect the most significant aspects of the theoretical mechanisms that have been proposed to explain the observed time-scales.

 5.1 Damping of oscillations by thermal mechanisms
  5.1.1 Non-adiabatic magnetoacoustic waves in prominence slabs
  5.1.2 Non-adiabatic magnetoacoustic waves in a single thread with mass flows
  5.1.3 Non-adiabatic magnetoacoustic waves in a two-thread system with mass flows
 5.2 Damping of oscillations by ion-neutral collisions
  5.2.1 Homogeneous and unbounded prominence medium
  5.2.2 Cylindrical filament thread model
 5.3 Resonant damping of infinitely long thread oscillations
  5.3.1 Resonant damping in the Alfvén continuum
  5.3.2 Resonant damping in the slow continuum
 5.4 Resonant damping in partially ionized infinitely long threads
  5.4.1 Temporal damping
  5.4.2 Spatial damping
 5.5 Resonant damping in partially ionized finite length threads
 5.6 Damping by wave leakage

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